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THE OPUS MAJUS

OF

ROGER BACON

VOL. I.

HENRY FROWDE, M.A.

PUBLISHER TO THE UNIVERSITY OF OXFORD

LONDON, EDINBURGH AND NEW YORK

an GERE

THE
OPUS MAJUS

ROGER BACON

EDITED, WITH

INTRODUCTION AND ANALYTICAL TABLE
BY

JOHN HENRY BRIDGES

FELLOW OF THE ROYAL COLLEGE OF PHYSICIANS
SOMETIME FELLOW OF ORIEL COLLEGE

‘Induire pour déduire afin de construire '
AucusTE ComTe

' Omnes scientiae sunt connexae, et mutuis se fovent auxiliis, sicut tes ejusdem
: par J
totius, quarum quaelibet opus suum peragit non solum pro se sed pro aliis '
P
Rocer Bacon, Ofws Tertium

VOLUME !

14 HENRIETTA STREET, COVENT GARDEN, LONDON
so SOUTH FREDERICK STREET, EDINBURGH
AND 7 BROAD STREET, OXFORD

WILLIAMS AND NORGATE
Ig00

© 'f- A. 4 SM.

COLLEGIO REGALI MEDICORUM LONDINENSI
CUJUS OLIM PRAESIDENS
RICARDUS MEAD
LITTERIS PERINDE AC SCIENTIIS ILLUSTRIS
PRIMUM BACONIS EDITOREM CONSILIIS INSTIGAVIT JUVIT

ALTERAM EDITIONEM DEDICO

PREFACE

— Qd —À

A SUFFICIENT reason for a new edition of Roger
Bacon's principal work would be the extreme rarity of
the edition of the Opus Majus published by Jebb in
1733, and reprinted seventeen years afterwards in
Venice. But a more cogent reason is that this edition
is incomplete. The work, as we learn from Bacon's
account of it in his Ofus Zerttum, consisted of seven
parts; and the seventh part, a discourse on Moral
Philosophy, was omitted by the editor.

Why Jebb should have taken this course is not
clear. In his preface he speaks of the work as con-
sisting of six parts, ‘in sex partes distributum, and adds,
' tractatum de Morali Philosophia ad calcem adjunxit.
In 1858 a paper was read by Dr. Ingram before the
Royal Irish Academy, and was printed in the seventh
volume of the Proceedings of this institution, in which
the writer showed conclusively the continuity of this
seventh part of the Opus Mazus with all that had gone
before. The continuity is marked unmistakably in
the very title of the section, /»:25: septtma pars hujus
persuastonis de Moral: Philosophia, and in its opening
words, ‘ Manifestavi in praecedentibus, &c. Repeated
references to the foregoing parts will be found ; and if

viii PREFACE.

further proof were wanting, it is supplied in abundance
by the two appendages to the Opus Mazus which were
sent by Bacon to Pope Clement IV within a few
months of the dispatch of the principal work, published
by Professor Brewer in 1859, in the Rolls Series, as
Opera Inedita. Special mention is made in the Opus
Minus (Brewer, p. 315) of passages of this seventh
section which the author regarded as of special im-
portance. In the Opus Tertium (Brewer, pp. 48-52),
a brief account is given of each of the six divisions of
which it consisted.

Dr. Ingram's paper was carefully studied by Victor
Cousin, who had already devoted much time to the
study of Bacon's unpublished works. He remarked
upon it (Yournal des Savants, 1859, p. 717), ' Nous
croyons qu'il n'y a pas d'exemple dans l'histoire litté-
raire d'une erreur semblable a celle de Jebb. Elle
est vraiment étonnante, mais elle est incontestable.’
And in truth the omission is of much greater signifi-
cance than the mere loss of Bacon's opinions on a
subject of importance would imply. "Throughout the
Opus Majus there is an orderly arrangement of the
subject-matter formed with a definite purpose, and
leading up to a central theme, the consolidation of the
Catholic faith as the supreme agency for the civiliza-
tion and ennoblement of mankind. For this end
a complete renovation and reorganization of man's
intellectual forces was needed. After a brief exposition
of the four principal impediments to wisdom—autho-
rity, habit, prejudice, and false conceit of knowledge—
Bacon proceeds in his second part to explain the
inseparable connexion of philosophy with the highest
truths of religion. In primaeval ages both were
entrusted to the patriarchs. Subsequently, while the

PREFACE. ix

evolution of religious truth was proceeding in Judaea,
Greece became the scene of the growth of philosophy.
Both were alike ordained in God's providence. In our
own times, as in those of antiquity, the study of both
should be carried on continuously. But for this
purpose it was essential that the wisdom of the ancients
should be studied in the language in which it was
originally set forth. To limit students to Latin trans-
lations is to ensure the multiplication of error. Most
of these translations, especially those of the Bible and
of Aristotle, are deplorably defective, and have been
made by men imperfectly acquainted with the subject
treated of. The first condition, therefore, of a renova-
tion of learning is the systematic study of at least three
languages besides Latin, namely, Hebrew, Greek, and
Arabic.

The second condition was the application of mathe-
matical method to all objects of study, whether in the
world or in the Church. Mathematic is the ‘ gateway
and the key to all other sciences’; it raises the under-
standing to the plane at which knowledge can be
distinguished from ignorance. Without it other sciences
are unintelligible. It reveals to us the motions of the
heavenly bodies, and the laws of the propagation of
force in things terrestrial, of which the propagation of
light may be taken as a type; without it we are
incapable of regulating the festivals of the Church ;
we remain in ignorance of the influences of climate
upon character; of the position of cities and of the
boundaries of nations whom it is the function of the
Catholic Church to bring within her pale, and to control
spiritually. With these subjects the fourth and fifth
sections of the Opus Mazjus are occupied; they form
the principal bulk of its contents. But mathematical

x PREFACE.

method, though essential, is insufficient. It must be
supplemented by the method of experiment. Even
a purely geometrical proof is not convincing or con-
clusive, until the execution of the diagram has enabled
us to add ocular, that is to say, experimental, evidence
that the demonstration is sound. This method,
moreover, will lead us into new regions into which
mathematical procedure is not able to penetrate.
Experimental science governs all the preceding sciences
(' domina est omnium scientiarum praecedentium ), it
controls their methods; in prosecuting its own special
researches it makes use of their results.

Here then ends the Opus /Zajus as presented in the
edition of 1733. A glance at the fourteenth and pre-
ceding chapters of the Opus Tertium, in which the
structure and purpose of the Opus Mazus are reviewed,
will show how disastrously the suppression of the
seventh section of the work has mutilated it. ‘All
these foregoing sciences,’ says Bacon, ‘are, properly
speaking, speculative. There is indeed in every
science a practical side, as Avicenna teaches in the
first book of his Avt of Medicine. Nevertheless; of
Moral Philosophy alone can it be said that it is in the
special and autonomatic sense practical, dealing as it
does with human conduct with reference to virtue and
vice, beatitude and misery. All other sciences are
called speculative: they are not concerned with the
deeds of the present or future life affecting man’s
salvation or damnation. All procedures of art and of
nature are directed to these moral actions, and exist on
account of them. They are of no account except in
that they help forward right action. Thus practical
and operative sciences, as experimental alchemy and
the rest, are regarded as speculative in reference to the

PREFACE. xi

operations with which moral or political science is con-
cerned. This science is the mistress of every depart-
ment of philosophy. It employs and controls them
for the advantage of states and kingdoms. It directs
the choice of men who are to study in sciences and
arts for the common good. It orders all members of
the state or kingdom so that none shall remain without
his proper work.'

The seventh part of the Opus Mayzus is for the first
time printed in this edition. Unfortunately it is not
complete. It consisted, as we learn from the fourteenth
chapter of the Opus Tertzum, of six divisions; and the
only two MSS. of it as yet discovered, those of Dublin
and Oxford (the first of which, as will be shown after-
wards, is copied from the second), stop short before the
conclusion of the fourth. We gather, however, that
the missing portions are not of primary importance.

Another alteration of considerable importance has
been made in the present edition. Professor Émile
Charles, in his very important monograph on Roger
Bacon (Bordeaux, 1861), pointed out that the treatise
De Multiplicatione Specierum, which in Jebb's edition
of the Ofus Majus is placed between the fifth and
sixth sections of the work, does not in reality belong
toit. And indeed the second sentence of the treatise
makes this evident. ‘ Recolendum est, Bacon observes,
'quod in tertia parte hujus operis tactum est quod
essentia, substantia, natura, potestas, potentia, virtus,
vis, significant eandem rem. No such passage is to
be found in any part of the Opus Magus, least of all in
the third part, which deals with Comparative Philology.
Here again the Opus Tertzum comes to our aid. Several
references will be found there to a distinct treatise
sent to Pope Clement IV simultaneously with the Opus

xii PREFACE.

Majus (Brewer, pp. 38, 99, 117, 227). It is a treatise
on the propagation of radiant forces, usually spoken of
as Multiplicatio Specierum, but in one passage entitled
Tractatus de Radws, quem. vobis misi separatim ab
Opere Majori. In the present edition this treatise
will be found in its proper place as an appendix to the
Opus Majus.

It must be added that the text, as edited, is in
certain parts of the work far from perfect. This
remark applies especially to the third and sixth sections.
In the third section several missing pages have been
supplied from a Cottonian MS. (Julius D.v.), con-
taining amongst other things a Greek and a Hebrew
alphabet. It is the more remarkable that Jebb should
have omitted these passages, since it is clear that he
had consulted this MS. and had made frequent correc-
tions from it. The sixth section, on Experimental
Science, has been so carelessly edited that it seems
probable that the editor must have entrusted the
work to a less competent assistant. Contractions of
the most ordinary kind are misinterpreted (as e.g.
‘e converso' is rendered ‘ ergo, ‘conclusio’ is written
' quaestio, &c.), and in some passages sentences have
: been omitted. While indicating these shortcomings,
it ought at the same time to be added that other
parts of the work give proof of great labour and care
in the collation of the MSS. consulted. This is
especially the case with the fourth and fifth parts,
which form a very large proportion of the whole work.
Having spent much time over the MSS. used by Jebb,
in addition to others, I can bear testimony to the
accuracy with which variations have here been noted.
All of them which are of more than verbal importance
have been noted in the present edition.

PREFACE. xil

A further change has been made in the arrangement
of the diagrams, which in Jebb's edition were collected
into two tables, and thus rendered inconvenient for
comparison with the text, and which, moreover, in
many cases are incorrectly drawn. They have been
carefully re-copied from a MS. in the British Museum
(Royal, 7 F. viii), which Sir E. Maunde Thompson,
who was so kind as to examine this and several other
Baconian MSS. in the British Museum for me, pro-
nounces to be of the latter part oí the thirteenth
century, i.e. contemporary, or very nearly so, with
Bacon. Each diagram has been placed in its proper
context.

It was found that in many cases the reasoning of

the author had been entirely nullified by defective
punctuation. This has been entirely revised, and the
number of distinct sentences and paragraphs has been
very largely increased. Students of the Ofws aus
have found the work difficult to refer to, owing to the
multiplicity and diversity of the subjects treated, and the
want of such guidance as page-headings or marginal
notes can supply. This defect has been remedied, an
analysis of the work has been prefixed, and an improved
index added.

A few remarks on the MSS. of the Ofus Jajus.

Jebb's edition was founded on a MS. in the library of

Trinity College, Dublin, which at that time was the
only MS. known to contain the complete work. 1t con-
tains a note in Archbishop Usher's handwriting to the
effect that the MS. was presented to the Colleve by
Gordian Strowbridge, and that the diagrams were
drawn by Sir Christopher Heyden. lhis M5. is very
clearly written in 249 folios of four columns. Sir
Christopher Heyden, of Baconsthorpe, in Norfolk, was

xiv PREFACE.

. & well-known astrological writer who died in 1623,
which fixes the date of this MS. at the end of the
sixteenth or beginning of the seventeenth century.
A glance at the MS. shows that the figures were
drawn simultaneously with the text, room being left
in each page for their insertion. The character of the
writing quite corresponds with this date. It is referred
to in this edition as D.

In 1825 another MS. of the Opus Majus was
bought for the Bodleian Library. It belonged at one
time to Thomas Allen, the astrologer of Gloucester
Hall, who early in the seventeenth century gave twenty
MSS. to the Bodleian. This one, however, passed
into the possession of Sir Kenelm Digby, whose well-
known signature and motto are inscribed on the first
page. It is now numbered 235 of the Digby MSS.
The greater part of it is of the fifteenth century.
But a portion of it (pp. 249-295) is in an older and
more beautiful handwriting, considered by Mr. Coxe
to be of the fourteenth century. This portion in-
cludes a considerable portion of the Perspectzva.

These two MSS. have been carefully collated for
the present edition. In the course of the collation
unmistakable proof was given that the Dublin MS.
was a copy of that in the Bodleian. At the close of
p. 470, col. 2, of this latter, the sentence breaks off
midway, and is continued on the first line of p. 487,
col 1. An error of this kind, analogous to that caused
by the transposition of sheets in binding a modern
book, is easily explicable. In the Dublin MS. the
same rupture of the sentence occurs, but in the middle
of a column (fol. 224, col. a, line 12), the sentence
being ultimately continued on fol. 229, col. d, line 14.
It may be added that these two MSS. exhibit through-

PREFACE. XV

out an almost exact correspondence in their errors and
in their variants. The Oxford MS. has therefore been
taken as the foundation of the present edition, and
is denoted by the letter O. It is, however, by no
means perfect, especially in the second and third
sections of the work: and recourse was had both by
Jebb and by the present editor to various MSS. in
the British Museum and elsewhere to supply the
imperfections. Foremost among these are the two
Cottonian MSS., Julius D.v., and Tiberius C.v. (desig-
nated here as Jul. and Tib.). The first of these,
unfortunately much injured in the fire of 1731, gives
the first three sections of the work and a large part of
the fourth. The second gives the whole of the fourth.

For the geographical portion of the fourth section,
I was allowed to consult the MS. in the possession of
Corpus Christi College, Cambridge. It is not, how-
ever, believed to be of earlier date than the middle or
later part of the fifteenth century. Occasional reference
has been made to a MS. of the fifth section of the work
(Perspectzva) in the possession of Magdalene College,
Cambridge, which I was permitted to examine. It is
not, however, of earlier date than the Bodleian MS.,
and its variants are not of great importance.

Of the MSS. of the Perspectiva and of the Le
Mwultzplicattoue Specterum which appear to have been
transcribed more frequently than other portions of the
work, by far the most important is the British Museum
MS. (Royal, 7 F. viii), already spoken of as contem-
porary, or nearly so, with Bacon. This, as I have said,
was carefully collated by Jebb, who indeed has in
certain places copied on the margin extracts from
Combach's printed edition of the Perspectzva of 1614.

The diagrams of this MS. are of special value. The

xvi PREFACE.

Sloane MS. 2156, and the Harletan MS. 80, 60b,
have also been consulted.

The sixth section of the Opus JM ajus (Sctentia
Experimentahs) appears to have been seldom copied.
In the third volume of Baconian MSS. presented to
University College, Oxford, by John Elmhurst, there
is a MS. of this section which is described as copied
from Allens MSS. (see Brewer, p. xlii) It may,
therefore, be merely copied from the Oxford MS. of
the Opus Mazus. But it offers some variants, and in
one or two passages it has proved serviceable. It is
spoken of in this edition as U.

Of the seventh section, here printed for the first
time, there is a MS. in the Royal Library (8, F. ii)
containing the first two parts and a portion of the
third. This has been carefully collated with the
corresponding parts of the Dublin and Oxford MSS.
The variations will be seen to be of no great impor-
tance. The MS. appears to be of the middle of the
fifteenth century.

Besides these MSS., others have been consulted
which throw light on Bacon's life and work. Chief
amongst these is the important MS. of the Mazarin
library (formerly numbered 1271, but at present 3576),
from which Professor Émile Charles gives copious ex-
tracts in his monograph entitled Roger Bacon, sa vie, ses
ouvrages, ses doctrines, d'aprós des textes inédits (Bor-
deaux, 1861). More will be said afterwards of its
contents. They offer a considerable instalment of
the Scrzpium Principale, of which the Opus Mazus,
inclusive of its adjuncts, the Opus Minus and the
Opus Tertium, was but the prelude.

Another valuable fragment of this final work is
preserved in the British Museum among the Sloane

PREFACE. xvii

MSS. (2156). It contains the first book and part of
the second of the Communza Mathematicae. Attention
was called to it both by Brewer and by Charles, and
occasional references to it have been made in the
present edition.

Yet a third fragment is the elementary work on
Greek grammar in the possession of Corpus Christi
College, Oxford, which was sent to the Bodleian for
my perusal An imperfect copy, in seventeenth cen-
tury handwriting, apparently made from the Corpus
MS., is contained among the Baconian MSS. of
University College.

Bacon's commentary on the Secretum Secretorum
(Tanner MSS. 116) has also been examined. It throws
light on the astrological side of his work.

Among the books consulted for this edition, far the
most important are those of Professors Brewer and
Emile Charles, already spoken of. It is unfortunate that
two such assiduous and able investigators should have
worked simultaneously and without communication.
Several not unimportant errors migbt have been
avoided, had either of them known of the other's
work. Charles had a far more extensive knowledge
than Brewer of Bacon's unpublished works; and his
extracts from them are so copious as to render it
desirable that his monograph, which has already
become extremely rare, should be republished. He
makes, however, the erroneous statement (p. 62) that
the missing portion of the Opus Majus (here printed
for the first time) had been published in Dublin; and
he does not appreciate the distinction, so clearly
demonstrated by Professor Brewer, between the Opus
Tertium (which is at once an introduction and a supple-
ment to the Ofus /Majus), and the far vaster Scrzptum

VOL. I. b

xviii PREFACE.

Principale projected by Bacon, but only in part
executed. On these points, and on the bibliography
of Bacon generally, Mr. Littles Grey Friars in Oxford
is of great value. Other works consulted will be
noted as reference is made to them. Attention, how-
ever, may be specially called to Govi's recent edition
of the Latin translation of Ptolemy's Of£trcza, so fre-
quently used by Bacon (Turin, 1885), a publication
of the greatest value for the history of science; and
to Heiberg's edition of Euclid's Optzca (vol. vii. of
his edition of Euclid, Leipsic, 1895). Wuestenfeld's
Geschichte der Arabischen Aerzte (Gottingen, 1840),
and Cantor's Geschichte der Mathematzk (Leipsic, 1880—
1892), throw light on the mediaeval men of science,
Eastern or Western, mentioned by Bacon. Hauréau's
Histoire de la Philosophte Scolastigue (Paris, 1872)
defines, with some acerbity, Bacon's position among
the schooimen. Jourdain’s Recherches critiques sur
les traductions latines d' Aristote (nouvelle édit., 1843)
contain indispensable information as to the translators
of whose shortcomings Bacon so often complains.

For the geographical section of the work, in addition
to the classical works of Yule and Bunbury, frequent
reference is made to the complete version of the travels
of Rubruquis and Carpini, published by the Paris
Geographical Society, in the fourth volume of their
Recueil de Voyages et de Mémoires (1839).

As Seneca occupies so large a place in the seventh
section of the Opus Mazus, it may be mentioned that
the edition used for this work is that of Haase (Leipsic,
1887). As to Aristotle, the references are to Didot's
edition (Paris, 1848-1872).

It remains for me to express my thanks to the
Master and Fellows of Trinity College, Cambridge ; to

PREFACE. xix

the Master and Fellows of Corpus Christi College,
Cambridge; the Master and Fellows of Magdalene
College, Cambridge; and the President and Fellows
of Corpus Christi College, Oxford, for permission to
examine the MSS. of Bacon belonging respectively
to these societies.

J. H. B.
March 26, 1897.

FACTS RELATING TO BACON'S LIFE

Contemporary Events.

1900, Condemnation of
Aristotle’s Physic and
Metaphysic in Paris.

1915. Confirmation of this
by Papal Legate. (Cp.
Opus Tertium, cap. 9. :

12923. Alexander of Hales
enters the Franciscan
Order, and teaches phi-
losophy in Paris.

1331, Condemnation of
Physic and Metaphysic
partially removed by
Gregory IX.

1288, Alexander of Hales
resigns his post as a
teacher of philosophy.

1246-8. First residence of
Thomas Aquinas in Paris
with Albertus Magnus.

1249. Death of William
of Auvergne (Bishop of
Paris).

12962. Second residence of
Aquinas in Paris of un-
certain duration.

19858. Death of Grosseteste.

1288. Bonaventura becomes
General of Franciscans.

1858. Bagdad captured from
Saracens by Tartars.

18085. Guy Fulcodi elected
Pope Clement IV.

1968. Dcath of Clement IV.

1970. Death of Saint Louis.

1974. Death of Bonaven-

tura; Jerome of Ascoli

becomes | General of
Franciscans.
Death of Thomas
Aquinas.
(P Birth of Duns Scotus.
1880. Death of Albertus
Magnus.
1889. Jerome of Ascoli
becomes Nicolas IV;

Raymundo Galtredi suc.
ceeds him as General.
1208 Death of Nicolas IV.

Statements resting on later
authority.

1210-15. Born near _II-
chester in Dorsetshire,
or, according to another
tradition, in the parish
of Bisley in Gloucester-
shire. (Cf. Brewer, p.
Ixxxv.)

1940. Went from Oxford
to Paris about 1240.
Probably entered Fran-
ciscan Order a few years
later.

1950-7. Probablyin Oxford.
Legend as to Bacon's
Tower may perhaps be
referred to this period.

1278. Imprisonment propier
novitales suspectas, 1278.
(See Summa Historialis
of Antoninus.Archbishop
of Florence, a writer of
the fifteenth century.)

1202. Release from prison
probably ra92. Died
1292 or 1294. Buried
in Franciscan Church in
Oxford. Legend as to
exposure of his writings
to wind and weather
told by Wood.

Facts verified by Bacon's state-

ment or by contemporary
authorety.

1230. Michael Scot intro-
duces his translations
of Aristotle. (Op. May.
vol. i. p. 55.)

1938. Interview of Bacon
with Henry III at Ox-
ford, as described by
Matthew Paris.

1245. Heard William of
Auvergne (Bishop of
Paris) lecture on tn-
tellectus agens. (Op. Tert.
cap. 23.)

1250. Saw the leader of the
Pastoureaux marching
through France in 1250.
(Op. Maj. vol. i. p. 401.)

1257. ‘Exile’ from Oxford
to Paris began. (Of.
Tert. cap. 1.)

1258-67. His family took
the King's side in war
with barons. (Of. Tert.
cap. 3.)

1264-5. Enters into rela-
tions with Guy Fulcodi.

1266. Bacon ordered to send
his writings to the Pope.

1266-7. Composition of
Opus Majus,Opus Minus,
Opus Tertium.

1268. Death of Clement IV.

1271. Writes the Compen-
dium Studi Philosophiae,
denouncing the corrup-
tions ofthe Church. (See
Brewer, p. liv.)

1902. Writes Compendrem
Theologiae. See MS. of
this work (Br M. Royal
7 F vii. fol. 154).

[ xix* ]

NOTE.

IN the July issue of the English Historical Review, 1897,
Dr. Gasquet publishes a MS. of Bacon which he has found
in the Vatican, and which he inclines to think is a preface
to the Opus Majus.

There is much to justify this view. The work in question
describes Bacon’s overflowing gratitude for Pope Clement’s
message to him; apologizes for the delay in the transmission
of his works by pointing out that none of these works were
in a complete state; egplains the obstacles interposed by the
distress of his family, ruined in the civil wars, and by the re-
strictions of his Order ; introduces his disciple John, who had
been for seven years under his tuition ; and finally concludes
with a brief summary of the contents of the Opus Majus. This
he describes, not as his principal work, but as a Perssasio.
It has seven parts. After briefly noting the contents of the
first two, Bacon passes to the seventh (published for the first
time in this edition) and then comments successively on the
sixth, fifth, fourth, and third.

It will be observed by readers of this short treatise that it
contains little that is not set forth with much greater fullness
in the Opus Tertium, which is to be regarded as the real
Introduction to the collection of writings sent by Bacon in
1267 to Pope Clement IV. The first chapter of Dr. Gasquet's
MS. is almost exactly identical with pp. 7-12 in Brewer's edition
of Opus Tertium, the latter, however, having certain sentences
not contained in the former. The fifth chapter is a repetition
of Opus Majus, pt. i. cap. 16. One or two sentences, however,
of this newly published work deserve attention. We learn
from it that Bacon's life in Paris between 1257 and 1267 was
a time of comparative inaction: a decem annis propter languores

[ xx* ]

multos et infirmitates varias occupationibus extertoribus studi non
vacavi. He had written, he says, much before entering the
Franciscan Order, with a view to the instruction of youth (sulfa
in alio. statu conscripseram | propler. juvenum. rudimenta\; and
of late years he had sent fragments of his works to friends
(aliqua capitula nunc de una scientia nunc de alia ad tnstantiam
amicorum. aliquando. more transitorio compilavt, No treatise,
however, on any department of philosophy had been issued in
a complete form.

On the whole I am inclined to think that the short work
edited by Dr. Gasquet is a first draft of what was afterwards
expanded into the Opus Tertium. Bacon tells us that he was
in the habit of writing his discourses several times over until
they were brought into satisfactory shape. Sentiens meam
imbecillitatem nthil scribo. difficile quod non transeat. usque ad
quartum vel quintum exemplum antequam habeam quod intendo.

J. H. B.
July 21, 1897.

Bacoi's Opus Majus.]

INTRODUCTION

I. BACON'S LIFE.

IN considering the little that is known of the life of Bacon,
it is well to give precedence to the few facts that are fixed
with perfect precision by his own statement. We know with
entire accuracy the date of the composition of the Opus
Majus, and of the two subsidiary works, the Opus Minus and
the Opus Tertium. Pope Clement! IV's instructions to him
to transmit the results of his labours were issued June 22,
1266 from Viterbo. Within the year that followed, the Opus
Majus, with its supplement, the Opus Minus, and its intro-
duction, the Opus Tertius, had been completed and sent to
the Pope. At this time he speaks of himself as an old man,
and he says that he had been studying language, science,
and philosophy for nearly forty years (Opus Tertium, cap. 20).
From this it may be supposed that he was born between 1210
and 1215. But the place of his birth cannot be said to be
fixed with certainty.

One, and only one, notice of his name occurs in a con-

! Guy Fulcodi (or Foulques), who succeeded to the Papacy in 1265 as
Clement IV, was born at Saint Gilles in Languedoc. He began his career by
studying law, in which he achieved great distinction. He was married and had
several children. He seems to have acted for some time as a private secretary
to Louis IX. After his wife's death he entered the Church, was made arch-
bishop of Narbonne in 1259, and cardinal bishop of S. Sabina in 1261. (See
Fleury, Hist. Ecclésiastique, liv. 85, whose spelling of the name Guy Fulcodi is
here adopted.) Brewer conjectures (pp. xi et seq.) that he entered into
relations with Bacon on the occasion of his mission to England as Papal legate
in 1263 or 1264. But Bacon was then in Paris, and had been there for several
years. Guy Fulcodi had far better opportunities of hearing about Bacon in Paris
than could have occurred during the time of his stormy and ineffectual legation
to England.

xxii INTRODUCTION.

temporary writer. Matthew Paris relates, under the year
1233, that Henry III convoked the counts and barons of the
kingdom to a council at Oxford. Their animosity against
Pierre des Roches, Bishop of Winchester, the king's chief
adviser, who had surrounded his person with a body-guard of
Poitevins and filled England with these foreigners, led them
to refuse the summons. While the king was debating what
measures to take against the recalcitrant barons, a Dominican
preacher, Robert Bacon by name, told him frankly that there
would be no hope of permanent peace in the kingdom so long
as the Bishop of Winchester and his son, or kinsman, Peter of
Rievaulx, retained power. Robert Bacon's opinion was echoed
by others, and the king was induced to listen to it patiently.
‘Then a certain clerk who was present at the Court, Roger
Bacon by name, a man of mirthful speech, said with pleasant
yet pointed wit, * My lord king, what is that which is most
hurtful and fearful to those that sail across the sea?" “Those
know it," the king replied, “ who have much experience of the
waters.” “My lord,” said the clerk, “I will tell you; stones
and rocks”; meaning thereby Pierre des Roches.’ It has
been thought that the date of the dialogue was too early to
refer to the Roger Bacon with whom we are here concerned.
But since he might well be more than twenty years old at
the time, the doubt seems hardly founded.

What is certain from Bacon’s own statement is that his
family was one of some wealth, since he himself had been
able to spend much money on experimental research. It
appears also that this family had taken the royal side through-
out the disputes between Henry and his barons, and had
suffered pecuniary loss and exile for their loyalty. He tells
Pope Clement that, being in sore distress for the money
necessary for the transcription and conveyance of his MSS.,
* I wrote to my brother, a rich man in my country. But he,
belonging as he did to the king's party, was in exile with my
mother, brothers, and the whole family. Ruined and reduced
to utter poverty, he was unable to help me, and up to the
present day he has sent me no reply. (Op. 7ert. cap. 3)

The forty years of study, of which he speaks in 1267, may

BACON'S LIFE. xxiii

be divided into two periods, apparently of nearly equal length ;
the periods before and after his admission into the Franciscan
Order. In the seventeenth chapter of the Opus Tertium he
speaks of having devoted more than twenty years to the study
of languages and of science. ‘I sought,’ he says, ‘the friend-
ship of all wise men among the Latins; and I caused young
men to be trained in languages, in geometrical figures, in
numbers, in the construction of tables, in the use of instru-
ments, and in many other necessary things. . . During this
time I spent more than two thousand pounds in those things
and in the purchase of books and instruments. We may
presume that the pounds were French, which at that time
would correspond to between 600 and 700 pounds sterling.
The sum was a large one. And whether large or small, it
would be quite incompatible with the profession of an Order
specially devoted to poverty. It may be inferred, therefore,
that since he had studied independently for some twenty
years, it was not till some time between 1245 and 1250 that
Bacon became a Franciscan.

Among the men distinguished for their learning whose
friendship he cultivated at this part of his career may be
counted, in all probability, Adam de Marisco; Edmund Rich,
afterwards Archbishop of Canterbury and ultimately canonized ;
Thomas Bungay, whose name was one day to be associated
with his own as a worker of magic; Thomas, Bishop of
St. David; John of Basingstoke, scholar and traveller; John
Peckham, afterwards Archbishop of Canterbury ; Hermann,
one of the principal translators of Aristotle; Shirwood, the
treasurer of Lincoln; and last and greatest, the illustrious
Bishop of Lincoln, Robert Grosseteste. In Bacon's earlier
years of study, Grosseteste had not plunged into the arduous
and absorbing work of his episcopate. Novet scientias, Bacon
says of him. He was rector scholarum, and also Chancellor
of Oxford, and in 1224 was the rector of the Franciscans
recently established there. The terms in which Bacon bears
testimony to his encouragement of philology, to his attempts
to apply mathematical method to the study of physical
phenomena, to his disregard of the philosophy of the schools

xxiv INTRODUCTION.

as founded on bad translations of Aristotle (Brewer, Compend.
Studit, cap. 8), would be conclusive as to his personal contact
with this great man, even though it were not confirmed by
reference to Grosseteste's scientific writings, in which Bacon's
debt to him is unmistakable. His treatise De Physicis Linets,
Angulis, et Figuris contains passages as to the spherical radia-
tion of force, and as to the change in its direction by reflection
and refraction, which bear a close resemblance to the lan-
guage used many years afterwards by Bacon.

It would appear that, at the beginning of the thirteenth
century, there was a stronger impulse towards scientific study
in Oxford than in Paris. In the eleventh chapter of the Opus
Tertium, when speaking of the science of Optics, Bacon
observes, ' On this science no lectures have as yet been given
in Paris, nor anywhere among the Latins, except twice at
Oxford. It is not stated that the lecturer was Grosseteste ;
but we may well believe it. It may be supposed that the
influence of Adelard of Bath, the first translator of Euclid, had
left its traces. Twenty years before the close of the twelfth
century we hear of two Englishmen, Alexander Neckham and .
Alfred Sershall, lecturing in Paris on the Physics of Aristotle,
then recently introduced from the school of translators from
Arabic directed by Archbishop Raymond of Toledo.

But the University of Paris, placed nearer the centre of the
spiritual forces that swayed mediaeval society, had grown up
under the dialectical influences of thcological controversy ;
and when Bacon went there, perhaps about 1240, he found
what is called, vaguely and inaccurately enough, the scholastic
philosophy in the fullness of its growth, with the enlarged
scope given to it by the recent permission to study the Physics;
Metaphysics, and Psychology of Aristotle. Its two most
prominent representatives were at this time Alexander of
Hales and William of Auvergne. Of the methods and the
controversies then current Bacon made himself a master, and
received the title of doctor. To be able to speak the language
of the schools with authority was the first condition of obtain-
ing a hearing. But he was not slow to perceive that the men
who taught this philosophy were, for the most part, wholly

BACON' S LIFE. XXV

destitute of positive knowledge. They knew no language but
Latin. Beyond the shreds of arithmetic, mensuration, and
astronomy taught in the manuals of the Quadrivium, they
were ignorant of mathematics. Of the possibility of applying
mathematical knowledge to the facts of nature they had
formed no conception whatever. Their philosophy was a
tangle of barren controversies reducible, for the most part. to
verbal disputes. It bore no relation to the facts of real life.
It held out no hope of raising the Catholic Church to the
position of intellectual domination needed for establishing her
authority over the Asiatic world, from which dangers were
looming of appalling magnitude.

It was in Paris that Bacon came into contact with a remark-
able man of whom very little would be known to us but for
Bacon’s eulcgies, Peter of Maricourt!, a native of Picardy.
From the description given of him in the thirteenth chapter
of the Opus Tertium, he would seem to have been an un-
ambitious man, anxious only to pursue his researches in
private, regardless of the metaphysical turmoil around him.
Speaking of experimental research, Bacon says: ‘One man
I know, and one only, who can be praised for his achievements
in this science. Of discourses and battles of words he takes
no heed: he follows the works of wisdom, and in these finds
rest. What others strive to see dimly and blindly, like bats
in twilight, he gazes at in the full light of day, because he is
a master of experiment. Through experiment he gains know-
ledge of natural things, medical, chemical, indeed of everything
in the heavens or earth. He is ashamed that things should
be known to laymen, old women, soldiers, ploughmen, of
which he is ignorant. Therefore he has looked closely into
the doings of those who work in metals and minerals of all

» There is some doubt as to the orthography of the name, though none can
now be left as to the identity of the person indicated. Emile Charles (pp. 16-
17) mentions a MS. in the Paris library (Bibliothéque Nationale, Manuscrits
Latins, 73,8* in which the only known work of Peter Peregrinus is spoken of as
* Epistola Petri Peregrini de Maricourt ad Sygerium de Fontancourt de Magnete."
Charles adds that there is a village called Mehariscourt in Picardy near the
abbey of Corbie. The Latin form of the word in one MS. of the Opus Tertium
is written Maharncuria, but in others Mahariscuria. Cf. vol. ii. p. 203 of the
present work ; see also Bertelli's Declinasione Magnetica (Rome, 1892).

xxvi INTRODUCTION.

kinds; he knows everything relating to the art of war, the
making of weapons, and the chase; he has looked closely into
agriculture, mensuration, and farming work ; he has even taken
note of the remedies, lot-casting, and charms used by old
women and by wizards and magicians, and of the deceptions
and devices of conjurors, so that nothing which deserves
inquiry should escape him, and that he may be able to expose
the falsehoods of magicians. If philosophy is to be carried
to its perfection and is to be handled with utility and certainty,
his aid is indispensable. As for reward, he neither receives
nor seeks it. If he frequented kings and princes, he would
easily find those who would bestow on him honours and wealth.
Or, if in Paris he would display the results of his researches,
the whole world would follow him. But since either of these
courses would hinder him from pursuing the great experiments
in which he delights, he puts honour and wealth aside, knowing
well that his wisdom would secure him wealth whenever he
chose. For the last three years he has been working at the
production of a mirror that shall produce combustion at a fixed
distance ; a problem which the Latins have neither solved nor
attempted, though books have been written upon the subject.'

Of this remarkable man little is known but what Bacon
tells us in the foregoing and other passages of the Opus
Tertium, and the Opus Majus. But what we know is not
inconsistent with Bacon's eulogy. Libri, in a note contained
in the second volume of his Hts tory of Mathematics, transcribes
a letter written by Peter Peregrinus of Maricourt to a certain
Sigermus of Fontancourt, which is a treatise on the properties
of the magic stone, on the relations of its poles to those of
the heavens and earth, on the way to find these poles; on the
repulsion in two magnets of poles of the same name, and the
attraction of those of different names ; and on the construction
of a globe which should revolve with the revolution of the
heavens, and thus supply the place of the ordinary observation
by the astrolabe. This is, no doubt, the invention of which
Bacon speaks in the sixth part of the Opus Majus. Gilbert,
in his great work on Magnetism, makes frequent mention of
this treatise of Peter Peregrinus; and a careful comparison

BACON'S LIFE. xxvii

of the two works, separated as they are by an interval of
more than three centuries, shows undoubted and weighty
obligations of Gilbert to his predecessor. In the construction
of globular magnets (the ‘terrella,’ or model of the earth), in
the mode of finding their poles, the procedure, and indeed
the very language of Peter, is closely followed by the later
inquirer.

To a mind so original as Bacon's, trained in scientific method
by Grosseteste and other members of the English mathe-
matical school, the influence of an experimental thinker
like Peter of Maricourt must have been stimulating in the
extreme. Bacon was thirsting for reality in a barren land
infested with metaphysical mirage. From the horse-load of
verbal controversies contained in the Summa of Alexander
of Hales, from the interminable series of tedious commentaries
on Aristotle, of which so great a master as Albert was setting
the first fatal example, he took refuge in the visions of the
harvest of new truth that was to be reaped by patient observa-
tion of Nature, by submission of her processes to experimental
questioning, by following the lowly paths used by plain men
in their daily avocations. ‘The wiser men are,’ he said, ‘the
more humbly will they submit to learn from others; they do
not disdain the simplicity of those who teach them ; they are
willing to lower themselves to the level of husbandmen, of
poor women, of children. Mamy things are known to the
simple and unlearned which escape the notice of the wise.
I have learned more important truth beyond comparison from
men of humble station, who are not named in the schools, than
from all the famous doctors. Let no man therefore boast of
his wisdom, or look down upon the lowly, who have knowledge
of many secret things which God has not shown to those
renowned for wisdom’ (Opus Majus, vol. i. p. 10).

Assuming that Bacon entered the Franciscan Order about
1247, he would be at that time still in Paris. The degree of
doctor, rarely conferred before the age of thirty-five, was
probably received about the same time. He tells us (Opus
Tertium, cap.23) that he heard William of Auvergne lecturing
to the University on the ‘active intellect. This must have been

— —1

xxviti INTRODUCTION.

before 1248, the date of William's death. We know that he
must have been still in France in 1250, for in that year the
revolt of the Pastoureaux broke out; and Bacon tells us that
he ‘saw their leader walking barefoot in a troup of armed men
carrying something in his hands with the care with which
a man carries a sacred relic’ (Opus Majus, vol. i. p. 401).

For some time between this date and 1257 he was probably
in Oxford. Whether he lectured there publicly we do not
know. But that he incurred the suspicion of his superiors in
the Franciscan Order is certain ; whether by audacity in specu-
lation, by experiments looked upon as magical, or by frank
exposure of the ignorance of professorial magnates, cannot be
said with certainty. His old friends and teachers, Edmund
Rich and Adam de Marisco, had passed from the scene.
Grosseteste, his revered master, was dead, or died (1253)
shortly after his return, in despair at the corruption of the
Papacy, and half doubting whether Rome had not become
the seat of Antichrist. No one was left to promote the study
of Greek, which for aught we know died out in Oxford till
Erasmus witnessed its revival. In 1255, John of Fidanza,
better known as Bonaventura, became General of the
Franciscan Order, a man of exalted and aspiring mysticism,
eager to revive the spirit of St. Francis, and not likely to
care much for new learning that might lead he knew not
whither. Perhaps it was by his direction that Roger Bacon,
about 1257, was removed from Oxford, and placed under
close supervision in the Paris house.

What degree of restriction was placed upon his liberty is
not very easy to define with precision. He was not forbidden
to write, although he implies that he had not availed himself
of the power to do so to any considerable extent. To multiply
books by copyists was impracticable ; first, because copyists
outside the Order could not be trusted to make an honest
use of the copies at their disposal; and secondly, because
a strict prohibition was laid down and enforced against com-
municating any manuscripts to those who were not members
of the Order. When Pope Clement's message reached him
requiring him to transmit his works with the least possible

BACON’S LIFE. xxix

delay, these works for the most part were still unwritten. Never-
theless there were exceptions. He had compiled, he tells us,
from time to time, certain chapters on various subjects at the
instance of friends (Opus Tertium, cap. 2). Among these
chapters is probably to be reckoned the treatise De Multipis-
catione Specierum, which was sent to the Pope by the same
messenger who conveyed the Opus Majus, though it does not,
. strictly speaking, form a part of that work. Careful examina-
tion shows it to be a portion of the more complete philosophical
treatise to the completion of which Bacon always aspired, till
the time came, ten years afterwards, when his philosophical:
career was fatally arrested. Its style is different from that of
the other three treatises, M/ajus, Minus, and Tertium. It is
not like these a Persuasio, that is a more or less popular
discourse addressed to a reader like Clement IV ; a reader
of keen understanding doubtless, but at the same time the
busiest man in Christendom. The Muluplicatio Specierum is
a fragment of a systematic work written with full observance
of philosophic language and of the dialectic of the schools.

Whatever the discipline imposed during this period of his
life, one important sphere of activity undoubtedly remained
open to him. For many years he had been striving to form
a school of young men, who should carry on the work which he
had begun. We have seen in the treatise which throws so
much light on the details of his life (Opus Tertium, cap. 17),
that he had been engaged for a long time in instructing young
men in languages, in geometry, in arithmetic, in the construc-
tion of tables, and in the use of scientific instruments. From
this part of his work he was evidently not cut off during his
life in Paris from 1257 to 1267. The messenger whom he
selected to convey his manuscripts to Pope Clement was a poor
lad whom he had been training in this way for five or six
years. On the whole it seems probable that the restrictions
placed on his liberty at this period of his life were not of
extreme severity.

Of the reception given to Bacon's manuscripts in Rome we
know absolutely nothing. A few months after their arrival
Clement IV died; and the papal see remained vacant for

XXX INTRODUCTION.

three years. The Pope elected in 1271 (Gregory X) was
a Franciscan. Owing his elevation to St. Bonaventura, he
was not likely to show favour to a suspected member of his
Order. Yet it was in this year or shortly afterwards that Bacon
wrote the work known as Compendium Studit Philosophiae !, an
introductory discourse, perhaps, for the encyclopaedic Srriptum
Principale, at the completion of which he was always aiming.
In this treatise Bacon plunged into stronger invective against
the intellectual and moral vices of his time than he had ever
used before. In no previous writing had the moral corrup-
‘tion of the Church, from the court of Rome downwards, been
so fiercely stigmatized ; ‘the whole clergy is given up to pride,
luxury, and avarice. Wherever clergymen are gathered to-
gether, as at Paris and Oxford, their quarrels, their contentions,
and their vices are a scandal to laymen.’ Unbridled violence
among kings and nobles, fraud and falsehood among trades-
men and artificers were the inevitable result. Progress in
wisdom was hopeless when the moral condition of those who
should promote it was so far below that of the teachers of the
pagan world Unless sweeping remedies were applied by
a reforming Pope, there was no prospect but the advent of
Antichrist in the near future (Brewer, pp. 399-404).

Perhaps even these denunciations roused less antagonism
than the sweeping attacks on the scholastic pedantry of his
contemporaries, their false conceit of wisdom, and their pre-
ference of metaphysical subtleties and verbal strifes to the
pursuit of real knowledge. Of these charges his previous
writings had been full, but they were now renewed and
emphasized. Aristotelian study, which at the beginning of
the century had been the great stimulant of thought, was
already becoming the great obstruction, and was preparing
for the next century a reign of darkness. Based on false and
ignorant translations, it were better, Bacon said, to do away
with it altogether than that it should be carried on by men
ignorant of the language in which Aristotle wrote, and
destitute of the scientific training which alone could qualify
them for explaining him (Brewer, pp. 469-473).

! Contained in Brewer's work, pp. 393-519.

BACON'S LIFE. XXXi

‘The storm of indignation had long been gathering : and in
1277 it broke. In that year Jerome d'Ascoli, who four years
before had succeeded Bonaventura as General of the Franciscan
Order, held a chapter in Paris. Bacon was summoned on
account of ‘certain suspected novelties.’ He was condemned,
and thrown into prison. What were the ‘novelties’ that
constituted his crime we do not know. His works abounded
in them. It was not perhaps difficult to show that he had
gone too far in connecting changes in religious faith with
conjunctions of Jupiter and Mercury; and in hinting that
underneath the jugglery of the magicians, valuable truths
might sometimes lie concealed. The real motives for stifling
his voice lay far deeper.

That he should have held the history of Greek philosophy
to have been under the keeping and guidance of Providence
no less than the history of Judaea; that he should have
regarded the teaching of the Stoics on personal morality as
superior to that of any Christian teacher; that he should
have dwelt with such frequent emphasis on the ethical value
of Mohammedan writers like Alfarabius, Avicenna, and
Algazel—these were things likely to startle even the most
tolerant and thoughtful of his contemporaries, much more
the common average of his Order, who had suspected him
of unsound views for twenty years. Not indeed that his
career would have been impeded by the fact that the founder
of the Franciscans had shown disregard, if not dislike of
worldly knowledge. Alexander of Hales had joined the
brotherhood before the death of St. Francis, and had
dominated the schools of Paris long before the voice of
Albert had been heard there, and while Aquinas was a child.
To a man of ordinary temper, addicted to bold speculation,
the protection of so powerful a corporation as the Francis-
cans had become when Bacon joined them would have been
invaluable. But Bacon threw his chances away. He attacked
the celebrities of his own Order as severely as those of its
rival. His fiery and impatient spirit was to be bound by no
shackles of prudence. He had come to Paris fresh from the
teaching of men like Grosseteste, eager for the promotion

xxxii INTRODUCTION.

and diffusion of science, no less than for the reform of the
Church. He found the great university immersed in dialec-
tical controversy. Many of the controverted questions were
of momentous importance, and Bacon was prepared to take
his part in them. But they were prosecuted by men devoid
of scientific training, unprepared therefore to distinguish
truth from error, verbal subtleties from fundamental realities ;
unwiling even to take the trouble to study Aristotle and
the Bible in their original language. He saw that philosophy
without science could not fail to degenerate (as history, ancient
and modern, shows that it always has degenerated) into .
academic pedantry, and would confirm that one of the aber-
rations of intellect which he looked on as the worst and the
most fatal, the false conceit of knowledge. Against ignorance
under the cloak of wisdom he urged, like Socrates, a lifelong
war ; and, like Galileo, he met with a worse fate than that of
Socrates, the martyrdom of enforced silence.

No crusade has been conducted by blameless crusaders.
It cannot be denied that Bacon's indiscriminating zeal in-
cluded, with pedants and obscurantists who were his lawful
prey, two men who were his equals, one of them, perhaps, his
superior. Albert was a student of nature as well as a philo-
sopher. Aquinas, as a student of man and of society, and
as the constructive thinker who gave coherency to the vast
fabric of Catholic discipline, achieved results which, judged at
the distance of six centuries, Bacon neither equalled nor
approached. Jealousy of the rival Dominican Order, of
which these men were the chief ornaments, cannot account
for Bacon's failure to recognize their value; for the Irre-
fragable Doctor, Alexander of Hales, was a Franciscan, and
was criticized more harshly than either. In their failure to
appreciate duly the importance of scientific culture as a basis
of Catholic action on a doubting and unbelieving world,
the doctors of the Paris schools were all alike involved in
his unmeasured strictures. We may understand, though we
cannot justify, his impatience. He has bitterly expiated it by
many centuries of neglect.

It can hardly be doubted that the seclusion consequent

BACON’S LIFE. xxxiii

on his condemnation in 1277 was effective and rigorous.
Appeals to the Pope had been anticipated by Jerome, who
took care to impress on the court of Rome the expediency
of confirming his decision. All hopes of completing the
Seriptum Principale were shattered. He remained a prisoner,
so it is thought, for fourteen years. Jerome meantime had
become Pope Nicholas IV. After his death in 1292,
a chapter of the Franciscans was held in Paris, at which
Raymond Gaufredi, then General of the Order, set free some
of those who had been condemned in 1277. It may be
looked upon as nearly certain that Bacon was of the
number. Certain at least it is from his own words that in
that year he was again at work, on his last treatise, the Com-
pendium | Theologiae, in which the date 1292 is expressly
mentioned. Whether he died in this year, or two years
afterwards, is uncertain. He was buried in the Franciscan
church in Oxford.

The legend that his works were nailed to the walls of the
library and allowed to perish ignominiously may be dismissed.
But that his life-long efforts to establish a Catholic school of
progressive learning utterly failed, there can be no doubt
whatever. Such men as Rich, Grosseteste, and Bacon, were
not seen at Oxford in the fourteenth century. Greek, mathe-
matics, and experimental science were overwhelmed in the
paralyzing mists of Scotian dialectic. Nevertheless it would
be an error to suppose that his life-work was a failure.
Here and there throughout Europe the tradition of the Doctor
Mirabilis survived as a stimulating force, and kept the embers
of scientific study alive till the time of the Renascence.

In proof of this, three instances may be given :—

1. Peter d'Ailly, in his /mago Mundi, written early in the
fifteenth century, discussing the relations of the extreme east
and west of the habitable globe, has a long passage treating
of the probable proximity of Spain and India. For all that
appears in the work this passage is his own. But in fact it is
a verbal quotation from the fourth part of the Opus Majus,
vol. i.p.290. And it has a history worth recording. For it is
cited in 1498 in a letter from Columbus to Ferdinand and

VOL. I. le

xxxiv INTRODUCTION.

Isabella, as one of the authorities that had put it into his mind
to venture on his great voyage.

2. John Dee. in a memorial addressed to Queen Elizabeth
in 1582 on the reformation of the Calendar, speaking of
those who had advocated this change, says! : * None hath done
it more earnestly, neither with better reason and skill, than
hath a subject of this British Sceptre Royal done, named as
some think David Dee of Radik, but otherwise and most
commonly (upon his name altered at the alteration of state
into friarly profession) called Roger Bacon: who at large
wrote thereof divers treatises and discourses to Pope Clement
the fifth (sic) about the year of our Lord 1267. To whom
he wrote and sent also great volumes exquisitely compiled of
all sciences and singularities, philosophical and mathematical,
as they might be available to the state of Christ his Catholic
Church.' Dee proceeds to give extracts from Bacon's works
in proof of these assertions ; and remarks that Paul of Middle-
burg, who was much occupied with the question of the Calen-
dar, and had treated of it in his work Paulina de recta Paschae
celebratione, had made great use of Bacon. ' His great volume
is more than half thereof written (though not acknowledged),
by such order and method generally and particularly as our
Roger Bacon laid out for the handling of the matter. "When
we remember that it was Paul of Middleburg by whom
Copernicus was urged with a view to this very problem to
construct more accurate astronomical tables, we shall gladly
acknowledge that here, too, Bacon's labour was not lost.

3. No part of Bacon's work was more frequently transcribed
than his Perspectiva. Based as it was upon the great work
of Alhazen, which was itself a development of the Optics of
Euclid and Ptolemy, and claiming indeed to be but an
abridgement or condensation of the truths laid down by his
predecessor with wearisome copiousness, it was in fact much
more than this. It selected from a mass of propositions,

! Dee's memorial is contained among the Bryan Twyne MSS. in Corpus
Christi College, Oxford. The supposition that Roger Bacon changed his name
ntrancg into the Franciscan Order appears to rest on no authority but that

in Dee's very erratic imagination,

BACON'S LIFE. XXXV

many of them mere displays of geometrical ingenuity, pre-
cisely those which aimed at the interpretation of nature, and
at the adaptation of the laws of luminous radiation to human
purposes. He was aware of what was unknown to Ptolemy
and Alhazen, the concentration of parallel rays from reflecting
surfaces formed by revolutions of a conic section; though how
far he was indebted for this knowledge to Peter Peregrinus
or to Vitello cannot be stated with certainty. Of the magnify-
ing powers of convex lenses Bacon had a clear comprehension.
He imagined, and was within measurable distance of effecting,
the combination of lenses which was to bring far things near,
but which was not to be realized till the time of Galileo.

In 1614, four years after the invention of the telescope,
Combach, professor of philosophy in the University of Mar-
purg, published this great work of Bacon, ' viri eminentissimi.’
It would be interesting to know whether the allusion in the
Novum Organum (lib. i. 80) to the work of an obscure monk
(* monachi alicujus in cellula') has reference to this work. The
Cogitata et Visa was written before Combach's edition was
published ; but examples of the Perspectiva were numerous,
and it can hardly have been unknown to Francis Bacon. In
any case it must have been known to Descartes, to whose
epoch-making researches on Droptrique it assuredly contributed
a stimulating influence. This at least they have in common,
that light is looked upon as correlated with other modes of
propagation of force through the Ether.

With the scientific Renascence of the sixteenth century,
Roger Bacon's name slowly emerged from the darkness which
had enwrapped it for three centuries. Astrologers like Dee,
Heyden, and Allen hailed him as a champion of their out-
worn creed. Men of greater mark and sounder judgement,
like Selden and Mead, were struck by his emancipation from
the pedantry of the schools, and by his forecasts, made at so
remote a time, of an age of industrial and scientific discovery.
His central aim, the enlistment of progressive intellect in the
cause of moral and religious renovation, was appreciated by
none. But since the publication of his principal work in the

eighteenth century, his name has gradually ascended towards
Cc 2

xxxvi INTRODUCTION.

its permanent position, on the lofty summits which were the
earliest to take the morning’ of European thought.

II. BACON’S POSITION IN THE METAPHYSICAL CONTRO-
VERSIES OF THE THIRTEENTH CENTURY.

It is too often forgotten that Bacon was a schoolman ;
trained in scholastic methods, and ready to take part in the
philosophic discussions which interested his contemporaries.
It is not perhaps surprising that this side of his work should
have been ignored; for in the Opus Mayjus, though visible
enough to an attentive reader, it is thrown into the shade by
the prominence given to positive science, and by the practical
application of science to political and religious purposes.
Certain chapters of the Opus Tertium, which supplement too
hasty or imperfect treatment in the larger work (chapters
38-52), afford better illustrations of Bacon's aptitude for
metaphysical discussion. Nevertheless, the position of Bacon
in the scholastic controversies of the thirteenth century
remained an unknown quantity till the appearance of Professor
Charles's monograph. - His comprehensive survey of Bacon’s
unpublished works includes a careful study of, and copious
extracts from the important fragment of the Scriptum Princi-
pale, entitled * Communia Naturalium,’ of which copies exist
in the Mazarine library in Paris and in the British Museum.

Hauréau's comprehensive work on Scholastic Philosophy has
made it easy to refute the illusion, still, however, not entirely dis-
sipated, that scholasticism implies a special set of philosophical
tenets or an uniform method of treatment. Philosophical writers
in the thirteenth century differed from one another no less than
philosophical writers in the nineteenth; though in either case
a certain similarity in the subjects considered, and in the mode
of handling them, was impressed by the circumstances of the
time. Scholastic philosophy means simply philosophy taught
in mediaeval schools. And between the schools of the twelfth,
of the thirteenth, and of the fourteenth centuries, there were
great and essential differences.

POSITION AMONG SCHOOLMEN. xxxvii

To pass from the reading of the Polycraticus of John of
Salisbury, who knew nothing of Aristotle but his logic, and that
imperfectly, to a treatise of Albert or of Aquinas seems, and
is, a transition quite as abrupt as to exchange a volume of
Addison or Swift for one of Schopenhauer or Carlyle. In the
one case as in the other, a tide of revolution had swept between
thecenturies. For it was nothing less than a revolution for the
western mind to receive very suddenly from the Mohammedan
world the results of three centuries of Arabian learning, includ-
ing as it did all the more serious part of Aristotle's work,
enriched with keen-witted and audacious comment, and accom-
panied by the scientific results of the schools of Alexandria :
the Syzn/axis of Ptolemy and the biology of Galen.

Isolated thinkers like Adelard of Bath, the first translator of
Euclid into Latin, had already entered this field of study, when
Raymond, archbishop of Toledo, established in the middle
of the twelfth century a systematic school of translators
from the Arabic, of whom the Jew, John Avendeath (other-
wise known as Johannes Hispalensis), Dominic Gundisalvi,
archdeacon of Segovia, the translator of Algazel, and Gerard
of Cremona, best known by his translations of the Almagest
and of Alhazen, were the most prominent representatives !.
Their translations of Aristotle, including his Physics, Meta-
physics and Psychology, were not long in finding their way
across the Pyrenees. Alexander Neckham, afterwards abbot
of Cirencester, lectured upon them in Paris in 1180. His
junior contemporary and countryman, Alfred of Sershall,
pursued a similar course. Neither of these men roused
suspicion. But the case was far otherwise with David of
Dinant and Amaury of Bennes. Though we know little

' See Jourdain, Recherches sur lage et l'origine des traductions Latines
d" Anstole, pp. 107-124 (ed. 1843). The history of mediaeval translations from
Greek into Arabic, sometimes through intermediate Syriac versions, and
from Arabic into Latin, deserves more elaborate treatment than it has yet
received; provided always that the writer of such a history combined the two
conditions so constantly insisted on by Bacon: knowledge of the languages
concerned and knowledge of the subjects treated. Meantime much useful
preliminary work has been done in this direction by such writers as Wuesten-
feld and Jourdain.

xxxviii INTRODUCTION.

of either, except through the criticism of their opponents,
notably through that of Albert and Aquinas, yet such criti-
cism is too detailed and definite to admit of doubt that their
deductions from Aristotle and from his Arabian commen-
tators led them to the assertion of the unity of substance ;
in other words, to the ultimate identity of matter, mind, and
God. As quoted by Albert, the language of David was:
‘It is manifest that there is one sole substance, not only
of all bodies, but also of all souls, and that this is nothing
but God himself. God, matter, and mind, are one and the
same sole substance’ (Albert. Summa Theolog. part II.
tract. xii. quaest. 72, memb. 4, art. 2). David kept himself
within the limits of philosophic theory. He is said to have
been personally intimate with Innocent III; and at least
during his lifetime his heresies escaped notice. It was
otherwise with his contemporary Amaury of Bennes, who,
maintaining the same opinions, was condemned by the Pope
and forced publicly to disavow them. But they survived in
his disciples, who used them in ways directly hostile to
Catholic faith and discipline. A Council was held in Paris
in 1210. Amaury's body was disinterred and buried in un-
consecrated ground; several of his followers were burnt. It
was at this council, the decrees of which were confirmed and
enforced five years afterwards by Robert de Courcon, the
papal legate, that the study of the Physic and Metaphysic of
Aristotle was prohibited, on the mistaken supposition that
the ultimate source of these heresies was to be found there ;
a mistake due probably to the comments of Averroes, with
which the first translations of these works into Latin were
accompanied !.

How to deal with the problem of matter so as to give no
countenance to pantheistic error, was therefore an urgent and
momentous question, to which the schoolmen of the thirteenth
century, and Albert especially, devoted their full powers.

! See Jean de Launoy's work De varia Aristotelis in Academia Parisiensi
fortuna liber (Paris, 1653), in which seven stages are noted, from the condemna-
tion of Aristotle in 1209, to the condemnation of his opponents by the Parlement
of Paris in 1624. Cf. Hauréau, ist. de la Philos. Scolast., Part WU. vol. ii.

75. 73-1 19.

POSITION AMONG SCHOOLMEN. XXXIX

Terrestrial substance, said Aristotle, was made up of matter
and form. Apart from form, what then was matter? A pure
essence, having the capacity, potentia, to become the subject of
form, was the reply. How, then, distinguish matter from this
potentia? Yet, if this be so, if matter is potentially the subject
of all possible forms, we have in matter something that under-
lies all substance. Suppose all forms destroyed, matter holding
in itself all the conditions of existence still remains. How,
then, distinguish matter from God ?

Albert's attempted solution of the problem is involved and
obscure in the extreme, and it must not occupy us here. We
are concerned with Bacon's. Dacon attacked the problem in
his own way, and with a full sense of its importance. His
conclusions are expressed in the seventh chapter of the fourth
part of the Opus Majus, and in the thirty-eighth chapter of
the Opus Tertzum ; and a still further exposition of them is
found in the unpublished work of Bacon already mentioned,
entitled * Communia Naturalium.’ This treatise on Physical
Philosophy consists of four parts, of which the discussion of
Matter occupies the second.

Substance, Bacon maintains, can be predicated neither of
matter nor of form ; but only of the compound which results
from their union. ‘Compositum habet rationem per se exis-
tendi in ordine entium: non sic materia et forma.' Matter and
form are not substances: substance results from their union.
Proceeding from above downwards through the hierarchy of
being in the order of increasing speciality, we have, as the
genus generalissimum, ‘Substantia composita universalis.'
This may be corporal or spiritual. Corporal substance may
be terrestrial or celestial. Terrestrial substance may be
a mixture of elements, or a single element. Mixed substance
may be animate or inanimate. Animate substance may be
sensitive (i.e. animal) or vegetal. Animal substance may be
rational or irrational.

To each of these grades in the hierarchy of substance belong
corresponding grades, not merely in the hierarchy of form, but
also in the hierarchy of matter. ‘ Matter,’ says Bacon, ‘is not
what most teachers of philosophy maintain it to be, "una

xl INTRODUCTION.

numero." In the descending scale from general to special,
each grade of matter, like each grade of form, is distinct from
the preceding. One kind of matter is separated from another
by specific differences, just as form is separated from form.
The difference between an ass and a horse is not a difference
of form only; it is a difference of matter' ( Commun. Natur.'
Part II. Dist. ii. ch. 6).

Bacon has condensed these views in the diagrammatic form
shown in the subjoined schedules, which I have copied from
the Mazarine MS. pp. 23, 24. (They have been collated with
those of the Br. Mus. MS. Royal, 7 F. vii. fol. 91 and 92.
The variants in this MS. for the schedules of substantia com-
posita and forma are unimportant. Those of materia are
omitted ; this MS. being in other respects less perfect than
that of the Mazarine library.)

How are we to estimate these speculations? It is obvious
in the first place that they stand in marked opposition to, or
at least in distinction from, theories current among Bacon's
contemporaries. To judge rightly of them we must bear in
mind that throughout the greater part of the thirteenth
century questions were being agitated of even greater impor-
tance than the controversy between realism and nominalism.
The pantheistic tendencies discernible in Averroes and other
Arabian thinkers had been diffused, as we have seen, by men
like Amaury and David of Dinant They were responsible,
as some thought, for the disastrous anarchy which early in
the century had devastated southern France. Bacon was
quick to perceive the danger of maintaining the unity of
matter. It had been defended, as he points out (Op. May.
vol. i. p. 144), by passages from Aristotle which he wishes to
believe had been badly translated. In any case, he says,
‘the error is enormous, as great as any that can possibly be
found in speculative questions. If it be granted, it is im-
possible to comprehend the generation of things, and the
whole course of nature will be misunderstood. And what is
more, if this error be looked at closely, it will be found to
tend towards heresy, or rather to be the profanest of heresies,
since the inevitable result of it is to endow matter with the

Divi8stO SUBSTANTIAE COMPOSITAE UNIVERSALIS.

CORPUS
UNIVERSALE
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IRRATIONALIS ANIMA RATJONALIS SINGULARIS EST HUJUS
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Divisio MATERIAE PRIMAE UNIVERSALIS.

MATERIA
UNIVERSALIS
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ALIA EST ANIMATI
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EST STATUS !N LINEA MATERIARUM UNIVERSALIUM, CUI RESPON-
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POSITION AMONG SCHOOLMEN. xli

creative power of God.’ Whatever dangers were involved in
the unity of matter, Bacon met by a bold denial of such
unity. ‘Divide et impera, he said in effect ; matter, thus
split up into sections, is no longer to be feared.

Looking at Bacon's theory by the light of subsequent cen-
turies, it is not difficult to see that its value lay in its solvent
and destructive power. His aim from beginning to end of
his career was to draw men away from verbal subtleties and
concentrate them on the realities of life, as plain men under-
stand them. *You ask me, he would say to the young
students around him, ' what is this matter which remains apart
from all form, with capacity for receiving all? But who told.
you that it was one and indivisible? There are as many kinds
and degrees of matter as there are of things. Look at the
things, try them, see how they act on you, how you can act
on them. As to the matter and form that may underlie
them, leave that to God.’

Bacon's part in the great controversy between realism and
nominalism will lead us to a similar conclusion. It was a less
burning controversy in the thirteenth century than in the days
of Roscelin and Abelard, or than it became afterwards in the
days of Duns Scotus and William of Ockham; and it was
debated by Albert and by Aquinas with the far larger and
deeper understanding of its complications, that might be
expected from men who were not merely trained like their
predecessors in the study of Aristotle's Logic, but had become
conversant with the problems raised in his Physic and
Metaphysic. Both these thinkers rejected the independent
existence of universals i5 re as clearly as Aristotle had
done. They were clear that universals had no existence
except in the mind. ‘ Non est universale nisi dum intelli-
gitur' (Albert. 7e. lib. v. tract. vi. cap. 7). ‘Una et eadem
natura quae singularis erat et individuatur per materiam in
singularibus hominibus efficitur postea universalis per actionem
intellectus depurantis illam a conditionibus quae sunt hic et
nunc’ (Aquinas, 7ractatus primus de universalibus). Never-
theless, both of them left a place for the universal amze rem,
not indeed in the fantastic world of Ideas which Plato had

xlii INTRODUCTION.

portrayed, but as radiations centred in the primal form, the
mind of God.

Turning to Bacon, who discusses the question of universals
at considerable length and with extreme independence, we
find the same tendency to emancipate himself from bondage
to words, entities, and verbal discussions, and to dig down to
a foundation of solid fact. One individual, he says!, is of more
account than all the universals in the world. A universal is
nothing but the similarity of several individuals ; * convenientia
plurium individuorum. ‘Two things, he goes on to say,
‘are needful for the individual. The first is absolute: it
is that which constitutes his existence, as when we say,
“This man is made of soul and body." The second is
that in which he resembles another man, and not an ass or
a pig. This is his universal. But the absolute nature of an
individual is of far more importance than his related nature.
It is ixed and absolute by itself. Thus the singular is of
more account (o$:/ivs) than its universal, Experience leads
us to this conclusion, and so also does theology. God has
not created the world for the sake of the universal man, but
for the sake of individual persons.’ * Individuum est natura
absoluta et fixa habens esse per se; et universale non est nisi
convenientia individui respectu alterius."

In some passages Bacon appears to go much further in
the direction of nominalism than Albert and Aquinas. ‘The
prevalent view, he remarks, ‘is that universals exist only in
the mind. Yet two stones would be like one another, even .
though there should be no mind to perceive them. But it is
precisely this likeness of the two stones that constitutes their
universal’ (* Commun. Natur.’ Part II. Dist. ii. ch. 10).

Closely allied with the controversy as to universals was the
question of Individuation. Are things individualized by form
or by matter? Albert and Aquinas took the latter view,
Bonaventura the former. ‘Individuorum multitudo, says
Albert (De Coelo, tract. iii. c. 8), ‘fit omnis per divisionem
materiae. Formae quae sunt receptibiles in materia indivi-

! On the question of Universals, and also on that of Individuation, cf. the
extracts from the Communia Naturalium given by Emile Charles, pp. 383-386.

SCRIPTUM PRINCIPALE. xliii

duantur per materiam. (Cf. Aquinas, Summa Theol. i. quaest.
iii. cert. 2.) Aquinas was obliged, however, to add that this
materia must be ‘signata’: must be quantified. 'Signatio ejus
est esse sub certis signationibus quae faciunt esse hic et nunc.’
This addition went far to neutralize the Thomist view of
Individuation ; for as his opponents at once rejoined, ‘ What
determines quantity if not form ?'

In opposition to Aquinas, Bonaventura maintained that
‘species est totum esse individui! Substance consisting of
the union of matter and form, matter was uniform in all: the
form was that which distinguished, individualized.

Bacon (* Commun. Natur.' Pt. II. Dist. ii. ch. 9), in opposition
to either view, maintained that the question was meaningless
and foolish. All substances, whether universal or singular,
have their own constitutive principles. Soul and body make
man. This soul and this body make this man. In the inten-
tion and procedure of nature, ‘this man’ is prior to ‘man’;
‘man’ comes in as something subsidiary, ‘extra essentiam
ejus, similis accidenti, as the means of comparison with other
individuals. There is no more reason for inquiring what
causes individuation than for inquiring what causes universality.
There is no answer to such a question, except that the Creator
makes everything as its nature requires. Individual matter
and form is made in one way : specific or generic matter and
form is made in another. *Stultitia magna est in hujusmodi
quaestione quam faciunt de individuatione.'

III. BACON' S * SCRIPTUM PRINCIPALE.

The foregoing remarks, which it would be easy, but not, in
this place, justifiable to prolong, will illustrate Bacon's position
as a schoolman, thoroughly versed in the technique of scho-
lastic controversy. But he was a schoolman whom a long and
laborious study of the realities of life, whether in nature or in
man, had taught to distinguish things from words: solid facts
from subtle figments. He was not alone in this. Albert and
Aquinas were solid thinkers like himself. Less versed in
natural science than Bacon, they had more than he to do

xliv INTRODUCTION.

with the science of man; they had to face the difficult and
urgent problems connected with the spiritual government of
mankind. Their philosophy, like his, dealt with real things.
And if theirs was less positive, less free from metaphysical
figments, it is only that the complications of human nature
were less adapted for positive treatment than the physical
phenomena to which Bacon devoted so large a share of his
attention.

But in contrast with these three great schoolmen stand the
weavers of word-systems, like Alexander of Hales, Henry of
Ghent, and Duns Scotus, wasting their own and other men's
time and energy in defining, dividing, and refining with infinite
ingenuity, and with such result as when children build sand-
castles on the shore. With such men it may have been
needful to fight, yet fighting was but beating the air. Of
what avail to discuss Individuation with dialecticians who
explained it by ‘ laecceitas ! ' ?

In all Bacon's discussion of scholastic problems, the solution
he reached was of a kind to favour the falling off of the meta-
physical husk, and to bring to light the real and positive
problem which lay beneath it. His scholastic theories are
therefore for us, and in all probability were for him, of far
greater negative than constructive value. But his central aim
lay in another direction above and beyond scholasticism. We
shall best learn how to appreciate it by looking at the pro-
gramme of the encyclopaedic work, the * scriptum principale,’
often spoken of in the Opus Majus and the Opus Tertium, but

! This word is believed to be due rather to the disciples of Duns Scotus than
to the master himself. Happily for Bacon's peace of mind, he did not live to
witness the triumphal career of the Doctor Subtilis. Of Hauréau's careful
appreciation of his work the final words may be quoted: ‘Cette philosophie
n'explique pas la nature, elle l'invente ; substituant l'ordre rationnel à l'ordre
réel, elle dispense, il est vrai, de l'étude des choses; mais, quand aprés avoir
admire l'économie d'un systéme si complet, si habilement ordonné, on abaisse
ses regards vers ces choses dont on a jusqu'alors dédaigné de s'enquérir, on
soupconne dés l'abord qu'on vient d'achever un réve, et bientót, devant le
spectacle qu'offre la réalité, s'effacent, s'évanouissent l'une aprés l'autre toutes
les abstractions décevantes, toutes les chiméres dont Ja création appartient au
systéme, à lui seul.’ [Hrst. de la Philos. Scholastique, Part II. vol. ii. pp. 171-
259, ed. 1872 -8o. |

SCRIPTUM PRINCIPALE. xlv

of which the persecutions and imprisonment of his later life
never allowed him to execute more than a few íragments.
And of these fragments many are lost.

This ‘ scriptum principale,’ as he tells us in the first chapter
of the unpublished work entitled ‘Communia Naturalium,’
consisted, or was intended to consist, of four volumes. The
first volume dealt with Grammar and Logic, the second with
Mathematic, the third with Physic, the fourth with Metaphysic
and Morals.

The second chapter of the * Communia Naturalium ‘is entitled,
‘De universo ordine scientiarum naturalium.' He distinguishes
eight natural sciences. The first treats of the principles
common to Natural Philosophy. The others are:—(1) Per-
spective or Optic, (2) Astronomy, (3) Barology, (4) Alchemy,
(5) Agriculture, (6) Medicine, (7) Experimental Science. The
general principles of Physics form the subject of the first
treatise here spoken of. Of the seven special sciences, the
first three form part of what would in the present day be
called Physics. Under Astronomy is included not merely the
study of planetary motions, but the scientific determination of
terrestrial positions, in óther words, Geography, and also the
influence of the stars and the sun on the earth and man:
that is to say, the study of climate and of astrological forces.
As to the third of the special sciences, * scientia de elementis,
or as he also calls it, *scientia de Ponderibus, what in the
present day would be called Barology, it is not without
interest to find it thus set apart as a distinct department of
speculation. The fourth, Alkimia, corresponds, so far as the
description of its purpose goes, very nearly to the modern
science of Chemistry. It deals, says Bacon, with the ‘ mis-
tiones elementorum, with the generation of liquids, gases, and
solids (humores et spiritus et corpora"), with all inanimate
substances, including organic products (* usque ad partes ani-
malium et plantarum inclusive’).

The title of the fifth science, Agricultura, would be mis-
leading, if Bacon had not given us a clear explanation of its
purpose'. It is the science of living bodies, vegetal and

! Cf. the long extract given by Charles, pp. 370-374. The unfortunate rarity

xlvi INTRODUCTION.

animal; reserving, however, the subject of man's physical
nature for subsequent treatment under the head of medicine.
Before man be properly investigated, we must know the
nature and surroundings of other animate things. First we
must distinguish the soil fit for different kinds of plants,
arable land, forest land, pasture land, garden land. We then
examine the whole subject of plants which has been left in-
complete in the treatise attributed to Aristotle, De Vegetabilibus.
But as lands cannot be tilled without domestic animals, and
as forests, pastures, and deserts depend for their value on the
wild animals they contain, the science we are now speaking of
embraces the full consideration of animal life. on which, as
Bacon believed, Aristotle wrote far more volumes than have
come down to us In the sixth science we proceed to the
study of the ànimal possessing reason, the study of Man.

of Charles’ work is my excuse for citing the portion of this extract relating to
the study of living bodies, based, as Bacon explains, on the preliminary study of
Alkimia speculativa. * Deinceps de plantarum natura et animalium specialis
scientia et maxima constituitur, scilicet de omnibus animatis praeterquam de
homine, de quo propter nobilitatem suam et dignitatem constituitur scientia
propria quae dicitur medicina. Sed in ordine disciplinae prima est scientia
animatorum praecedentium hominem et ejus usui necessariorum, quae primo
descendit ad omne genus agri et terrae, distinguens quatuor species agrorum,
propter vegetabilia e terra nascentia in eis. Est enim ager in quo serunt segetes
et legumina ; est ager consitus arboribus, ut nemus ; est ager pascivus, ut prata
et deserta; est ager qui hortus dicitur, in quo domesticae arbores et caules et
herbae et radices tam nutritivae quam medicinales parantur. Haec igitur
scientia extendit se ad perfectam considerationem omnium vegetabilium quorum
notitia nimig imperfecta traditur in libro De Vegetabilibus Aristotelis; et ideo
necessaria est scientia sufficiens de plantis et animalibus supplens defectus
librorum communium Aristotelis vulgatorum apud Latinos, qui vocantur De
Plantis et Antmalibus. Sed cum agrorum cultura non potest fieri sine copia
animalium domesticorum, neque utilitas agrorum, praecipue consitorum arboribus,
et pascuorum et desertorum, posset haberi nisi nutrirentur animalia sylvestria,
ideo extendit se haec scientia ad plenam considerationem animalium omnium;
et ad horum cognitionem misit Aristoteles plura millia hominum per regiones
mundi, et fecit illa praeclara quinquaginta volumina prius memorata. Haec
autem scientia traditur in libris Plinii, in libro Palladii De Agricultura, et in libro
Georgicorum Virgilii non ignobili, cum expositione egregii commentatoris ejus.

Scientia septima est de animali rationali, scilicet de homine, et praecipue de
sanitate et infirmitate ejus; et ideo de ejus compositione et generatione illius,
sine quibus sanitas et infirmitas ejus non possunt intelligi nec doceri. Constat
vero quod homo est res naturalis, et ideo scientia ejus naturalibus constituta
erit inter naturales comprehensa.

SCRIPTUM PRINCIPALE. xlvii

Our aim being to understand the conditions of his health or
disease, we have first to examine his structure and develop-
ment, without which health and disease cannot be understood
or spoken of.

Finally, to complete the whole, comes Experimental science.
It is, he says, a final judge of the assertions and reasonings put
forth in all the foregoing sciences. More than this: it gives
directions to those engaged in other sciences as to the construc-
tion of instruments by which their conclusions are to be tested,
in the same way in which a navigator instructs a shipwright as
to the building of a ship. Thus, for instance, it instructs the
geometer to make a mirror such that the rays reflected from
it shall converge in a single point. It scrutinizes every natural,
every artificial force. It sifts the artifices of magic, as logic
sifts the reasonings of the sophist, so as to dissipate falsehood
and error, and leave nothing but truth remaining.

How Bacon would have treated this part of the subject we
have no means of judging, other than the sixth section of the
Opus Majus. But even the summary exposition there given is
enough to show how large was his conception of experimental
method, and at the same time how carefully he steered clear
of the danger of undervaluing the mathematical or deductive
process of discovery. So far as was possible the two should
be pursued simultaneously and in close alliance. Euclid's
demonstration of his first proposition would, he says, fail to
carry complefe conviction unless visual evidence of it were
forthcoming in the construction of the figure. And on the
other hand, we see that his inductive investigations of the
rainbow were controlled at every step by deductions from
astronomy.

With these general remarks, we may now pass to each of
the principal divisions of the * Scriptum Principale,’ which in
the main correspond to the order followed in the Opus Majus.
" First comes Language, as the channel through which the
thoughts of other men are handed down to us; then follows
Mathematic, embracing the four branches of the Quadrivium,
geometry, arithmetic, astronomy, and music. Thence we
pass to Physic, which included the study of the propagation

xlviii INTRODUCTION.

of force, specially illustrated by the radiation of light and heat.
Next comes Alkimia Speculativa, not the mere metallurgy
of the gold-seekers, but the study of the transformation of
matter from its simplest to its most complicated state. The
study of living matter followed, ending with Medicine, the
science dealing with the physical structure of man. Finally,
the edifice of the sciences is crowned by Ethic and Metaphysic.

Of this comprehensive scheme let us see what fragments
are forthcoming.

IV. BACON'S PHILOLOGY.

In urging that the comparative study of language should
form part of the University curriculum, Bacon stood nearly
alone. He does indeed full justice to those among. his con-
temporaries who had promoted the translation of Greek books
into Latin ; and, first among those, to the illustrious bishop of
Lincoln, his forerunner and counsellor. But though Grosseteste
had caused many books to be translated for the sake of their
contents, it does not appear that he or any one else had
proposed to carry the study of language, as such, beyond the
routine of grammar presented in the Trivium; the Latin
accidence and syntax of Priscian or Donatus.

What Bacon proposed was the systematic and comparative
study of Hebrew, Arabic, and Greek, with the dialects belonging
to each. With Hebrew went Chaldaean, and, in more distant
relationship, Arabic: with Greek its various dialects, which
were, he tells us, comparable to the Picard, Norman, or Bur-
gundian dialects of French, or to the northern, southern,
eastern, and western dialects of English. *I do not mean,
says Bacon, ‘that every one should learn these languages as
he learns his mother tongue, so as to be able to speak them
as we speak English, French, and Latin; nor again that we
should content ourselves with being able to translate into our
own language the Latin versions. There is an intermediate
degree of attainment quite easy to those who have teachers.
We should know enough to be able to understand how these

PHILOLOGY. xlix

languages should be rendered in Latin. The point is that
a man should be able to read these languages, and understand
their grammatical structure ('accidentia partium orationis,'
Compendium Studii, Brewer, p. 433).

What Bacon’s linguistic attainments were cannot be pre-
cisely decided. No work of his, published or unpublished,
that I am aware of, affords evidence of knowledge of Arabic.
His own words in the twenty-fifth chapter of Opus Tertium
are scarcely decisive on the point. ‘De Arabica tango locis
suis ; sed nihil scribo Arabice, sicut Hebraee, Graece, et Latine,
quia evidentius et facilius ostenditur propositum meum in his.
Nam pro studio theologiae parum valet, licet pro philosophia
multum, et pro conversione infidelium.’ Some pages printed
for the first time in this edition show acquaintance at least
with the Hebrew alphabet. An elementary Greek grammar,
in the possession of Corpus Christi College, Oxford, testifies to
his knowledge of Greek, which indeed is sufficiently apparent
in the present work, and still more in the ninth and following
chapters of the Compendium Studii (Brewer, pp. 495-519).
This grammar is incomplete, dealing chiefly with the alphabet,
with the Greek system of accentuation, aspiration, and
quantity, and with the numeral system. It concludes with the
paradigm of the verb rvzre. .Its opening sentence seems to
indicate that it formed a part of Bacon's encyclopaedic work.
‘Here begins the first book of the volume on the grammar of
languages other than Latin. This book deals with Greek
grammar. ‘I have already, he continues, ‘ spoken of the ad-
vantage to the Latin world of knowing. the four languages,
Greek, Hebrew, Arabic, and Chaldaean ; and in the preface to
this volume devoted to grammar I have explained the division
of subjects and their order. I now proceed to consider Greek
grammar, beginning with such rudiments as boys are taught in
Latin in order that they may read, write, and construe simple
passages, and may pass thence to points of greater difficulty.’

A point of interest presents itself as to Bacon's pronuncia-
tion of Greck. Much attention is given to the transliteration of
the Greek alphabet into its Latin equivalents. The Lord's
Prayer, the Salutation to the Virgin, and the Apostles’ Creed

VOL. I. d

] INTRODUCTION.

are written out in Latin, underlined first with the Greek words
in Roman character, and secondly with the same words in
Greek. The second of these is here given as an example:

Ave Maria X gratiosa Dominus cum te benedicta
Chere Maria kecharitomeni ho Kyrios meta su eulogimeni
Xaipe Mapla xeyapvropévg — ó Kuiptos pera cot ebroynuern

tu in mulieribus et benedictus fructus ventris tui.
sy en gynexi ke eulogimenos ho karpos tis kilias su.
‘ov ép yvvail— kal ebAoynpévos 6 xapmós tis KotAias aod.

Amen.
Amen.
"Apajv.

Itis evident from the transliteration of vowels and diphthongs
here adopted, with which may be compared pp. 75-76 of the
Opus Majus, printed for the first time in this edition that these
were pronounced as in modern Greek!. It appears also in the
subsequent discussion on accents, that accents were considered,
no less than quantity, in pronunciation. Bacon may not im-
probably have learnt the language from one of the Greeks
who had been invited into England by Grosseteste. Some
of these, he tells us, had become permanent residents. (In
Compend. Studii, Brewer, pp. 495-514, the same subject
is treated.) |

In urging so strongly the study of language, Bacon had two
main purposes in view: an improved text of the Bible, and an

! [n the Corpus Coll. Grammar, a systematic scheme of transliteration and of
pronunciation is also given. We learn from it that the second letter of the
alphabet was pronounced like the modern English v; and that there was no
single letter rendering the sound of our b. ‘Item m post yz vel v, sive in eadem
dictione, sive in diversis, dummodo sine intervallo proferantur, sonum nostri 6
habet, quem aliter non habent, ut Aapwds, duwedov. Similiter 7 post p vel» sonat
nostrum d, quod aliter non habent, ut ávriypioTos.' All this is in accordance
with modern Greek pronunciation. The transliteration of the dipbthongs av
and ev was a matter of some difficulty owing to the confusion between x and v.
Bacon usually renders them as af and ef. But in modern Greek it is only before
0, «, €, 7,0, 7, $, X, V, that they are thus pronounced ; before other letters they
would have the sound of av or ev. With regard to accents, Bacon’s language
(both in the Corpus MS. and in the Compendium Studs) puts it beyond all
doubt that they governed his pronunciation of the language.

PHILOLOGY. li

intelligible translation of Aristotle. Under both these heads
the minor works, edited by Brewer, contain much for which in
the Opus Majus Bacon had not found room. With regard
to the first, the valuable memoir published in 1858 by Abbé
Martin may be consulted'. It appears that, towards the end
of the twelfth or the beginning of the thirteenth century, a text
of the Bible had become generally current in Paris under the
title of * Textus Parisiensis. Bacon, writing in 1267, speaks of
it as having been hastily compiled, about forty years before, by
second-rate theologians and carelessly copied by uncritical
booksellers (Opus Minus, Brewer, p. 333). It abounded in
errors and in interpolations inserted from patristic quotations,
from liturgies, and from the works of Josephus. Many of.
these errors attracted notice, and attempts were made, prin-
cipally by members of the mendicant orders, to correct them.
But these attempts, in Bacon's judgement, only resulted in
making the matter worse. Each critic worked independently
and without adequate critical apparatus. Not merely did
Franciscan differ from Dominican, but the members of each
Order differed amongst themselves. Successive corrected
versions were put forward, each worse than the preceding.
By the middle of the century the Paris text had fallen into
hopeless confusion ; and it had become, in Bacon's judgement,
far the lesser evil to use the uncorrected text than any of
those which had been so uncritically amended. Of these strong
remarks he gives many pointed illustrations.

So devoid were these successive editors, not merely of
linguistic knowledge, but of the critical spirit, that they seem
to have been entirely unaware of the origin and history of the
Vulgate. Bacon's history of the various Biblical versions,
ending with that of Jerome, as given in the Opus 7erfrinr,
PP- 334-349, is not one of the least interesting portions of his
work. His principal result was to show that, before Jerome's
translation from the Hebrew, the version regarded as authen-
tic by the Church was the Septuagint ; although theologians
had felt themselves at liberty to correct that version from
that of Aquila, Symmachus, and above all of Theodotion.

! See note on vol. i. p. 77.
d 2

lii INTRODUCTION. .

After the time of Jerome, the translation from the Septuagint
continued to be used in the Psalter; but, with that exception,
Jerome’s translation from the Hebrew constituted the Vulgate,
and was received as authentic by the Church. Bacon is care-
ful to add that Jerome’s version is by no means free from
error, due partly to over-haste, partly to his unwillingness to
offend his contemporaries by making too many changes in
the text hitherto accepted.

With Aristotle the case was even worse than with the
Bible. The brilliant hopes with which the century had
opened, of re-entering the temple of Greek wisdom, and
listening to the voice of the greatest of ancient thinkers,
had been falsified by the failure of Aristotle's translators
to comply with the two elementary conditions of transla-
tion; knowledge of the language in which, and compre-
hension of the subject about which, the book was written.
Something has already been said of the Toledo school of
translators instituted by Archbishop Raymond in the twelfth
century. A new and vigorous impulse was given forty or
fifty years afterwards by the Emperor Frederic II, whose
preference of Mahommedanism to Christianity, had he
occupied a humbler station, would assuredly have subjected
him to a worse fate than that of Bacon. Leaving out of
account translations of Aristotle's Organum, parts of which
were familiar to the western world from the times of Augustine
and Boethius, the translators of Aristotle’s philosophic and
scientific work in the twelfth and thirteenth century, to whom
Bacon calls attention, were five: Gerard of Cremona, Alured
or Alfred of England, Michael Scot, Hermann the German,
William of Moerbeke, otherwise called the Fleming. Of
these, Gerard, Scot, and Hermann translated from Arabic
versions. Gerard spent many years in Spain, attained a
thorough knowledge of Arabic, and translated Ptolemy’s
Almagest, and Aristotle's Afeteorologics, also the astronomy
of Alfraganus, several works of Alkindi, and, almost certainly,
the Optics of Alhazen. He died in 1187. Michael Scot
flourished in the first half of the thirteenth century. He
was a friend of the Emperor Frederic II, under whose

PHILOLOGY. liii

patronage he visited Spain, and translated from the Arabic
many of Aristotles works, with the comments of Averroes.
Albertus Magnus says of him that he was ignorant of natural
things, and that he did not thoroughly understand Aristotle's
books. Bacon, who speaks of the impression produced in
the schools when he appeared in 1230, with translations of
Aristotle's metaphysical and scientific treatises, says that he
was ignorant of words and of things, and that the greater
part of his work was due to Andrew the Jew. Scot’s transla-
tion of Avicenna's treatise De Animalibus, as I have remarked
in a note (vol. ii. p. 85), certainly seems to bear out this
severe judgement. Hermann, the German, was personally
known to Bacon; he worked in Spain, and with the help of
Arab interpreters, produced translations of the Rhetoric,
Poetic, and Ethic of Aristotle. He mentions incidentally
(Fourdain, p. 140) that Grosseteste had produced a more
complete rendering of the Ethic directly from the Greek.
Hermann, in answer to some questions put to him by Bacon as
to Aristotle's logical works, frankly confessed his ignorance of
logic. ‘Nor was he well acquainted,’ Bacon continues, ‘ with
Arabic, being rather an encourager of translations than a
translator himself; the principal part of his work was done
by Saracens in his employment’ (Compend. Studi, cap. 8).
William the Fleming (of Moerbeke) had the advantage
over these men that he translated directly from the Greek.
His work is believed to have been done at the special request
of Thomas Aquinas, who made use of it in his Commentaries
on Aristotle. ‘ But it was notorious in Paris,’ says Bacon, ‘that
William of Moerbeke was totally ignorant of science, and his
translations are consequently full of errors.’ On the whole.
he concludes that it would have been better that Aristotle
should never have been translated, rather than that such
a mass of error should be propagated under the shelter of his
name. Had I the power of disposing of these works, I would
have them all burnt: it is a waste of time to study them,
a source of error and of diffusion of ignorance greater than
can be described. *Aristotle's works, he continues, ‘are the
foundation of all wisdom, but they must be studied in the

liv INTRODUCTION.

original to be of any profit’ (Compend. Studii, Brewer,
P. 469).

Every one who considers Bacon's efforts in promoting the
study of language must agree with Professor Brewer (p. 1xii)
that ' his labours in this respect have attracted less attention
than they deserve. .. . It is as creditable to his discernment
as to his courage that he should have seen, better than Lord
Bacon did, the paramount importance of philology, and urged
it repeatedly on his contemporaries. It is amazing to hear
a scholar of the thirteenth century insisting on the necessity of
constant references to original authorities as the only sure
foundation of sacred criticism.’

It may be that Bacon’s exhortations, reiterated as we feel
sure they would be, not in writing merely, but in conversation
with the young men whom he gathered round him, were not
entirely without effect on the following generation. In the
council convoked in 1312 by Clement V at Vienne, one of
the provisions, says Fleury (7st. Eccl. book 91), was ‘ the
establishment in the Roman Curia, and in the Universities of
Paris, Oxford, Bologna, and Salamanca, of teachers for the
three languages, Hebrew, Arabic, and Chaldaean, two for
each. They were to be maintained in Rome by the Pope, in
Paris by the King of France, and in the other cities by the
prelates, bishops, and chapters of the country.’ This subject
has been carefully studied by Mr. Rashdall in his important
work on the Universities of Europe in the middle ages. He
gives strong authority for the belief that Greek was included ;
and if so, the avowed purpose of the ordinance, which was
the conversion of the Mahommedans and Jews, may not have
been the only purpose ; some faint echo of Bacon's exhorta-
tion to study Aristotle and the Bible in the original, with the
view of understanding them better, may have been still audible.
Few and short-lived were the attempts made to carry the
decree of this Council into effect. In 1320 we hear of a rate
levied upon benefices in the province of Canterbury for the
support of a converted Jew alleged to be teaching Greek at
Oxford. But Oxford was already passing under the spell of
the enchanter. The fine webs of Duns Scotus, which the

MATHEMATICS. lv

sword of Ockham might cleave but could not dissipate, were
paralyzing her energies. Five generations were to pass before
she could again begin to promote the study of 'languages
other than Latin!'; and even then not in the comprehensive
spirit which Bacon had advocated. It is tempting, though
painful and perhaps useless, to imagine how far European
culture might have advanced had schools of Oriental languages,
concurrently with those of Greek and Latin, been instituted
and continuously maintained from the thirteenth century.

V. BACON'S MATHEMATICS.

In the Opus Majus, though much is said of the importance
and necessity of mathematical method, there is very little
display of mathematical knowledge. Frequent references are
made to Euclid, whose Elements had been introduced to the
western world early in the previous century, by Adelard of
Bath, and more completely in the thirteenth century by Cam-
panus of Novara. Archimedes and Apollonius are rarely
mentioned. But in his Optics Bacon shows that he was
acquainted with the properties of parabolic concave mirrors.
and of their power of causing parallel rays to converge after
reflection to a focus. In this respect he was in advance of his
principal teachers in Optic, Euclid, Ptolemy, and Alhazen.

Of the Calculus, arithmetical or algebraical, Bacon has but
slight occasion to speak in the Opus Majus. It has always
to be remembered that this work, with its appendices, the
Opus Minus and Opus Tertium, was not, properly speaking,
a philosophical treatise, but an exhortation addressed to a
statesman, absorbed in ecclesiastical and political struggles,
to exert his authority for the revival of learning. Hence it
is uniformly spoken of as a Persuasto. It contains just as
much learning and science as was thought needful to convince
the Pope that learning and science were capable of strengthen-
ing the Church. It is but the preamble to the * Scriptum

! The organized teaching of Greek in Oxford is due to Richard Foxe, the
founder of Corpus Christi College (1515-16). But when Erasmus was in Oxford
about twenty years earlier, such men as Thomas Linacre and William Grocyn
had already become Greek scholars, under the teaching, perhaps, of Cornelio
Vitelli. (Cf. Hallam, Lit. Hist. of Europe, part i. ch. 3.)

lvi INTRODUCTION.

Principale, which there is reason for thinking that Bacon
had already begun, but which he regretfully expresses his
inability to send at such short notice. Hence though it deals,
often very cursorily, with every department of knowledge
then recognized, we must not infer Bacon's ignorance of
a subject from the fact that this provisional treatise makes
no mention of it.

Among the fragments of the ' Scriptum Principale' which
have come down to us, is a portion of the first book on
Mathematics, preserved among the Sloane MSS.(2156). This
first book contained three parts. We have the first part of
this book, and a considerable part of the second. A few
fragments more are to be found in the Bodleian (Digby MSS.
76). As far as I am aware nothing more is extant.

The first part deals with preliminary principles (* quaedam
preambula ad interiora mathematicae ’).

It has five divisions or distinctions. The subjects dealt
with are the relation of mathematic to metaphysic: its dis-
tinction from magic; the hindrances to its culture offered by
the four causes of error, viz. false conceit of wisdom, authority,
custom, and popular prejudice ; the utility of mathematics, its
importance to the preliminary studies of logic and grammar.
The final chapter of this section is.curious. The final purpose,
says Bacon, of logic is conviction. But conviction is not
reached by argumentative process alone, but by the arts of
rhetoric and poetry, which are therefore in a true sense
departments of logic. But the-e arts are governed by the
laws of music, which is a branch of mathematical science.

The second division deals with the definition of the parts
of quantity. Certain general terms, such as simultaneity in
space and time, limit, continuity, infinity, dimension, are
explained. The distinction is drawn between continuous and
discrete quantity. Continuous quantity in one, two, and three
dimensions is defined. Discrete quantity is distinguished into
what is permanent, as number; what is not permanent, as
sound.

The third division expounds the distinction between the
soeculative and the practical departments of geometry and

MATHEMATICS. lvii

of arithmetic. The section on practical or applied geometry
is of much interest as illustrating Bacon's enlarged views of
scientific training. He indicates eight departments of this
branch of science. (1) Agriculture, in a far wider sense than
is usually given to the word, comprising mensuration, archi-
tecture, civil, mechanical, and military engineering. (2) The
fabrication of astronomical instruments. (3) Of musical in-
struments. (4) Of optical instruments. (5) Of barological
instruments. (6) Of instruments of experimental science.
(7) Of medical and surgical appliances. (8) Of chemical
apparatus.

In connexion with the practical branch of arithmetic, after
speaking of the use of the Abacus, he mentions ' vias algorithmi,
scilicet quomodo conjugantur numeri et dividuntur, secundum
omnem speciem algorithmi, tam in particularibus fractionibus
quam in integris, In this connexion he speaks of ‘ Algebra
quae est negotiatio, et almochabala quae est census. How
far Bacon had assimilated the work of Mohammed ben Musa!,
whose surname, Al Chwarismi, is incorporated in the word
Algorithm, we cannot tell. But with the work of one of the
two great mathematicians of the thirteenth century, Jordanus
Nemorarius, he was certainly familiar, as may be seen by
reference to vol. i. pp. 158, 169 of the Opus Majus. Among
other branches of practical arithmetic he includes the con-
struction of astronomical tables, mensuration, alloys and
coinage, partnership, and other operations of commerce.
These things are treated of at great length in the Lzber
Abaci of Leonard of Pisa, the other great mathematician
of the timc, whose work, dedicated to Michael Scot, Bacon

! Muhammed ibn Misa Alchwarismi was born in the first quarter of the ninth
century. He constructed astronomical tables for the Caliph Al Mamoun, which
were translated into Latin by Adelard of Bath. Of more importance, however,
are his Arithmetic and his Algebra. The first of these remained for a long time
unknown. But it was discovered in Cambridge in 1857, and is included among
the 7ratíati d Antmetica published by Boncompagni. A full account of this
work and of the Algebra, translated and edited by Rosen (London, 1831), will
be found in Cantor, vol. i. pp. 611-629. Cantor (p. 612) explains clearly the
passage of the word Alchwarismi into Algorithm. Bacon's interpretation of the
words Aldschebr walmukábala, which Alchwarismi uses, is incorrect. Dschebr
means Restoration, mukabala means opposition.

lviii INTRODUCTION.

had possibly seen and studied; though he makes no mention
of it, in any work known to us '.

Astrology and astronomy come next. The first is the
speculative branch, dealing with planetary motions, with the
figure of the earth and of its various regions. Astronomy,
the practical branch, has to do with the construction of tables
and with the forecast of future events. Bacon admits that this
use of the words has not been universally adopted, but main-
tains its correctness. *Astrologia componitur ex hoc nomine
astron quod est stella, et hoc nomine logos quod est verbum,
vel ratio, vel sermo, quia est sermo de stellis. Astronomia vero
dicitur lex stellarum et nomos est lex. Unde quia lex univer-
saliter sonat in practicum, ut in morali philosophia lex est ipsa
practica, ita similiter Astronomia est practica astronomiae."

In the fourth division music is considered. This includes -
not merely sound but gesture. Audible music is considered
under the two heads of vocal and instrumental. In the vocal
division every branch of elocution is included. Finally, the
effect of music on the temper and health both of men and of
animals should be systematically studied.

Abstraction is the subject of the fifth division. First we
have the abstraction common to all science, since science
deals with universals, not with particulars. There is then the
abstraction of a first cause from secondary causes and of spirit
from body, which the metaphysician deals with. Mathematical
abstraction has to do with the study of quantity apart from
the substance to which it belongs: apart from all natural
changes such as growth, diminution or change of place.

This first part closes with an explanation of the difference
between axioms, postulates, and definitions.

The second part begins with the study of whole numbers
and fractions: passing from this to the subject of arithmetical,
geometrical, and harmonic ratio, and to the question of pro-
portion generally. Continuous and discontinuous proportion
are considered ; and Euclid's definition of proportion is care-
fully considered.

! To each of these two mathematicians Cantor devotes a full chapter. Cf.
Gesch. der Math. vol. ii. pp. 3-79.

ASTROLOGY. lix

Here the portion of the work contained in the Sloane MSS.
ends. We find it continued, however, in a somewhat frag-
mentary way in the Bodleian Digby MSS. No. 76. The
author proceeds to the consideration of geometrical truths,
professing his intention to select those which were of para-
mount importance, since it was obvious that the number of
possible problems in geometry was infinite.

‘Illae (veritates)! he says, ‘sunt eligendae quae possunt
vocari radices et elementa respectu ramorum et foliorum,
quorum fructus vadit in infinitum.’ Proof is given in this
part of the work that Bacon was acquainted with the geometry
of Apollonius as well as with that of Euclid. After defining
the cone (‘ pyramis rotunda’) he mentions its three sections,
presenting curves of a different form from the circle, one of
which was of use in the construction of mirrors capable of
rendering rays convergent to a point. He promises to deal
with these curves later in the work.

Of the whole, so far as the fragment of his mathematical
work preserved to us enables us to judge, it would seem that
Bacon had made himself acquainted with the highest mathe-
matics of his time; though no evidence is forthcoming to show
that he contributed personally to the advance of the science,
otherwise than by strongly insisting on its culture, and by
pointing out new fields for its practical application, in the
better government of the Church, and in the development of
industry. His interest, like that of Galileo, lay in applied
rather than in abstract mathematics. Whether the study of
equations as carried on by the Italian algebraists of the
fourteenth and fifteenth centuries would have interested
him is doubtful. But he would have eagerly welcomed the
invention of logarithms, as facilitating the construction of
astronomical tables.

VI. BACON'S ASTROLOGY.

The transition from Mathematics to Physics supplies the
best opportunity for a few remarks on the subject of Bacon's
Astrology, on which something is also said in a note to vol. i.
p. 269. Bacon dwelt frequently and emphatically on the

ix INTRODUCTION. '

unity and the correlation of the sciences. In passing from
Mathematics to the direct study of Nature, he found a con-
necting link in the imaginary science of Astrology, which
he studied zealously. That the fixed stars and the planets
exercised a powerful influence on all earthly things and not
least on man; that the careful observation of their position :
at the moment of birth would do much to reveal the hidden
springs of character, and make it possible to form a forecast
of the ensuing life, that the influences radiating from them
acted with greater or less potency according as the course of
the rays was perpendicular or oblique, and that in this way
an explanation could be given of climate, temperament, and
of the thousand complex chances and changes of mortal life,
was a belief firmly held by Bacon, and it operated powerfully
over his whole view of mans position in the world. He has
been much reproached for holding it ; and it has been supposed
to be an explanation, if not an excuse, for the disastrous
repression exercised over him by his superiors, and for the
popular discredit attaching to his name. ]

But this would be an entire misconception of the beliefs
current in Bacon's time. The influence of the stars over
human life was a belief almost universally held by all instructed
men from the thirteenth to the sixteenth century; and
abundant traces of it are,visible throughout the seventeenth,
not to speak of still later times. The Divina Commedia is full
ofit. Beatrice, admonishing Dante at her first meeting with
him in the Earthly Paradise, speaks of the rich endowment
with which he came into the world,

‘Per ovra delle ruote magne,
Che drizzan ciascun seme ad alcun fine,
Secondo che le stelle son compagne !'

! Purgat, xxx. 109-11. Even more significant is the passage, Parad. viii.
127-32 :—

‘La circular natura, ch’ @ suggello
Alla cera mortal, fa ben sua arte
Ma non distingue l'un dall' altro ostello.

Quinci addivien ch' Esaü si diparte
Per seme da Jacób, e vien Quirino
Da si vil padre che si rende a Marte.'

ASTROLOGY. Ixi:

By Dante's master in theology, Thomas Aquinas, the reality
of astrological influences is laid down with perfect clearness
in S. 7. Pars Prima (quaest. 115, art. 3 and 4). In the
first instance the question is put whether heavenly bodies are
a cause of things that take place in terrestrial bodies. This
after the usual statement of reasons, for and against, is answered
emphatically in the affirmative. ‘Celestial bodies causally
affect all the varied motions of terrestrial bodies!.' The second
question is, Are heavenly bodies a cause of human actions?
The authoritative conclusion here is, Directly speaking, they
are not, but indirectly they are”. ‘Indirectly, and by accident,
impressions of celestial bodies may reach intellect and will,
since both intellect and will receive somewhat from inferior
faculties which are bound up with bodily organs. A dis-
tinction is, however, to be made between will and intellect.
The intellect is of necessity affected by the lower apprehen-
sive faculties of imagination. thought, or memory, and when
these are stirred, the intellect is stirred likewise. But the
will does not of necessity follow the promptings of the
lower appetite. For although the passions of anger and
desire have a certain power of moving the will; yet it
remains in the power of will to follow passion or to repu-
diate it. Thus the influence of celestial bodies, so far as
it produces change in the lower faculties, has to do rather
with intellect than with will; and will is the proximate cause
of human action.’

Finally Aquinas remarks that ‘most men follow passions,
which are motions of the sensitive appetite; and with these
heavenly bodies may have to do. For few are the wise who
withstand such passions. And thus it is that astrologers
may often foretell truly; but for the most part rather in
general than in special, since nothing hinders any one man

! The words are: ‘Corpora caelestia cum tantum mobilia sint secundum
lationis motum, causa sunt omnium eorum quae in his corporibus inferioribus
variis motibus aguntur."

2 ‘Cum intellectus et voluntas, quae humanorum actuum principia sunt,
corporeis organis vires alligatae minime sint; non possunt corpora ipsa caelestia

humanorum actuum causae directe esse, sed indirecte, agendo per se in corpora
quac ad utriusque potentiae opera conducunt."

Ixii INTRODUCTION

from withstanding passions by free will. Hence, astrologers
themselves say that the wise man governs the stars, in so far,
namely, as he governs his own passions. Further on, in
Prima Secundae, quaest. ix. art, 5, this subject is again dis-
cussed. The question asked is, ‘Can will be influenced by
a heavenly body?’ The conclusion is, ‘Since will is a faculty
absolutely immaterial and incorporeal, it can only be in-
fluenced by heavenly bodies indirectly. And in his comment
Aquinas observes, ‘So far as will is influenced by any out-
ward object, it can evidently be influenced by heavenly
bodies: since all external bodies, which, when presented to
the senses, move will, and even the very organs of sensitive
faculties, are influenced by the motions of the heavens. But
there is no direct action of heavenly bodies upon the will.
For the will, as Aristotle says (De Anima, lib. iii) resides in
reason; and reason is a power of the soul not bound to
a bodily organ... .. On the other hand. he adds, * Sensitive
appetite is the function (actus) of a bodily organ. Wherefore
nothing hinders impressions of celestial bodies from rendering
some men apt to anger, or to lust, or to some passion of this
kind; and thus from natural complexion many men follow
passions, and wise men alone withstand them. And so, in
a general way, are verified those things that are foretold of
the actions of men in accordance with the consideration
of heavenly bodies.’

Now the view taken by Bacon coincides precisely with that
of Aquinas. Confusion, he says (Opus Majus, p. 150), had
arisen in the matter in consequence of the equivocal meaning
of the word, Mathematics, sometimes held to be derived from
pavtixn, sometimes from pdOnots. The characteristic, he says,
of false mathematic, was to assert that through the powers of
the constellations all things took place of necessity. No place
was left for contingent matter, for judgement, for free will.
Such a view of nature was condemned not only by theologians
but by philosophers. Aristotle and Plato, Cicero and Pliny.
Avicenna and Albumazar were unanimous in holding that
free will remained uncoerced by the motions of heavenly
bodies. ‘True mathematicians and astrologers lay down no

ASTROLOGY. Ixiii

necessity, no infallibility, in their predictions of contingent
events. . . . What they do is to consider the way in which the
body may be affected by celestial things, and the way in
which the body may act upon the mind in private affairs or
public, always without prejudice to the freedom of the will.
For although the reasonable soul is not coerced to any future
actions, yet it may be strongly stirred and induced, so as
freely to will those things towards which celestial force may
incline it; as we see men in community taking counsel, or
through fear or love, and feelings of this kind, freely choosing
what before they would not, though not forced to do so; like
the sailor who to save himself from drowning throws precious
merchandise into the sea. We see, indeed, that impressions
from things on earth may so act upon sense as to stir men to
will what before they had no care for, so that they take no
account of death or disgrace or fear, if only they accomplish
their desire, as with those who see and hear the onset of their
enemies, and are borne onwards at all hazards to avenge them-
selves. Far more potent than the impressions of earthly
things are those of the heavenly upon bodily organs, which
being strongly moved, men are led on to actions of which they
had not thought before, yet always with full reservation of
the freedom of the will.'

There are perhaps few fictitious creeds for the origin of
which it is so easy to account as for the belief that the position
of the planets.with regard to one another and to the constella-
tions of the zodiac were of significance to man and his
environment. With populations whose religion was astrolatric
rather than polytheistic, taking shape in worship of the heavens
rather in that of invisible but manlike gods, astrology would
be an easy and almost inevitable deduction from their creed.
The immense majority of the Asiatic population, whether
Semitic or Mongol, were, unlike the Indians and the Greeks,
not polytheists but astrolaters. When the Arabs received
and enlarged their inheritance of Ptolemaic astronomy, their
astrologic beliefs, far from being dissipated, were strongly
confirmed. Of the seven wanderers of the sky, the influence
on earthly things of two, the Sun and the Moon, was too

Ixiv INTRODUCTION.

obvious to be disputed. The one swayed the tides, the other
brought summer and winter. Why should the rest be sup-
posed inert? Was it not probable that the successive and
infinitely varying connexion of each of them, singly or com-
bined. with the fixed groups of the starry vault, indicated
changes or tendencies to change here below which careful and
prolonged study might at last interpret?

So it was that with the growth of knowledge, and with
increasing strength of the conviction that all nature was under
the dominion of fixed laws, astrology came to be regarded as
the key to the understanding of all that was specially con-
tingent and variable in man's environment ; the phenomena
of temperament and of disease; the revolutions of states, and
even of religions. The boundary of its lawful application was
drawn differently by different thinkers. Apart from charlatans
and miracle-mongers, few stretched it farther than Bacon.
But by him, as strictly as by Aquinas, the saving clause, ‘salva
arbitrii libertate, was always added. Outside influences
might suggest motive and kindle passion; they could never
trench upon the sacred domain of the freedom of the will !.

What is strange is not that the belief in the convergence of

! Comte has pointed out | Ph:losophie Positive, vol. iii. pp. 273—280, ed. Littré)
that in order to appreciate astrology with any approach to justice, it is needful
to keep steadily in view the very real connexion between the sciences of
astronomy and biology. On the relations of mass and of distance between
the sun and earth, involving as they do the familiar facts of weight, equilibrium
of fluids, temperature, life on our planet is obviously dependent. If we consider
the period and velocity of the earth's rotation, the degree of ellipticity of her
orbit, the angle at which the axis of rotation is inclined to the plane of the orbit,
the same truth is impressed upon us even more strongly. *In the early stages
ofthe human mind these connecting links between astronomy and biology were
studied from a very different point of view ; but at least they were studied and not
left out of sight, as is the common tendency in our own time under the restricting
influence of a nascent and incomplete positivism. Beneath the chimerical belieís
of the old philosophy in the physiological influence of the stars, therelay a strong
though confused recognition of the truth that the facts of life were in some way
dependent on the solar system. Like all primitive inspirations of man's intelli-
gence this feeling needed rectification by positive science, but not destruction ;
though unhappily in science, as in politics, it is often hard to reorganize without
some brief period of overthrow.’ This was written in 1836. Much has been
done since by Mr. Spencer and others to familiarize the European mind with

the dependence of life on its astronomical conditions. But the injustice in our
historical judgement of mediaeval astrology still remains.

PROPAGATION OF FORCE Ixv

stellar influences towards the central point of a closed universe
should have arisen, but that it should so long and so per-
sistently have survived the discovery that the universe was not
closed but boundless. That Francis Bacon, who rejected or
doubted the Copernican theory, should have retained his belief
in astrology is not surprising. But we should have expected
that with men like Kepler and Campanella, it would have
vanished like the morning mist. Yet it was not so.

VII. THE PROPAGATION OF FORCE.

Bacon's views of stellar influences must be taken in con-
nexion with his speculations as to the transmissions of force
through space. These are set forth briefly in the second and
third Distinctions of the fourth part of the Opus Majus ; and
more in detail in the special treatise De Multiplicatione
Specierum, which in this edition is given as an appendix. _

‘Species’ is the word chosen by Bacon to express the
emanation of force which he conceives to be continually pro-
ceeding from every bodily object in all directions. Body of
every kind is endowed with force which indeed is identical
with its substance or essence. The first result of this force,
resembling it in character, is its species, otherwise called
likeness, or image, or intention. or impression — In other
words, body is a centre of activity or force radiating in every
direction. Species is the first result of this force, the ray
proceeding from the body. Tracing back this doctrine to its
origin, we find it expounded in the fourth book of Lucretius,
in Diogenes Laertius' account of the system of Epicurus, and
in the traces that remain to us of older philosophers, notably
of Democritus. Aristotle, in his short treatise on Divination
by dreams, alludes to the theory of Democritus that ciéwa.
and axdpporat were continually emitted from objects which in
the stillness of the night were capable of affecting the sleeper.
By Epicurus, in his letter to Herodotus quoted in his biography
by Diogenes Laertius, the theory is more fully detailed. * There
are, moulds, he says, 'corresponding to all solid bodies pre-
serving the same shape and arrangement as these bodies

VOL. I. e

Ixvi INTRODUCTION.

which emanate from them, and are conveyed through space
with incredible velocity. These may be called images. "Their
flow from bodies is continuous so that they are not separately
perceived.’ The description of them by Lucretius is more
definite and better known. ‘Pictures of things and thin
shapes are emitted from things off their surface; these are
like films or may each be named a rind, because each image
bears an appearance and form like to the thing, whatever it is,
from whose body it is shed and wanders forth’ (Lucretius
iv. 40, Monro's translation). And again, ‘Many idols are be-
gotten in a short time, so that the birth of such things is with
good reason named a rapid one. And as the sun must send
forth many rays of light in a short time in order that all things
may be continually filled with it, so also for a like reason
there must be carried away from things in a moment of time
idols of things, many in number, in many ways, in all directions
round. ... As soon as ever the brightness of water is set down
in the open air, if the heaven is starry, in a moment the clear
radiant constellations of aether imaged in the water correspond
to those in the heaven. Now do you see in what a moment
of time an image drops down from the borders of heaven to
the borders of earth ' (Lucretius iv. 159 and 211). He goes on
to explain that not the sense of sight only, but all the senses,
are affected by these emanations.

But it would be an entire misapprehension of Bacon's views
as to the propagation of force to identify them with the crude
physics of Epicurus.

In the first place, Bacon wholly rejects the notion that the
species is something emitted from the agent, or acting body
(De Mult. Spec. pp. 432-438). If it were so, the agent would
be weakened and ultimately destroycd by the emission, which
is not the case. Nor again does the agent create the species
out of nothing. Nor does it collect the species from sur-
rounding space and send it on into the body on which action
takes place—the patient. Nor, as some have supposed, does
the agent impress the patient as with a seal. |

What happens is that the agent stimulates the potential
activity of the matter of the patient. The species is generated

PROPAGATION OF FORCE. Ixvii

out of the matter acted on. ‘Fit species de potentia activa
materiae patientis. The agent acts on the first part of the
body of the patient, and stimulates its latent energy to the
generation of the species. That part thus transmuted acts on
the part next succeeding ; and so the action proceeds (De Mult.
, Spec. p. 457).

While the agent acts on the patient, the patient re-acts on
the agent. 'Omne agens physice patitur et transmutatur
insimul dum agit, et omne patiens physice agit’ (De Mult.
Spec. p. 439). Heavenly bodies as they act on one another, so
do they receive emanations of force from terrestrial bodies.
Not that they are so affected by them as to be destroyed,
being incorruptible. Nevertheless there is in this way an
interchange of force between all parts of the universe (p. 448).

The ray, or species, is of corporeal nature ; but this corporeal
nature is not distinct from that of the medium ; it is generated
from the substance of the medium, and is continually re-formed
out of successive portions of the medium occurring in the line
along which the force is propagated (p. 505). If wind is
driving the air transversely to the line of force, this in no way
affects this line. The species is formed and reformed from
particles of the medium presented in the line of propagation,
and from no others.

Finally the propagation of rays occupies time (vol. ii. pp.
67-72 and 525-9), though its velocity is such that the time
occupied in passing through so vast a space as the diameter
of the universe is imperceptible to sense.

It will be seen from the foregoing how wide is the divergence
between Democritean and Baconian physics. Though Bacon
retains the word ‘species’ in his theory, the word has almost
entirely lost the significance attached to it by Lucretius.
We are no longer dealing with the notion that bodies emit
from their surface films or moulds which are transmitted
through space. Like the word ‘ray, which is retained by the
modern physicist who accepts the undulatory theory, ‘ species’
for Bacon has become a mere word to denote the propagation
of force in certain definite directions. Indeed the multiplica-
tion of species as defined by him has much in common with

e 2

Ixviii INTRODUCTION.

the undulatory theory. He formally rejects the contrasted
theory of emission. The species, like the wave, is a motion
or change in successive portions of the aerial or ethereal
medium ; occupying time in its transit: propagated so long
as the medium be homogeneous, in direct lines; liable to
deflection when the medium alters its character.

In Bacon's theory of the radiation of forces two very
important points are to be noted. The first is his clear grasp
of the principle that time was occupied in their transmission.
He discusses, in the passages already cited, the view of Aristotle
and others that the propagation of light differed from that of
sound and odour by being instantaneous. We might admit,
Aristotle had said, that light could pass through short spaces
without our being able to detect any interval of time during
the passage. But when light passes from east to west through
the universe, the space is so vast that if time were occupied
we could not fail to detect it. Bacon’s conception of the
subject is far more scientific. Our inability to perceive minute
intervals of time is no evidence, he said, for their non-existence.
Imperceptible time, he remarks, has many degrees. There
is, first, the interval of time occupied by a single propagation
of force (or, as we should say, undulation) followed by the
interval of rest before the next propagation begins. Take
such a multiple of that interval as would suffice for the whole
distance between the extremities of a diameter of the universe,
and that multiple may still remain below the limits of our
power of perception. It is interesting to compare with this
passage the speculations of the second Bacon on the same
subject (ov. Org. ii. 46). Francis Bacon had formed the
conjecture that the transit of light from the stars occupied
time. But he did not grasp this conjecture with the same
firmness as Roger Bacon, and he follows it up with ingenious
arguments which explain it away.

Radiant force, in Bacon's view, proceeded independently of
man's power to perceive it. Opaque bodies, he observes,
offered resistance to the passage of a luminous ray (De Mult.
Spec. p. 478; see also vol. i. p. 114). But ‘no substance is so
dense as altogether to prevent rays from passing. Matter

OPTICS. Ixix

is common to all things, and thus there is no substance on
which the action: involved in the passage of a ray may not
produce a change. Thus it is that rays of heat and sound
penetrate through the walls of a vessel of gold or brass. It
is said by Boetius that a lynx's eye will pierce through thick
walls. In this case the wall would be permeable to visual
rays. In any case there are many dense bodies which
altogether interfere with the visual and other senses of man,
so that rays cannot pass with such energy as to produce an
effect on human sense, and yet nevertheless rays do really
pass, though without our being aware of it. Recent dis-
coveries have given significance to this remarkable passage ;
which, not merely to his contemporaries but to succeeding
generations, must have seemed in the highest degree fan-
tastical.

VIII. BACON'S OPTICS.

The most striking illustration of laws governing the transit
of force through space was obviously to be looked for in the
science of Optics (Perspectiva). The fifth section of the Opus
Majus, amounting to about one-fifth of the whole, is devoted
to this science ; and much supplemental matter is added in
the treatise De Multiplicatione Specierum. Optics had been
studied by the Greeks to much purpose. The works of Euclid,
Theon, and Ptolemy were translated into Arabic, and were
carefully studied by Arabian men of science, notably by Abà
"Ali al Hasan ibn al Hasan ibn Alhaitam, better known to
Occidentals under the name of Alhazen. Their principal
results are embodied in Bacon's work.

Euclid, or the author passing under his name!, was aware
that light proceeded in straight lines, and that visual rays were
reflected from plane mirrors in such a way that the angles

! Heiberg, in his recent edition of Euclid's Optica | forming the seventh volume
of the complete edition of Euclid, edited by Heiberg and Menge), remarks
p. xxviii of Prolegomena), ‘Optica qualia hic e codice Vindobonensi maxime
primo loco repetivimus, Euclidis esse, non est cur dubitemus, Sed cum recen-
tiores tantum extent codices, mirum non est locos nonnullos tam corruptos
esse ut verba Euclidis restitui nequeant.'

a a —

Ixx INTRODUCTION.

made with the surface on each side were equal. He con-
ceived the assemblage of rays as a cone having its apex in the
eye, and its base in the boundary of the object seen : that the
apparent magnitude of the object depended on the magnitude
of the angle of the cone. Thence followed the ordinary prin-
ciples of perspective, as that of equal magnitudes at unequal
distances ; those nearer to the eye appeared larger, and so on.
In the Catopirica (attributed to Euclid, but probably due to
Theon), from the equality of the angles of reflexion and inci-
dence in plane mirrors was deduced the convergence of rays
falling on a concave speculum.

Ptolemy ! carried the science much further than Euclid. To
the study of reflected light he added that of refraction. The
chief interest of his work lies in the application to the subject
of the experimental method, an instance of it unique, if we ex-
cept the Pythagorean experiments in acoustics, in the history
of Greek science. Using an extremely simple but ingenious
apparatus, he discovered, not merely that the luminous
ray in passing from one medium to another was deflected,
but, within certain limits, he ascertained the amount of de-
flexion and its dependence on two distinct factors, the angle
of incidence, and the nature of the two media concerned.
Ptolemy distinctly describes and explains the error introduced
by refraction into astronomical observations. The fact that
in his great astronomical treatise there is no mention of refrac-
tion had led to the conclusion that the A/magest and the
Optics must be attributed to distinct authors. The Opts,
however, may be a later work. We know it only from a trans-
lation from the Arabic into Latin, made in the twelfth century ;
it has been recently edited by Gilberto Govi, of Turin. The
researches of Euclid, Ptolemy, and others on Optics, engaged
the attention of the Arabian schools from an early period.

! On Ptolemy's Optics there is a very interesting chapter in Delambre's
Astronomie Ancienne, vol. ii. pp. 411-430, ed. 1817. (See also a note on p. li of
Preface to vol. i which modifies some of his conclusions.) All our knowledge
of Ptolemy's optical work comes from an imperfect Latin translation from the
Arabic made in the twelfth century by Admiral Eugenius of Sicily. There are
late MSS. of this work in Paris and in the Bodleian Library. But Govi's
recent edition is from a much older MS. in the Ambrosian Library of Milan.

OPTICS. Ixxi

Their knowledge of the subject is summed up in the work of
Alhazen, whose remarkable work, 7hesaurus Opticae, written
perhaps in the eleventh century, was translated in the twelfth
into Latin ; as Jourdain thinks, by Gerard of Cremona, the
translator of Ptolemy's A/magest. Alhazen was the writer on
whom Roger Bacon principally relied ; though he makes fre-
quent use of the optical treatises of Euclid, Ptolemy, Tideus,
and Alkindi.

Alhazen's work is copious in the extreme ; in some parts
extremely tedious. Its value as a document in the history of
science is, however, very great. It consists of seven books.
The first begins with a brief exposition of the nature of light
and colour, and proceeds to explain the anatomy of the organs
of vision. The second deals with the function of vision and
with the physiology of perception. The third, with imper-
fections and illusions incident to vision. The fourth, fifth. and
sixth are devoted to the subject of reflexion. Seven kinds of
mirrors are discussed, plane, spherical, cylindrical, and conical ;
the convex and concave forms of the three last being separately
considered. The multiplication and position of the ‘images
formed is treated with inordinate length, but with such
geometrical skill as to secure for him an abiding place in the
history of pure, no less than of applied mathematics. ‘ His
investigation, says Cantor (Geschichte der Mathemattk, vol. i.
p.677), ‘of the problem : In a spherical concave mirror, to find
the point from which an object of given position will be
reflected to an eye of given position, is one which, analytically
handled, leads to an equation of the fourth degree. Alhazen
solved it, as Govi remarks (Ptol. Opé. p. xix), by the use of
an hyperbola.

The seventh book of the 7hesaurus Opticae deals with re-
fraction. A very elaborate description is given of the instru-
ment for measuring it, part of which Bacon quotes. Moreover,
an attempt is made to explain the cause of refraction which is
substantially identical with Bacon's, as may be seen by com-
parison of Alhazen vii. 8 with De Mult. Specierum, Part II.
cap. 3. The apparatus for measuring the angle of refraction,
which was more accurately designed than that of Ptolemy,

Ixxii INTRODUCTION.

enabled a series of observations to be made of the angle of
refraction, in different media, on which the true law of the
variations of refraction at different angles and in different
media might ultimately be based. — Vitello!, Bacon's contem-
porary, drew up a table of refractions, as Ptolemy had done
before him, for the three media of air, water, and glass. It
was soon seen that the angle of refraction did not vary in
accordance with the angle of incidence. But more than three
centuries were to pass before the discovery of the lew of
sines, that is to say, the law that the ratio of the sines
of the angles of incidence and refraction is constant for
refraction in the same medium, was effected by Snell and
Descartes.

It might seem, at first sight, that the optical work of Bacon
was little more than an abridgement of that of Alhazen?. But
this view would render Bacon but scanty justice. Problems
of great importance were indicated by him which Alhazen had
entirely neglected. In considering the point on the axis of
a spherical concave mirror to which rays were reflected, Bacon
remarks that this point would be different for rays reflected
from each concentric circle traced round the centre of the
mirror. Such a mirror failed therefore to produce complete

! Of Vitello, or Witelo, very little is known. He describes himself in his
dedication to William of Morbeta (identified by Cantor as William of
Moerbeke) as filius Thuringorum et Polonorum. In lib. x. 74 of his work he
speaks of Poland as his country, and other passages (x. 42 and 67) show
thaf he travelled in Italy. His work on Optics was edited with great care, and
with many emendations, by Risner, and published at Bale in 1572 in the
same volume that contained Risner's edition of Alhazen. Indeed, it may
be described with little exaggeration as a revised edition of Alhazen's work ;
with many additions certainly from other authors, but with none of those
acknowledgements of his principal teacher of which Bacon's Perspectiva is full.
Vitello's tables of refraction have excited much admiration. They prove, how:
ever, on careful examination to be an almost exact repetition of those of Ptolemy.
Whether Bacon and Vitello ever came into contact there is no evidence
to show. Bacon was always ready to mention the sources of his knowledge.
Not so Vitello. If he borrowed from Bacon, he would not have said so.

* It must be owned that where Bacon differed from Alhazen, the advantage
was not always on his side. Alhazen contended vigordusly against the view of
the older oculists that vision took place by visual force issuing from the eye,
maintaining that the ray proceeded to the eye from the object. Bacon (vol. ii.
pP. 49 53) makes a fruitless attempt to conciliate these opposite views.

OPTICS. Ixxiii

convergence of rays. For such convergence the curvature
must be other than spherical, it must be that produced by the
rotation of a conic section.

Bacon, moreover, is distinguished from the Arabian optical
writers, and from other investigators of his own time, by his
sedulous endeavours to turn the discovery of the laws of re-
flexion and refraction to practical account. Neither in Alhazen
nor in Vitello is there any attempt to construct instruments
for the purpose of increasing the power of vision. With Bacon
this object was always held steadily in view. Of the simple
microscope he had a perfectly clear conception. His scientific
imagination played freely with the possibilities of bringing
distant objects near, and of indefinitely magnifying minute
objects, by giving suitable directions to refracted rays, and by
the use of appropriate media. It would be, however, an entire
exaggeration of his achievements to speak of him as the
inventor of the telescope. No evidence is forthcoming for his
having effected the simple combination of two convex lenses,
or of a convex with a concave lens, on which the power of
telescopic vision depends. All that can be claimed for him
' is that he was the first definitely and explicitly to bring the
problem forward, leaving it for after generations to solve. In
truth, his conception of an optical image, as constructed by the
assemblage of foci of rays proceeding from each point of the
object magnified, though in the main correct, was not always
clearly grasped. Of the distinction between virtual and real
images, his notion was entirely in default.

Nor, again, had Bacon a clear conception of the conditions of
distinct vision. He examined to much better purpose than
Alhazen had done the structures of the eye ; and he was aware
of the refraction produced by the curved surface of the cornea,
and by the doubly convex crystalline lens. But what he
failed to grasp ! was the necessity of a clear image of the object
defined on the retina; that image being produced by the
focussing on the retina of rays proceeding from each point of
the object. The phenomena of accommodation, produced by
the action of the ciliary muscle, which, by altering the curva-

1 See vol. ii. p. 159.

Ixxiv INTRODUCTION.

ture of the lens, enables rays from near objects to be accurately
focussed, were unknown to him. But this is only to say that
he had not anticipated the physiological knowledge of the
nineteenth century.

It must always be borne in mind that, in Bacon's view, the
radiation of light through space did not stand alone. It was
a type of other radiant activities, such as colour (then supposed
to be distinct from, though dependent on, light), heat, sound,
and odour. (With regard to sound, however, certain reserves
were made.) It is interesting to note Bacon's handling of an
important problem, not to be solved but by a more potent
calculus than any in his possession, how these various actions,
crossing one another’s paths in their passage through space,
retained their distinctness !.

IX. BACON'S ALCHEMY.

It will be remembered that among the various branches of
knowledge regarded by Bacon as falling under the head
of Physics, was Barology (Scientia ponderum). The treatise
of Jordanus Nemorarius, De Ponderibus, to which reference is
made, vol. i. p. 169, had perhaps suggested the treatment of
the phenomena of gravity as a distinct branch of science.
No treatise by Bacon upon this subject, so far as I am aware,
is extant; and the few remarks in the fourth section of the
Opus Majus (pp. 167-174) contain all that we know of his
speculations on the theory of gravitation.

Nor is anything known to us of the way in which Bacon
treated, if indeed he ever attempted, the science which he
called * Agricultura, which, as we have seen, was intended to
include the study of living bodies, vegetable and animal.
But the case is otherwise with the science regarded by him
as preparatory to the study of life,‘ Alkimia Speculativa. On
the subject of Alchemy, very little is said in the Opus Majus ;
and the omission was supplied in the provisional way, which
alone was possible under the hurry of compilation to satisfy
Pope Clement's orders, by the Opus Minus, the first of the

! See note on vol. ii. p. 46.

ALCHEM Y. Ixxv

two appendages to that work. Unfortunately the only text
of the Opus Minus which we possess has come down to us, not
merely incomplete, but in so corrupt a state as to render it
often very difficult to decipher Bacon's meaning. Enough
remains, however, to show the large and comprehensive spirit
in which Bacon regarded the subject.

The contempt expressed in much modern writing for
mediaeval alchemy might be well retorted on its authors.
Admit that some prosecutors of the occult art were deceivers
as well as deceived, and that others were impelled by wild
hopes of gain, has the pursuit of physical science in modern
times been wholly free from similar taints? Electricity
applied to medicine has been a fertile field for impostors.
And will any one maintain that the pursuit of chemistry has
not been stimulated by hopes of industrial profit? Yet such
things are not allowed to cast a shade on the names of
a Lavoisier, a Dalton, or a Faraday. Alchemy was chemistry
in its prescientific period. Under the guidance of hypotheses
which were not nearly so wild or crude as they at first appear,
it attacked, like the true science which gradually grew from
it, the important problem of the transmutation of matter by
artificial agencies. It took for granted that metals were
compound bodies, the elements of which might be separated
and recomposed. This was no unreasonable supposition.
Indeed, until modern spectrology had shown that the vapour of
many metals existed undecomposed in the intense heat of the
sun’s atmosphere, there was no adequate reason for abandon-
ing the attempt to decompose them. It would be hard to
find in alchemy any conjecture more baseless than that of
Phlogiston, the subtle spirit of flame, the loss of which by
combustion made the oxide heavier than the metal. Yet
Priestley accepted this hypothesis, and a Lavoisier was needed
to destroy it.

Alkimia, as conceived by Bacon, fell into two great divi-
sions—speculative and operative. Under the latter was
included the metallurgy of the gold-seekers, and generally
all the practical and industrial processes pursued, with more
or less wisdom, by men who had a definite purpose in view—

Ixxvi INTRODUCTION.

the transmutation of metals, the discovery of the philosopher's
egg, or the elixir vitae. But Bacon was one of the few who
saw that the empirical proceedings of the honest mystics or
scheming charlatans, who were toiling at their royal road to
wealth or longevity, covered speculations of a far deeper kind ;
the study of the transition of matter from the four Aristo-
telian elements, through increasing degrees of complexity, up
to the highly compound forms exhibited by organized bodies.
The * Alkimia Speculativa ' of Bacon was, indeed, not alchemy
at all as commonly understood: it was nothing less than
chemistry. ‘Alkimia Speculativa, he says, in the twelfth
chapter of the Opus Tertium, ‘treats of the generation of things
from their elements, and of all inanimate things—as of the
elements and liquids (Aumores) simple and compound ; common
stones, gems, and marbles; gold, and other metals; sulphur,
salts, pigments, lapis lazuli, minium, and other colours; oils,
bitumen, and very many other things—of which we find nothing
in the books of Aristotle; nor are the natural philosophers or
any of the Latins acquainted with these things. And being
ignorant of them, they can know nothing of what follows in
physics, that is, of the generation of animate things—as
vegetables, animals, and man—because knowing not what is
prior, they must remain ignorant of what is posterior. For
the generation of men, and of brutes, and of plants, is from
elemental and liquid substances, and is of like manner with the
generation of inanimate things. Wherefore, through ignorance
of this science, neither can natural philosophy, commonly so-
called, be known, nor the theory, and therefore neither the
practice, of medicine ; not merely because natural philosophy
and theoretical medicine are necessary for the practice, but
because all simple medicines are derived from inanimate
things by this science.’

Of such fundamental truths of chemical science—as the
composition of air and water, the theory of combustion, and
the chemistry of carbon—he, like his contemporaries, was
ignorant; but the ignorance was shared by the second Bacon
with the first, and was not to be dissipated for five centuries.
All that could be done in the meanwhile was to collect empi-

. — a ————— — b m

ALCHEMY. Ixxvii

rical information as to a few metals and their oxides, some of
the principal alkalis, acids, and salts. On all these things the
Arab investigators, from Geber downwards, had accumulated
a considerable mass of material It is not easy to define
the results of each inquirer, owing to the prevalent habit of
describing their procedure and results in mystical language.
Self-defence against charges of magic and imposture was
probably their motive. And that the danger was real, the
history of Bacon's life suffices to show. His efforts to refute
the charge of magic were incessant. In his treatise, De Secretis
Operibus Artis et Naturae et de nullitate Magiae, he describes
in detail the various procedures of the magician, sleight of
hand, ventriloquism, pretended movements of inanimate
things in dim light, the aid of accomplices, utterance of mys-
terious formulae, invocation of spirits. We gather from the
description that the lapse of six centuries has done little to
change the character of charlatanism. But Bacon was aware
that the charlatan was often in possession of valuable secrets.
‘Many books are held to be magical, he says, ‘which are not
really so, but which contain important truths; which are of
this kind, and which are not, it is for the experience of the
wise man to decide. If he find in them any result of natural
or artificial forces (opus naturae vel artis), let him accept this;
otherwise let him reject them as worthless.’ Bacon carefully
_ guards himself against denial of the mystical force of words
uttered under solemn conditions, as in the daily miracle of
the Eucharist, or in the solemn invocations that protected
the innocent when exposed to judicial ordeal. Such powers
might be exerted for good as for evil; and the unlawful use
of them was strictly and severely to be condemned.

But to whatever extent Bacon may have shared the illusions
of his time with regard to the practical operations of alchemy,
it is a striking proof of his scientific discernment that under
the head of Speculative Alchemy he should have formed a
clear, though distant survey, of chemical science as the inter-
mediate link between Aristotelian Physics and the science
of living bodies. As Physics followed on Mathematics so did
Chemistry, in Bacon’s arrangement of the sciences, succeed

Ixxviii INTRODUCTION.

Physics. After chemistry came the study of living bodies,
on which Bacon, while assigning to this science its natural
place in the series, has said little or nothing. But on the
study of plants and animals was based, under the name of
Medicina, the study of the physical structure and functions
of man. Here Bacon had for his guides, not Galen indeed,
to whom his references are few, but Avicenna, Haly, and
a host of Arabian professors of medical art, to whom Galen
had supplied a very substantial foundation of anatomical and
physiological knowledge. Bacon's short treatise, to which
reference is occasionally made in the Opus Majws, De re-
lardandis senectutis accidentibus, will sufficiently illustrate
his views on this branch of science.

X. EXPERIMENTAL SCIENCE.

Last among the series of the natural sciences comes that
which Bacon denotes as ‘Scientia Experimentalis.’ The
sample of it, for it can hardly be regarded as more than
a sample, given in the sixth section of the Opus Majus
indicates that it was connected in Bacon’s mind with no special
department of research, but was a general method used for
the double purpose of controlling results already reached by
mathematical procedure, and of stimulating new researches in
fields not as yet opened to inquiry. .

In some respects this is the most original part of his work.
Not that experiment was a new thing. Experiments without
number had been made by man from the time of his first
appearance on the planet. The Greeks towards the end of
their marvellous scientific career had begun to use experiment
in their investigations of natural truth. Galen had applied it
in his researches into the nervous system ; Ptolemy had arrived
by its means at his remarkable discovery of the refraction of
light. The Arab astronomers, far more skilful mechanicians
than the Greeks, had constructed extremely elaborate apparatus
for the same purpose, and also to verify the equality of the
angles of incidence and reflection. But no one before Bacon
had abstracted the method of experiment from the concrete

EXPERIMENTAL METHOD. Ixxix

problem, and had seen its bearing and importance as a uni-
versal method of research. -Implicitly men of science had
begun to recognize the value of experiment. What Bacon
did was to make the recognition explicit. Experiment took
its place as a distinct department of philosophy.

What makes this result peculiarly remarkable is that it was
reached by a thinker who was so profoundly penetrated by
the mathematical spirit. In this matter Roger Bacon compares
favourably with his illustrious namesake of the seventeenth
. century, who wholly failed to appreciate the import of mathe-
matical method. He rises to the level of one greater than
either—the author of the Dzscours sur la Méthode. For
Descartes as for Roger Bacon, mathematics was c/avis
sctentiarum, the key to the temple of science. But it was
held by both alike that experiment was needed to carry out
the researches which mathematical deduction had suggested ;
and that, as each science grew, the share taken by experiment
in its progress was to become more and more predominant.

XI. MORAL PHILOSOPHY.

Last in order, both in the Opus Majus and in the Scriptum
Principale, comes the science the study of which is the key-
stone and crown of the whole work—the science of life and
conduct. All the other sciences lead up to this. Their con-
clusions form its point of departure.

The analysis which has been given of this, as of other parts
of the work, renders it unnecessary to cover the ground a
second time. But a few remarks may be made on its salient
features. In the first book, which treats of man's relation to God,
Bacon follows the procedure common to Aquinas, indeed to most
of the schoolmen, of pushing metaphysical reasoning as far as
it can be made to go in support of the articles of the Catholic
faith. "Theology, says Aquinas (.S. 7. Pars I. Quaest. i. art. 5),
uses other sciences as her handmaids and assistants. Man is
more easily led on to things above reason, if he begins with
things which reason can demonstrate. It is true that unassisted
reason is incompetent to discover and demonstrate the doctrine

Ixxx INTRODUCTION.

of the Trinity. ‘Impossibile est, he says (Quaest. xxxii.
art. 1), ‘per rationem naturalem ad cognitionem Trinitatis
divinarum personarum pervenire. But he goes on to explain
that there are two modes of employing reason. One is to
discover and prove a principle: as in physics we prove the
uniformity of the motion of the heavens. The second mode
is, when the principle is admitted, to show that certain observed
effects are consistent with and follow from it. So, for instance,
assuming the reality of our hypotheses as to eccentrics and
epicycles, we can show that the movements of the planets
take place in accordance with these hypotheses. It is this
latter form of reasoning that we use in reference to the
Trinity. * Trinitate posita, congruunt hujusmodi rationes.'
We find analogies with this doctrine when we consider what
passes in our own minds. ‘Ipse conceptus cordis de ratione
sua habet quod ab alio procedat, scilicet a notitia concipientis '
(Quaest. xxxiv. art. 1). 'Quanto aliquid magis intelligitur,
tanto conceptio intellectualis est magis intima intelligenti et
magis unum... unde cum divinum intelligere sit in fine per-
fectionis. .. necesse est quod Verbum divinum sit perfecte
unum cum eo a quo procedit, absque omni diversitate" (Quaest.
xxvii. art. I). Similarly (art. 3), the procession of the Third
Person is likened to the operation of the will which we call in
human beings love. ‘Processio Verbi attenditur secundum
actionem intelligibilem. Secundum autem operationem volun-
tatis invenitur in nobis quaedam alia processio, scilicet processio
amoris, secundum quam amatum est in amante, sicut per
conceptionem verbi res dicta vel intellecta est in intelligente.
Unde et, praeter processionem Verbi, ponitur alia processio in
divinis, quae est processio amoris !.'

Bacon, as we might expect, was not less eager to find the
mysteries of revelation foreshadowed by human reason.
Holding, as he has fully explained in the second part of the

1 It is perhaps hardly necessary to refer in this connexion to Hampden's
lectures on The Scholastic Philosophy considered in tts relation to Christian
Theology. Compare p. 8r (second edition), ‘The object of the Scholastic
Theology was to detect and draw forth from the Scripture, by aid of the subtle
analysis of the philosophy of Aristotle, the mystical truths of God on which
the Scripture Revelation was conceived to be founded.’

MORAL PHILOSOPHY. Ixxxi

Opus Majus, that the rise and progress of Greek philosophy
was no less a part of divine providence than the succession of
the priests and prophets of Judaea, he found without surprise
that Aristotle, Plato, Porphyry and others had apprehended,
more or less dimly, some of the fundamental truths of Christian
theology ; among them being the Trinity, the Incarnation, the
existence of angels and the resurrection of the body. Moral
philosophy, as Bacon conceived it, was in every respect con-
current with theology. ‘ De iisdem negotiatur quibus theologia,
licet alio modo.’ It is perhaps more surprising that he should
have gathered these truths not merely from Greek and pre-
Christian writers, but from the great Mahommedan teachers;
such as Albumazar, Ávicenna, and Algazel. Some of thé
most remarkable passages in the first part of his moral
philosophy are quotations from Avicenna. More than once
he refers to the passage in which Avicenna, speaking of future
life in the unseen world, observes: Our present relation to
that life is like that of the deaf man who never listened to the
delights of harmony, though he never doubted that such
delights existed. Or again: We are like the palsied man to
whom delicious food is offered which yet we cannot taste till
the palsy be healed. Avicenna tells us how the soul's vision
is clogged by bodily impulses, and limited by the obtruding
influences of the visible world ; and he insists on the need of
purging the soul from sin, of concentration of its forces on
invisible things, and of acceptance of revealed truth. We
may well believe that the attempt to level up Mahommedan
philosophers to the level of Christian teachers was among the
novitates for which Jerome d'Ascoli cut short Bacon's philo-
sophical career.

The second part of the Moral Philosophy, dealíng with the
laws of civil and social life, is summarily disposed of in two
short chapters. Possibly a reason for this cursory treatment
may be found in Bacon's aversion to the introduction of
Roman law, which finds vehement expression in the twenty-
fourth chapter of the Opus Tertium, and again in the Com-
pendium Studii (Brewer, pp. 84-87, and 418).

! Something additional on this subject was probably said in the missing sixth

VOL. I.

Ixxxii INTRODUCTION.

We are here brought face to face with the failure, and the
cause of the failure, of Bacon's social and political ideal. He
was aiming at an enlarged and renovated Catholicism which
should bind together and incorporate all that was best and
noblest in Hebrew, Greek, and Arabic tradition in the fabric
of the Christian Church, for the spiritual government of the
world. The keystone of the fabric was supplied by the
mistress-science, theology, resting on Mosaic and Christian
revelation, consolidated by Aristotelian philosophy, and
penetrated by the vital and progressive spirit of natural
science. A progressive papacy, carrying on in continuous
and harmonious development the work which Mosaic law and
Greek intellect had begun—such was Bacon's vision: and the
marvellous upheaval of thought in Paris and elsewhere during
the thirteenth century seemed to bring that vision within reach
of fulfilment.

But while Paris was building up its systems of philosophic
theology, south of the Alps, in the rival university of Bologna,
work of another kind was going on. The study of the civil law
of Rome, which had never wholly ceased in the cities of North
Italy, had been stimulated early in the twelfth century by the
teaching of Irnerius and others; and from that teaching the
university of Bologna gradually arose, as the university of
Paris had arisen from the teaching of Abelard. It was
a momentous event in the history of Europe. Civil law was
a study as secular as the Roman empire itself. Clerical and
lay students sat at the lectures side by side. ‘ Very early in
the twelfth century men of mature age, men of good birth and
good position, beneficed and dignified ecclesiastics, or sons of
nobles, flocked from the remotest parts of Europe to the
lecture-rooms of Bologna’ (Rashdall, History of Universities,
i. 124). The civil law embraced the entire system of man’s
social relations, and dealt with them on principles with which
theology had no concern.

. The Church felt the danger, and coped with it in the only

part of the Moralis Philosophia. But his language on the subject does not
warrant the belief that the subject was fully dealt with. Cf. Of. Tert. cap. xiv.
Brewer, p. 52.

=~ D eee ee oe A —

MORAL PHILOSOPHY. Ixxxiii

way that was possible, by borrowing weapons from her lay '
rival, and arranging her own system of law in a form not
less comprehensive and systematic. Irnerius had hardly
finished his lectures when a fellow-citizen, the monk Gratian,
in 1143 published his great text-book of canon law known
as the Decretum, to which, in 1234, Gregory IX added five
books of Decretals.

Nominally the situation was saved, but at the cost of
secularizing the Church. For the canon law was in reality
based on the civil law. * Everything in the canon law was
Roman which was not of directly Christian or Jewish origin.’
‘After the age of Gratian the studies even of ecclesiastics
took a predominantly legal turn. Speculative theology was
abandoned in favour of the canon and even of the civil law;
while the estrangement of the canon law from theology

: kept pace with the increasing closeness of its union with
the faculty of civil law’ (Rashdall, i. p. 138). In 1219
Honorius III formally prohibited the study of civil law in
Paris on the ground that it threatened to extinguish the study
of theology in the one great theological school of Europe.
But prohibitions that were powerless to exclude Aristotle
were equally impotent against the invasion of Ulpian and
Justinian.

Bacon's pages reflect very vividly the conflict of clerical
with secular influences. * More praise, he says, *is gained in
the Church of God by a civil jurist, though he may know
nothing but civil law and be utterly ignorant of canon law
and theology, than by any master in theology, and he is more
quickly promoted to high ecclesiastical positions.’ ‘Oh that
the canon law might be purged from the superfluities of civil
law, and be ordered by theology, he exclaims, ‘then would
the government of the Church be carried on honourably and
suitably to its high position’ (Opus Tertium, ch. 24).

He recurs to the same subject in a later work. ‘For the last
forty years the abuse of the civil law of Italy has been under-
mining not merely the study of philosophy, but the Church of
God, and all the kingdoms of Christendom.’ ‘They monopo-
lize,’ he proceeds to say, ‘every office of emolument, so that

fa

Ixxxiv INTRODUCTION.

students of theology and philosophy are deprived of the
means of following their studies. And besides this, the study
of civil law is obliterating the distinction between clerical and
lay professions. The doctors of law of Bologna call them-
selves clerks and masters, though they have not the tonsure,
though they take to themselves wives, have families, and in
every respect adopt the ways and practices of laymen... If
clergymen and laymen are to be subject to the same law, at
least let it be the law of England for Englishmen, and of
France for Frenchmen, and not the law of Lombardy ' (Com-
pendium Studii, cap. 4).

When Bacon appealed to the Pope to arrest the diffusion
of civil law, he was like one who should attempt to stop the
tide or the courses of the stars. He was fighting against the
laws of historical evolution. It was written that the constitu-
tion of society should be settled on a human and secular, not
on a theological basis ; and the study of civil law, radiating in
the twelfth and thirteenth centuries from Bologna into every
part of Christendom, was one of the most significant among
many signs that the function of the Catholic Church, as the
organizer of political society, was gone.

Widely different was the future of that Church in all that re-
lated to personal morality. Yet here too there was much to be
desired. In the third section of the work this subject is discussed
with great fullness. ‘On virtue and vice, says Bacon, ‘the
ancient philosophers have spoken so wonderfully that a Chris-
tian man may well be astounded at men who were unbelievers
thus attaining the summits of morality.’ ‘On the Christian
virtues of faith, hope, and charity,’ he adds, ‘we can speak
things of which they knew nothing. But in the virtues needed
for integrity of life, and for human fellowship, we are not their
equals either in word or deed. Blameworthy and shameful in
us that it should be so.’ Acting on this view, Bacon has
composed this third part almost entirely of selections from

! This was written (as Brewer shows, p. lv) in 1271, three years after the
death of Clement IV. Guy Fulcodi, before his ecclesiastical career began, had
been a distinguished lawyer, and would hardly have tolerated such strong

language.

MORAL PHILOSOPHY. ]xxxv

Aristotle, Plato, Cicero, and above all, from Seneca, adding
the fewest words of his own that were needed to mould them
into systematic shape.

He begins by adopting Aristotle’s general scheme of the
moral virtues as means between opposing vices. From these
he passes to the consideration of special vices in the order
of the seven mortal sins of Catholic theology. ' Six of these
deal with man's conduct under prosperous circumstances ;
the seventh, anger, with his conduct in adversity. Dealing
briefly with the first class, Bacon devotes much more atten-
tion to the subject of anger. His reason for doing so lay in
the disturbing influences of this passion on the whole of man's
life public and private, and also that, in seeking remedies for
its ravages, we are led up to the state of inward peace and
resignation under outward trials which forms the highest plane
to which the soul can aspire.

Nearly the whole of Seneca's three dialogues on Anger are
quoted, but with complete rearrangement, in pursuance of the
aim in view. Beginning with a picture of this passion and its
disastrous effects on the highest qualities of the soul, such as
clemency, pity, and joy, he enlarges on examples of self-
restraint, and thence proceeds to consider remedial action ;
patient inquiry, time allowed for the mood to pass by,
and constant remembrance of human fellowship with the
offender.

This leads him to the wider subject of fortitude under
calamity, of forgiveness of injury and insult, of recognition of
the truth that whom God loves He chastens. He concludes
the section with long selections from the dialogues on consola-
tion under bereavement, exile, and poverty, on the shortness
of life and the state of inward bliss and spiritual peace. It
appears that though other parts of Seneca were well known,
especially the series of letters to Lucilius, these dialogues had
escaped notice till Bacon called attention to them. The
apocryphal correspondence between Seneca and St. Paul
shows that an affinity between Seneca and Christian teaching
had been widely recognized in the Church. Nowhere is this
affinity so strongly marked as in the dialogues De Providentia,

Ixxxvi INTRODUCTION.

De Vita Beata, and De Tranquillitate Animi, from which Bacon
has quoted so largely.

The fourth section of the Moral Philosophy contains the
_ first attempt ever made at the comparative study of the
religions of the world. These Bacon ranges in six classes:
Pagans, Idolaters, Tartars, Saracens, Jews, Christians. What
specially called attention to this subject in Bacon's time were
the events proceeding in Central Asia, and already seriously
affecting European politics. Mongol hordes had swept over
Russia and South Eastern Europe, and were threatening the
Western kingdoms. Franciscan and Dominican missionaries
had been sent by Pope Innocent IV and by Louis IX to
investigate the danger at its source. The reports brought
back by these missionaries, especially those of Carpini and
Rubruquis, brought the religious problem before the view of
the leaders of the Church in all its magnitude. It was seen
that beyond the Christian world, beyond the Mahommedan
world which bounded it, there lay regions of unsuspected
magnitude in the extreme East, where other creeds prevailed.
One of these was Buddhism, recently imported into Central
Asia from Tibet, with its elaborate monastic system, its image-
worship, and its complicated liturgy. This creed was always
spoken of by Rubruquis and Carpini, as by Marco Polo in
the succeeding generation, as Idolatry. Christianity of the
Nestorian type was widely disseminated ; though not, it would
seem, in its most highly militant form. Side by side with
these were tribes whose religion was of a lower grade, not
rising above the rudest fetichism ; these were spoken of as
Pagans. Between these various modes of faith the Tartar
chiefs held a doubtful and almost neutral attitude. If these
could be brought within the pale of the Catholic Church,
Mahommedanism, crushed between the forces of the West
and the extreme East, would cease to be a danger. The
issue remained undecided in Bacon's time. But we can
imagine with what interest he would confer, as he tells us
that he did, with Rubruquis on his return to Paris, and
listen to his story of the Parliament of Religions, Saracen,
Christian, and Buddhist, held at Kara Korum at the sug-

MORAL PHILOSOPHY. Ixxxvii

gestion, and under the presidence, of Mangu Kaan. (Cf.
vol. ii. p. 389.)

In Bacon's demonstration of the superiority of Christianity
to other religions, use is made of this singular experiment.
The majority of those who took part in it accepted the unity
of God. The Pagans were few in number. The Buddhists
(spoken of as Idolaters) raised the question of the origin of
evil as an objection to a single ruler of the Universe ; but
they allowed the question to be evaded. The Tartars, though
somewhat indifferent on religious matters, were disposed to
side with the Mahommedans and Christians in maintaining
the unity of God. On the whole, the conclusion to which
this conference tended was a fair sample, in Bacon's judgement,
of the preponderating voice of mankind.

Appeal is then made to Aristotelian reasoning as to the
necessity of a First Cause. The attributes of wisdom and
goodness are shown to follow from omnipotence. Man's duty
being to do God's will, how is man to know it? Evidently
by revelation. And which revelation is true? There can be
but one: for if there were more the human race could not
be united. ‘The unity of the Church follows from the unity
of God. If there were more Gods than one, more worlds
than one, and more mankinds than one, then there might be
more revelations than one, but not otherwise.’ Which, then,
is the true revelation? On a comparison of the six religions
before us, three, the Pagan, the Buddhist, and the Tartar, are
at once ruled out. Of the three that remain, the Jewish, the
Saracen, and the Christian, philosophic reasoning, external
and miraculous evidence, and ethical purity combine in giving
preference to the last. The book, as we have it, closes
with some ardent and rapturous words on the Sacra-
ment of the Altar, as the means whereby Christ always
remains present with His Church.

Of the missing books we are not left in entire ignorance.
We know from the fourteenth chapter of the Opus Tertium
that the purpose of the fifth book was, to insist upon such
modes of setting forth moral truth as were likely to impress,
not merely the intellect, but the emotions and character of

Ixxxvili INTRODUCTION.

the hearer. The art of preaching, Bacon thought, was one
demanding the most serious and systematic study. Rhetoric
was no mere field for the gratification of vanity by ornamental
display. It was a part of logic, and the most important part,
since by its means truth was so conveyed to the listener that
‘he is seized unawares and lifted above himself and filled with
thoughts beyond his power to control, so that if evil he is
absorbed by the love of good, if imperfect he receives the
spirit of perfection, not through violence, but through the
strong and gentle power of speech.’ Rhetoric thus conceived
implied the study of music in its widest sense, the study of
rhythm and metre, the management of voice and of gesture
(Opus Tertium, ch. 75).

The sixth and final section of Bacon's moral philosophy
treated, he says, of lawsuits and of justice. He implies, how-
ever, that he dealt with this subject cursorily.

XII. GENERAL CHARACTERISTICS OF THE OPUS M AJUS.

The question presents itself, How far can the Opus Majus,
with its two appendices, the Opus Minus and the Opus Ter-
tium, be accepted as the final exposition of Bacon's philosophy
and polity? It is spoken of by the author throughout as a
persuasio praeambula. It is a hortatory discourse addressed
to a busy statesman (for Clement IV, like most other popes
of the thirteenth century, may be so called), urging him to
initiate a reform of Christian education, with the direct object
of establishing the ascendency of the Catholic Church over
all nations and religions of the world.

A fundamental principle with Bacon was that truth of what-
ever kind was homogeneous. ‘ All the sciences,’ he said, ‘are
connected ; they lend each other material aid as parts of one
great whole, each doing its own work, not for itself alone, but
for the other parts: as the eye guides the whole body, and
the foot sustains it and leads it from place to place. As with
an eye torn out, or a foot cut off, so is it with the different
departments of wisdom; none can attain its proper result
separately, since all are parts of one and the same complete

THE OPUS MAJUS. Ixxxix

wisdom’ (Op. 7ert. ch. 4). Much light is thrown by passages
like these, and there are many such, on the varied and at first
sight heterogeneous character of the Opus Majus. <A glance
at the Index of this edition will give some notion of the
multiplicity of the topics treated. History of philosophy,
comparative philology, mathematics, astronomy, geography,
optics, the physiology of sensation, all find a place; and all
are subordinated to the service of the Catholic Church as the
guardian of the highest interests of man. Al] these topics
are handled so far and in such a way as to convince the Pope,
or others in authority, of the width of the field to be culti-
vated, and of the importance of the object in view. Bacon’s
procedure is like that of a traveller in a new world, who brings
back specimens of its produce, with the view of persuading the
authorities of his country to undertake a more systematic
exploration. To that further and more complete inquiry he
proposed to devote the remainder of his life. He speaks of
it in several passages of the present work under the title
of Seriptum Principale. But, as we have reason to believe,
of the twenty-five years of life that remained, more than half
were sterilized by his imprisonment. When released, though
he persevered, like Galileo, indomitably to the end, he was
too old to think with his former vigour, and was capable only
of such inferior work as the Compendium Theologiae, or the
Commentary on the Secretum Secretorum. There remain
the years between 1268 and 1278. They produced the Com-
pendium Studii (published by Brewer), the Communia Natu-
valium, the Communia Mathematicae, and other fragments
of the Scriptum Principale. But, making large allowance for
what may have been lost through neglect or through malig-
nant hostility, or for what may yet remain to be discovered,
the balance of probabilities indicates clearly enough that the
Seriptum Principale was never brought to completion. The
Opus Majus remains the one work in which the central
thought of Bacon is dominant from first to last; the unity
of science, and its subordination to the highest ethical pur-
pose conceivable by man.

Another characteristic of Bacon's philosophy, to which it

xc | INTRODUCTION.

seems to me that sufficient attention has not yet been called,
is the sense of historical continuity by which it is pervaded.
Not indeed that Bacon stood alone in this respect. Comte,
in a remarkable passage of his appreciation of the mediaeval
Church, called attention, perhaps for the first time, to the
awakening of the historic sense which the very constitution
of that Church involved ; rising as it did from the threefold
root of Roman law, Greek thought, and Hebrew theocracy
(Philosophie Posttive, vol. v. p. 247, ed. Littré). Asan example
of this influence, he proceeds to quote the example of Bossuet,
one of the first of European thinkers to form, in however
imperfect a way, a broad and definite conception of the unity
of history. But the example of Roger Bacon, writing four
centuries earlier, is even stronger and more startling. Two
centuries before the Renascence, he states explicitly what
others may have implicitly thought, but would have shrunk
from avowing even to themselves, that the whole course of
intellectual development of mankind from the beginning of the
world was not multiple but one, not discrete but continuous.
He takes pains to synchronize the demi-gods, the heroes and
the thinkers of Greece with the kings and prophets of Judaea.
In his conception, philosophy, science, and religious truth had
a common origin with the patriarchs: though separated in
later centuries, they pursued a parallel course in Judaea and
in Greece. The growth of science, no less than the growth
of religion, was a process of continuous evolution, taking place
under divine guidance. It may be said that traces of such
a doctrine as this may be found here and there in the early
fathers, and especially in the writings of St. Augustine. But
a comparison of the ninth and tenth books of De Civitate Dei
with the second and seventh sections of the Opus Magus, will
reveal a profound difference in the mode of treatment, even
more than in the conclusions reached. What the earlier
writer looks at as concessions wrung from an opponent, the
later hails as the testimony of a friend. Augustine dwells on
the points that separate the Christian from Porphyry and
Seneca ; Bacon on the points of union.

There are students of history even yet surviving to whom

THE OPUS MAJUS. xci

the centuries following the fall of the Western Empire seem
a chasm hard to pass; so that they prefer, with Vico, to con-
ceive of an ancient civilization which has run its course, and
a new cycle as beginning. For Roger Bacon the apparent
breach of continuity was in great part filled up by the long
series of thinkers and students, who kept the torch of science
alive in the Mahommedan schools of Mesopotamia and Spain.
A glance at the Index to this edition will show the use which
Bacon made of such men as Thabit ben Corra, Alfarabius,
Alfraganus, Alkindi, Alhazen, Albumazar, Avicenna, Hali,
and Averroes. They are spoken of, and most truly, not
merely as the principal channels through which Greek philo-
sophy and science were introduced to the Western world, but
as having increased the treasure entrusted to them ; a treasure
which the Westerns of the thirteenth century, * unless they are
dolts and asses, will regard it as their duty to transmit with
due interest to their posterity.

At the close of these introductory remarks, some attempt
may be made to assign Bacon's position in the history of
human thought. It appears on the surface that he belongs
to the order of thinkers, typified by Pythagoras rather than
by Aristotle, who engage in speculation, not for its own sake
alone, but for social or ethical results, that are to follow. His
protests against the intellectual prejudices of his time, his
forecasts of an age of industry and invention, the prominence
given to experiment, alike as the test of received opinion and
the guide to new fields of discovery, render comparison with
his great namesake of the sixteenth century unavoidable. Yet
the resemblance is perhaps less striking than the contrast.
Between the fiery Franciscan, doubly pledged by science and
by religion to a life of poverty, impatient of prejudice,
intolerant of dullness, reckless of personal fame or advance-
ment, and the wise man of the world richly endowed with
every literary gift, hampered in his philosophical achieve-
ments by a throng of dubious ambitions, there is but little in

‘common. In wealth of words, in brilliancy of imagination,

Francis Bacon was immeasurably superior. But Roger Bacon
had the sounder estimate and the firmer grasp of that com-

xcii INTRODUCTION.

bination of deductive with inductive method which marks the
scientific discoverer. Finally, Francis Bacon was of his time;
with Roger Bacon it was far otherwise. |

M. Hauréau, the historian of Scholastic philosophy, and
also M. Renan, have suggested a parallel (or, it may be, have
adopted it from Littré) between Roger Bacon and Auguste
Comte. Some anticipation of the Philosophie Positive there
assuredly is in Bacon's subordination of metaphysic to science,
in his serial arrangement of the sciences, and in his avowal
of a constructive purpose as the goal of speculative inquiry.
But it is well not to push such comparisons too far. We
shall best understand Bacon's life and work by regarding him
as a progressive schoolman. Like the other great schoolmen
of the thirteenth century, he set before himself the purpose
of strengthening the Church in her work of moral regenera-
tion, by surrounding her with every intellectual resource.
But the forces that he brought to bear were not limited, like
theirs, to the stationary dialectic of Aristotle; they were also,
in great part, drawn from the progressive culture of natural
and historical science. As compared with his successors of
the Renascence, his purpose was loftier; for, in urging the
continuous advancement of knowledge, he had higher things
than knowledge in view. His aim, pursued in no spirit of
utilitarian narrowness, yet steadily concentrated on the
moral progress of mankind, was, /uduire pour déduire afin de
construire.

ANALYSIS OF THE ‘OPUS MAJUS:

PART I.

THE FOUR GENERAL CAUSES OF HUMAN IGNORANCE.

CHAPTER I.
VOL. I. PAGES

True wisdom implies—1. Sound methods of gaining knowledge;
2. The application of knowledge to important purposes; as the
government of the Church, the conversion of the heathen, and
the repression of evil-doers. Such wisdom is hard to obtain, and
there are four principal causes of failure. These are—1. Subjection
to unworthy authority. 2. The influence of habit. 3. Popular
prejudice. 4. False conceit of our own wisdom. We will begin by
dealing with the three first: the fourth demands separate treat-

ment . . . . . . . e . . . . 1 - 4
CHAPTER II.
Opinions of philosophers on these defects.— Citations from Aristotle,
Seneca, Cicero, Averrhoes, Abelard, Jerome, Chrysostom . . 46

CHAPTER III.

Leaving authority, let us look to experience. Authority, habit,
and prejudice may sometimes lead to truth, but the probabilities
are much against it. We may take an illustration from arithmetic.
Of perfect numbers, there is but one among the first ten, one
between 10 and 100, one between 100 and 1,000, one between 1,000
and 10,000. Among men the number of the truly wise is even
smaller. Even of philosophers few are to be counted among them.
Aristotle, the wisest of all, was not perfect . . . «© « 68

CHAPTER IV.
Of the three first causes of error, popular prejudice is the most
potent. The truth that pearls should not be cast before swine is
confirmed by Aristotle and other philosophers 0 0. « o. 9-M

xciv ANALYSIS OF THE ‘OPUS MAJUS."

CHAPTER V.
VOL. I. PAGES

Continuation of the subject. Gratitude is to be shown to the
great founders of truth even where they have failed . . . 11-18

CHAPTER VI.

Errors are infinite, truth single. New generations inheriting the
results of their predecessors can see their mistakes. Avicenna sees
where Aristotle erred; Averroes corrects Avicenna. Among the
fathers of the Church we see the same thing. They acknowledge
their own errors and point out those of others . 05. « 18-15

CHAPTER VII.

Further illustrations, justifying cautious scrutiny of received
opinions. . .. . . . ^. «© . « « . lY

CHAPTER VIII.

By habit of discussing received opinion we cease to be s'aves
to it e. . . . . e . e . e e e 1?

CHAPTER IX.

But the fourth source of error, false conceit of our own wisdom, is
far the most dangerous. It fortifies itself with the results of the other
three by endowing this false wisdom with the force of authority, of
custom, and of popular prejudice. Prior to the detection of the
symptoms of this spiritual disease, we must acquire, as physicians of
the body do, some knowledge of universal causes from the study
of nature (communia naturalium). The potency of this source of
error is shown by historical examples . . . oe . 17-21

CHAPTER X.

Two things are to be distinguished : presumption of knowledge ;
concealment of ignorance. What each one of us can know is little
in comparison with what faith reveals; but both together are as
nothing to the unknown world which neither faith nor reason can
reach. Why then boast of knowledge? The labours of a long life
can be assimilated by an intelligent boy in a year. If this boy has
learnt at the right source he will be further advanced than many of
his learned seniors, as the youth entrusted with this work will prove.
Wise men know their ignorance, and are ready to learn from every
one. Ihavelearned more from plain men quite unknown to fame
than from allthe doctors . . . . . . . .. 21-28

CHAPTER XI.

The evil tends to multiply itself owing to the claims set up by
ignorance to authority. Yet men, however learned they may be in

PART I. XCV

VOL. I. PAGES
other ways, should be credited with no authority whatever in things
of which they know nothing . . . 00057 © « o 28-24

CHAPTER XII.

Many things known to the ancients we neglect, as the study of
mathematics and languages, from sheer ignorance of their value. In
other cases the fact that subjects are not studied by the fathers is
held a good reason for passing them by. We forget that the saints
and fathers were justified by the circumstances of their time, and
moreover that they were not infallible. Augustine found much fault
with Jerome, and so in other cases 2 000. . o. 24-26

CHAPTER XIII.

We must remember that the best Greek work was not known to
the Latin fathers. Plato indeed was translated and carefully studied ;
but Aristotle, from the very fact of being Plato's opponent, was
neglected. Yet Augustine had translated the Categories, a work
highly valued by Alcuin. Boethius also translated some of the
logical works. But if the greater works of Aristotle bad been known
to them, they would have gladly received these, and not have troubled
themselves about the ashes of his philosophy 005. 5. o 26-28

CHAPTER XIV.

The early Church made no use of Greek science except for the
purpose of regulating its calendar and its music. The explanation
of this neglect of ancient learning is fivefold. 1. Philosophy was the
foundation of law and government to all the nations of antiquity
except the Hebrews. 2. Therefore it was that philosophy resisted
Christianity. 3. Moreover these nations not merely studied philo-
sophy, but practised augury and oracular magic. 4. They persecuted
Christians. 5. The Church, finding her enemies occupied on the one
hand with the study of philosophy, and on the other with the study
of magic, associated these two things, and thus came to despise and
dislike philosophy. The truth is however that philosophy, so far from
being hostile to the Church, is capable of yielding it indispensable
support . TP e] . e . 28-80

CHAPTER XV.

Later ecclesiastical authorities have followed a similar course,
though without the excuse which justifies the early fathers. Though
Greek philosophy is no longer untranslated, they study only its most
trivial productions, neglecting the great works of science and
ethic . 1. . . . «© . .; 5. « «+ 80-81

xcvi ANALYSIS OF THE ‘OPUS MAJUS.

CHAPTER XVI.
VOL I. PAGES

Let me not be misunderstood. I am not proposing to your Holi-
ness any violent change in the ordinary course of studies. I am
merely suggesting free access to a land of plenty for those who care
to avail themselves of it. If once the leaders of thought become more
enlightened, the rest will soon follow . . . . . . 81-8

PART II.
THE CONNEXION OF PHILOSOPHY WITH THEOLOGY.

CHAPTER I.

Theology is the mistress-science. All truth is contained in the
Scriptures; but to elicit truth we need the help of the canon law
and of philosophy. Wisdom comes from one God, is given to one
world, for one purpose. Itself therefore is one. It cannot be
inconsistent with itself . . . TEC LC . .. 98-84

CHAPTER II.

The canon law has its root in Scripture. From that root spring
branch and fruit; the teaching of the fathers and doctors of the
Church and the rules finally laid down by them . . . . 84-85

CHAPTER III.
So with philosophy. Augustine dwells at length on the importance
of taking from it all that is precious, as the Hebrews of old borrowed
jewels from the Egyptians. He included in the word ethics, history,
knowledge of the arts, logic, and grammar . . . . . 90-94

CHAPTER IV.
Jerome and Bede used similar language. Bede remarks that, as
Solomon when building his temple called foreign workmen to his aid,
so has Christ availed himself of heathen philosophers in building his

Church. Paul, too, quotes heathen poets . . .. . .. 387-88.

CHAPTER V.

Wherever truth is found it belongs to Christ. We must distinguish
between infellectus agens and intellectus posstbilis. The first is no
part of our nature. Our minds are capable of receiving it and of
being stirred to action by it, but it comes from without. This can be

^

PART II. xcvii

VOL.I. PAGES
proved from Aristotle, when rightly interpreted, and from his com-
mentators Alpharabius and Avicenna. Reason comes from God:
therefore philosophy is divine. . . . . . . .. 88-41

CHAPTER VI.

But we may go farther. Wisdom was a direct revelation of God to
the philosophers of antiquity. Aristotle, Cicero, and Augustine may
becitedtoshowthis . .. . . . . . . . 41-42

CHAPTER VII.

Indeed the very purpose of philosophy is to lead up through know-
ledge of the creature to knowledge and service of the Creator . 42-43

CHAPTER VIII.

The Scriptures tell of the creature, and reveal its final cause:
leaving the efficient cause to be dealt with by philosophy, which as
yet has but imperfectly done her work. The rainbow is an illustra-
tion. . . . . . o. . . . o. . . 48-44

CHAPTER IX.

The most important point of all has now to be explained. Philo-
sophy is not an invention of heathen nations: it was revealed in its
entirety to the first patriarchs, by the same Spirit who revealed to
them the oracles of God. We learn from Josephus that Noah and
his sons taught the Chaldaeans; Abraham the Egyptians. That
philosophy originated with the patriarchs is admitted by Aristotle.
From the Chaldaeans and Egyptians, thus taught, further progress
ensued, the history of which may now be traced in parallel lines with
that of the Hebrews. Isis and Pallas were contemporary with Jacob
and Esau. Under Phoroneus, the second king of the Argives, a few
years later, moral philosophy was first taught. Then came Prometheus
and Atlas, contemporary with Moses. Hermes was the grandson of
Atlas; by him or by another wise man, Apollo, Asclepius was taught,
the founder of medical art; though probably medicine was better
known to the sons. of Adam and Noah, who thus attained great
longevity . . . e; . . . 2 . 44-49

CHAPTER X.

In the time of Othoniel, the Hebrew judge, Cadmus gave the art
of writing to the Greeks. [Under the name of Hercules as under
that of Apollo several distinct persons living at widely different
periods are included.] Orpheus was a contemporary of Gideon.

VOL. I. g

xcviii ANALYSIS OF THE ‘OPUS MAJUS.

VOL.I. PAGES
The Erythraean Sibyl lived between the taking of Troy and the
founding of Rome, in the seventh Olympiad, 433 years afterward.
Hesiod, Homer's successor, is prior to the foundation of Rome.
Romulus, Thales of Miletus, and Hezekiah were contemporaries . 49-51

CHAPTER XI.

With Thales began the series of the wise men of Greece; he
himself was in Josiah's time; Pittacus, Solon, Bias and others, were
contemporary with the Jewish captivity. Shortly afterwards arose
the Italic school of Greek philosophy, Pythagoras at their head, in
the time of the Jewish restoration; Tarquinius Superbus reigning
at Rome . . . . . . . . es . 91-92

CHAPTER XII.

Pythagoras was followed by Archytas, Timaeus, and others ; but
the great school of Greek philosophy, culminating in Aristotle, was
inherited from Thales, through Anaximander, Anaximenes, Anaxa-
goras, Archelaus, Socrates, and Plato. Plato, who travelled and
' studied in Egypt, and learnt much from the Pythagorean school,
uttered truths so profound that many have thought that while in
Egypt he must have been taught by the prophet Jeremiah though
chronology will hardly confirm this view . . . . 92-54

CHAPTER .XIII.

Aristotle studied under Socrates for three years, and for twenty
years under Plato, whom he survived by forty-three years. He is
the greatest of philosophers, rightly called The Philosopher. He
strove by diligence and observation of nature to bring philosophy to
the perfect state in which the patriarchs of old received it. But he
was not infallible ; and as long as the world lasts, additions to his
knowledge will continually be made. Little use was made of his
teaching till after the time of Mahomet, when Avicenna, Averroes
and others brought it to light. Boethius indeed had translated
some of his logical works. A great stimulus was given to the study
of Aristotle by Michael Scot's translations, with commentaries, of his
physical and metaphysical works. Of Avicenna's commentaries,
however, not more than a third part has yet been translated . 54-56

CHAPTER XIV.

The conclusion is that philosophy and theology are two aspects of
one inseparable whole. Philosophy leads us to the threshold of divine
truth ; apart from this function it has no meaning or value. But if
rightly regarded its work never ends. In the sight of God we are

PART 11. xcix

VOL. I. PAGES
but as children ever growing and learning: what we know is due to
those who have gone before us; it is for us, if we are not dolts, to
supply their shortcomings. As Christians it is our duty to avail
ourselves of their teaching as the foundation of our more perfect
doctrine, some glimpses of which, due to the tradition of the primitive
patriarchs, were not denied to heathen writers . . . . 96-59

CHAPTER XV.

Such glimpses are to be found in the Sibyls, who prophesied of
the death of Christ and of the last Judgement. Divine truth, as
Augustine has said, was not confined to the seed of Abraham. Job
believed in the Resurrection . . .. 99-61

,

CHAPTER XVI.

There are two principles of metaphysic which will lead us to the
same conclusion. The first is that the business of philosophy is to
furnish a criterion of knowledge. It is aware of the incompleteness
of its own knowledge in those matters which are of the greatest
importance. It concludes from the goodness of God that such know-
ledge must have been somewhere revealed : it finds this revelation
in the Christian church ; and shows that Christian doctrine supplies
the complement to its teaching which hitherto had been wanting. 61-62

CHAPTER XVII.

Secondly, we must consider that all speculative philosophy has
moral philosophy for its end and aim. The two are co-ordinated.
As the speculative philosophy of antiquity is related to tbe moral
philosophy of that time, so must our own speculative philosophy be
related to the moral philosophy of the Christian time, in other words,
to Christian theology. But Christian ethic, as all authorities admit,
assumes the previous existence of heathen ethic. So therefore must
it be with the speculative philosophy of Christians. It starts with the
speculative theories of antiquity and carries them many stages farther.
And in so doing the Christian theorist will not merely select from his
heathen predecessors those truths the relation of which to theology
is manifest. He will embrace all truths without distinction, arranging
each in the division to which it belongs; confident that all truth, in
whatever department, will conduce in one way or another to that
whichisdivine . .. . . . - « . 62-64

CHAPTER XVIII.

We see then that wisdom was revealed in its fullness to the first
patriarchs ; that, through the imposture of those who followed them,

g2

C ANALYSIS OF THE ‘OPUS MAJUS.

VOL. I. PAGES
it was afterwards hidden from men ; that Thales and his successors
down to Aristotle, aided by some trace of primitive tradition, revived
its culture. Philosophy, therefore, has its place in the divine govern-
ment of the world: its conclusions must be demonstrated, diffused,
and enlarged. It is a component partc of that perfect wisdom which
is contained in the Scriptures . . . . . . 64-65

PART III.

THE STUDY OF LANGUAGE.

Having seen the essential unity of wisdom as contained in
Scripture, the canon law, and philosophy, we pass to the divisions
of the subject. These are five. The first is the study of grammar,
not so much of Latin, as of the languages from which Latin received
its culture. 1. The quality of one language can never be perfectly
reproduced in another. This is true even of the dialects of a language:
far more true as between different languages. A literal translation of
Homer into Latin, and thence into a modern tanguage, results in utter

absurdity . . . . . 66-67
2. Secondly, Latin is altogether wanting in many of the necessary
words for the things described by foreign authors . 67

3. Thirdly, the translator must not only be perfectly acquainted
with his subject, but also with the two languages with which he deals.
Boethius and Robert Grosseteste fulfilled these conditions. But
most translators have failed, and especially the translators of
Aristotle. Jerome and Augustine have pointed out the errors
of the Septuagint version and of the other versions. Nevertheless
Jerome has left very many uncorrected . 0. 5. . o. 67-70

4. Fourthly, in the Latin texts now in our possession there are
vast omissions, as well as many confused and corrupt passages.

E. g. the third and fourth books of Maccabees are wanting: also the

books of Samuel, Nathan, and Gad. We need also good translations

of Josephus's book of Antiquities, of many of the Greek fathers, of

the second and third books of Avicenna, and of many essential treatises

of Aristotle, on metaphysics, on physical and mathematical science,

and on that part of his logic which deals with practical reason, the

part that is of the greatest importance in the guidance of human

life. .. . . . . 40-73
$. Fifthly, owing to our neglect of foreign languages, we fail to

understand the allusions to them contained in many writings of

PART III. ci

VOL.I. PAGES
antiquity. We are told, for instance, that certain parts of the
Scriptures are written not in Hebrew, but fn Chaldaean. The
precise relations of these two languages ought to be made familiar
tous. . . . 78-0

6. Sixthly, the Latin text of the Scriptures, as commonly used, is
extremely corrupt, and becomes more so as time goes on. It needs
careful correction by reference to the original Greek and Hebrew.
The versions in recent use by the Franciscans and Dominicans are
far inferior to the old versions . : . . 11-81

7. Seventhly, when the text is correct, there is ; often the greatest
obscurity as to the interpretation. The same Latin word corresponds
often to many totally distinct Hebrew words. . - « . 81-85

8. Eighthly, and lastly, since Latin grammar is formed on the
model of Greek and Hebrew grammar, much confusion arises from
this source. Latin words of foreign origin are not recognized ; and
conversely, to many words of Latin origin a foreign source is
erroneously given. Again mistakes occur as to the vowels and
diphthongs in Greek that correspond to a Latin vowel. The rules
for gender that hold good in Latin are not applicable to Greek. The
same holds good of pronunciation. The penultimate of possessive
adjectives, which is long in the case of words of Latin origin, as
bovinum, is short where they are derived from Greek, as in such
words as crystalinum, adamantinum . . . . . . 85-92

In conclusion, I must point out the importance to the Church of
linguistic studies ; (1) for explanation of the liturgy, (2) of the formulae
used in sacraments and consecrations, (3) for the due regulation of
foreign churches, (4) for throwing light on the future history of the
Church, (5) for intercourse with foreign nations. . . . 92-96

PART IV.
MATHEMATICAL SCIENCE.

First DisrTiNCTION.

CHAPTER I.

I pass now to mathematics, the foundation and the key to all
other sciences, studied from the earliest ages of the world, but of late
fallen into neglect. I shall deal successively with its application to
human knowledge, to divine knowledge, and to the government of
the Church. . .. . . e. 005. + o. 917-98

cii ANALYSIS OF THE ‘OPUS MAJUS.

CHAPTER II.
VOL.I. PAGES

There is high authority for this estimate of mathematics. In the
study of divine things and also of man's social life Boethius. and '
Ptolemy show that it is of great service, The various modes of
proportion have their analogue in civil polity. It is needed both in
grammar and logic, as Alpharabius and Cassiodorus have shown.
For prosody depends entirely on arithmetical relations. Logic, on
its practical side, has the same purpose as poetic and rhetoric, which
depend on harmony. Further, the subject-matter of logic is in-
timately connected with mathematic. This is obvious in the
Categories of quantity, of time, and of place. In the Category of
quality much belongs to the mathematical domain, as e.g. geo-
metrical form. The same may be said of the Category of relation.
Spiritual substances can only be known through the medium of
corporal: and the first step to the knowledge of body is the study
of the heavenly bodies. The dependence of astronomy on mathe-
matics is obvious . ; . 98-103

CHAPTER III.

We reach the same conc.usion by reasoning. (a) In all other
sciences we use mathematical examples, because they illustrate the
point without confusing complications ; e.g. in explaining the difference
between augmentation and change, we add a gnomon to a rectangle,
augmenting its magnitude without changing its shape. (2) Mathe-
matical knowledge is innate in us and only needs drawing out, as
Cicero explains, Quaest. Tusc. book i. (c) Mathematical truths
. are discovered prior to others. (4) They are simpler of compre-
hension than others. (e) Students attain them who are incapable
of proceeding further. (/) We see the same thing with children,
who easily appreciate the simple arithmetical relations on which
music depends. (7) We acquire our knowledge of things known to
ourselves more easily than of things known to nature (i.e. intrinsi-
cally simpler; as, for instance, the truths of theology). But mathe-
matics have the double character of being both relatively and absolutely
simpler. (4) In mathematics demons'ration is more complete:
its cogency has the force of necessity, which is not the case
either in physics, in metaphysic, in ethic. (7)In other sciences
the uncertainty of the premisses involves uncertainty in the con-
clusion. These principles require verification by some science more
perfect than themselves: i.e. by mathematics. (4) Finally, the
subject-matter of mathematics is more directly cognizable by our
senses. It deals with quantity, which lies at the root of all know-
ledge. The simplest process of intellect implies continuous quantity,

PART IV. ciii

VOL.I. PAGES
i.e. time. (2) Finally, we are confirmed by the experience of all who
have most distinguished themselves in science. They owe their
results to the mathematical foundation of their studies . . 108-108

SECOND DisTINCTION.

CHAPTER I.

Leaving method, and passing to the objects of study, we find it
impossible to make progress without mathematics. The number and
motions of the heavens, planetary motions, eclipses obviously require
this science. And things terrestrial no less, since they are governed
by things celestial. The sun, acting on the surrounding medium,
diffuses light. This may be taken as a type of the propagation, or
multiplication, of species, or forces, by other agents. Let us consider
howittakes place . . . . . . . . » 109-111

CHAPTER II.

Rays passing from a rarer medium to a denser, if they impinge upon
the latter perpendicularly, pursue a rectilinear course. Otherwise
they are refracted, i. e. diverted towards the perpendicular drawn to the
surface of contact. In passing from denser to rarer they are diverted
away from this perpendicular. Hence if the denser body be spherical,
the solar rays passing through it converge at a given point beyond it.
The convergence of many rays produces heat. If the second medium
is so dense that the *species' cannot pass through, or at least that its
transit cannot be appreciated by human vision, it is reflected. If
the ray falls perpendicular to this medium, reflexion is in the reverse
- direction of incidence. If otherwise, the angle of reflexion is equal to
the angle of incidence. By concave reflectors solar rays may be
concentrated. If the reflector is spherical, those rays will be focussed
which impinge on points in it corresponding to a circle placed at
right angles with its axis. But reflectors can be devised of such form
that all the rays shall fall on the reflecting surface at equal angles,
and thus be reflected to the same focus. We have further to consider
the diffusion of light impinging on objects not directly from the sun
but indirectly. Constant exposure to direct rays would be destructive.
Lastly, we have to consider the effect of light on the nerves of vision,
when there is no question of its following any rectilinear course,
its path being modified by the vital principle es . 111-117

CHAPTER III.

Rays issuing in infinite number from a point in every direction
find their termination on hollow surface of a sphere. Each point of

civ ANALYSIS OF THE ‘OPUS MAJUS.

VOL. |. PAGES
the surface acted on is the vertex of a cone of rays, of which the base
is the whole surface of the agent . . . . . . 117-119

THiRD DISTINCTION.

CHAPTER I.

Light and other forces not merely propagate themselves by
multiplication of species, but work ulterior effects; light produces
heat, heat putrefaction, putrefaction death, and so on. To these
effects the same law applies. Rectilinear action is more effective
than curvilinear; perpendicular than oblique. In refraction the
effect is greater than in reflexion, because in the latter the reflected
and incident rays neutralize each other. In refraction action is
stronger where the second medium is denser than the first, because
the ray is deflected towards, not away from, the perpendicular. In
reflexion more is done by oblique rays than by perpendicular. With
the latter there is neutralization of incident and reflected rays.
Further, there can be but one perpendicular ray, but infinite numbers
of oblique ; and these may all be made to converge. . . 119-123

CHAPTER II.

The rays of which a natural action consist form, as we have seen,
a cone. In the shorter cones the strength of the action is promoted
first by greater proximity of the agent, secondly by the greater
proximity of the conterminal rays after intersection. On the other
hand in the longer cones, the rays before intersection are the nearer
to each other, and in this respect the action will be more potent.
But the first of these conditions will outweigh the second. . 128-194

CHAPTER III.

When two equal spheres interact, the half of each which is averted
from the other is unaffected ; the extreme rays from each can only
embrace the half of the other sphere. But with unequal spheres, the
less receives rays from less than the hemisphere of the greater, which
touch more than its own hemisphere. From each point of a sphere
rays issue into space outside of the tangent plane. Of these rays
only one is perpendicular to the surface. This is the potent ray.
Rays vertical to a sphere are divergent. But when the object of
vision is very remote, as in the case of stellar bodies, they appear
to us to be parallel: just as the walls of a house seem parallel,
although their lines of direction converge to the earth's centre. 124-127

PART IV.

FounrH DIsTINCTION.

CHAPTER I.

Cv

VOL.L PAGES

By the foregoing principles and others akin to them, which for
want of space are here omitted, all natural actions are to be ex-
plained. A few illustrations may be given. The planets receive
their light from the sun. Hence when the earth is between the sun
and moon, the moon is eclipsed by the earth's shadow. The cone
of this shadow not reaching however to the other planets, these are
not eclipsed. Again, that the eye and the stars can mutually transmit
their emanations through the media of the planetary orbits, proves
these media to be of great rarity, to be invisible, and non-luminous.
The sphere of fire also is neither luminous nor visible. A planet
differs from the sphere in which it moves by greater condensation of
celestial substance; hence its luminosity. This, though ultimately
derived from the sun, is not due to the sun's reflected rays. The
diffusion of moonlight proves the moon to have independent
luminosity. Owing to the magnitude of the sun being 170 times
greater than that of the moon, much more than half of the earth is
illuminated by the sun ; and the same is the case with the moon and
planets. Other affections of the moon's light depend on her varying

conjunctions with planets and with constellations . . . 127-180

CHAPTER II.

The same principles may be applied to disprove the alleged
simplicity of cosmic structure. A star on the meridian is seen to be
further from the pole than at its rising. In the latter position
refraction displaces it. This shows the world to consist of distinct
substances of varying density ; for a ray would not be refracted while
passing through the same substance, even though its parts should be

of different density. el - «» « 180-182

CHAPTER III.

Hence it is that the temperatures of the various zones are explained.
Beneath the poles the cones of rays are prolonged, and therefore
feeble ; capable only of raising vapours from the earth and sea, so
that the air of those climates is heavy and cold, and unfit for living
things. Nevertheless, owing to the length of the days and of the
twilight in summer, the sun being never far distant, there may be
places in those regions, favoured by the position and inclination of
certain mountains, where the rays are so reflected that the climate is

temperate . . . . . . . . . « 182-185

en
LI

cvi ANALYSIS OF THE ‘OPUS MAJUS.

CHAPTER IV.
VOL.I. PAGES
Passing to the torrid zone, it would seem that the region under the
equinoctial circle must be the hottest, since twice in the year the sun's
rays there are vertical. But this is over-weighed by the fact that
under the tropical signs the sun is nearly stationary. The matter is
further complicated by the eccentricity of the solar orbit. . 135-137

CHAPTER V.

The emanations from the stars affect not merely climate, but
character; implanting on the new-born child dispositions to good
or evil, to quick or to dull apprehension : though free will, God's
grace, temptations of the devil, or education may modify these innate
tendencies . . . . . . . . . . . 187-189

CHAPTER VI.

Our theory may be applied to the tides. These evidently depend
on the moon. When the rays fall obliquely on the surface, their
_ effect is only to raise vapours from the surface and create ebuilition
and a consequent flow of water till the time comes when tbe rays fall
vertically, and with force enough to extract the vapour; and then the
reflux begins. This however leaves it unexplained why the same
thing happens in the hemisphere averted from the moon. We must
suppose the ninth or starry heaven to be solid and impenetrable, and
that the vertical rays of the moon are reflected from it, these
producing the same effect as the incident rays . . . . 139-142

CHAPTER VII.

The application of these principles to the preservation of life and
health is obvious. Protection must be sought against the vertical
rays of injurious emanations, as of the moon at night, of Saturn and
Mars, of persons infected with contagious disease, of the evil eye;
and we must adapt our bodies to the reception of emanations known
to be salubrious . . . . . . . . . . 142-143

CHAPTER VIII.

We may give mathematical disproof of what is one of the greatest
errors in philosophy: namely, that matter is of one kind only, the
differences of substance resulting only from difference in form. The
consequence of this error would be to elevate matter to equality with

PART IV.

cvii

VOL. I. PAGES

God. Nor is it enough to say that matter is infinite potentially, but
not in essence. Nor that it is potentially infinite in the sense in
which this is said of continuous quantity. For to attribute to matter
existence in indefinite numbers of substances is to attribute to it
infinity, not merely potentially, but in act. The contradiction in which
this lands us may be set forth geometrically. Nothing infinite can
have finite power, and conversely nothing finite can have infinite

power . . . . . . . . . e. . 143-148

CHAPTER IX.

When two spheres are brought together, and the straight lines from
their centres to the point of contact are continuous, the question
arises whether these lines become one, or whether we are to
regard them as two. Averroes maintained a distinction between
mathematical quantity and natural quantity. But this distinction
is untenable. The lines in question are two, although they have
the effect of one, and for convenience of speech may be spoken of
as one. Against the separability of different masses of matter it
is argued that if two circular planes are brought into contact
and then separated, air will penetrate into the outer portion before
the inner, hence for a moment there will be a vacuum in the central
part. But the answer is that the separation is not simultaneous
throughout the whole surface of the plane, so that the air penetrates
gradually. From the divisibility of matter, it is not to be argued that
the world is composed of an infinite number of material particles, as
Leucippus and Democritus maintained. Were this so, it might be
inferred that the diameter of the square was commensurable with its
side; which Euclid in the seventh proposition o of his tenth book has
shown to be impossible . M e . 148-

CHAPTER X.

On geometrical grounds the shape of the universe can be inferred
to be spherical. No other form would preclude the possibility of
a vacuum in the course of its revolution. Cylindrical or lenticular
form would suffice if revolution took place round a certain axis. With
the spherical form revolution round whatsoever axis would avoid
vacuum. Looked at from within, it must be concave and spherical;
otherwise lines drawn from the centre of the earth to the extremities
of the universe would not be equal. Further, the sphere is that form
which under a given surface has the greatest content. It is the
simplest and noblest of forms. The water, the air, and the fire

surrounding the earth concentrically, are of similar form . — . 152-

152

v

157

cviii ANALYSIS OF THE ‘OPUS MAJUS."

CHAPTER XI.
VOL. I. PAGES

Suppose two vessels similar in shape and equal in size ; one placed
at a higher level than the other. More water can be placed in the
lower, for its surface will be a portion of a smaller sphere: the
diameter of the rim of the vessel being equal in both cases . 157-159

CHAPTER XII.

The Platonic school maintained that heaven and the four elements
corresponded to the five regular solids. For there can be no more
than five. Since in the dodekahedron the other four can be inscribed,
this was regarded as representing heaven: fire was identified with
the tetrahedron, air with the octahedron, earth with the cube, water
with the icosihedron. But the difficulty in this theory is that,
though solid masses can be built up of tetrahedra and of cubes with-
out leaving vacua, this is not the case with the other three . 159-164

CHAPTER XIII.

There can be only one universe. For, on the supposition that
there were two, both being spherical would touch in one point only,
so that a vacuum would be left, which is impossible. Further, the
universe cannot be infinite, otherwise two infinite lines, from one of
which a given portion was cut off, would be equal; i.e. the part
would be equal to the whole, which is impossible . . . 164-165

CHAPTER XIV.

Unity of time does not imply unity of matter. Nor is it needful to
suppose plurality of ages (aeva). The subject of time is not matter,
but motion. The subject of motion is not matter, but body composed
of matter and form. Motion is of linear dimension. Prior excludes
posterior, past excludes future. But as to the present being a point
having no dimension, there is no such exclusion ; one point does not
exclude another: many points occupy the position of one. One
present moment suffices for all present moments. Hence time is one.
And so to the conception of aevum the same applies. It is single and
not multiple . CT . . "M . «+ 165-167

CHAPTER XV.

In a body falling to the earth's centre, a strain is involved: since,
though the central point of the body tends directly towards the
centre, the extreme points are prevented from doing so. From this
strain heat results. This is shown by experiment to be the fact. But
on geometrical grounds the reason of this fact appears; and our
knowledge of it becomes thus more complete . . . «. 167-109

PART IV.

CHAPTER XVI.

cix

VOL. I. PAGES

When two equal weights are placed in the scales of a balance, and
one scale is depressed, the lower scale being nearer the earth's centre,
will have greater gravity. But this is counterbalanced by the
tendency of the upper scale to fall in a curve of more rapid descent
than the lower. The oscillation of the arms of the balance above and
below the horizontal is due to the motion communicated to the

surrounding air . . . . . . M; . . 169-

THE APPLICATION OF MATHEMATICS TO SACRED

174

SUBJECTS . . 0. 5 175-404

We have now seen the potency of mathematics as applied to things
secular. We now pass to its application to things divine. Philosophy
is impossible without mathematics: theology without philosophy.
All knowledge is contained, directly or indirectly, in Scripture.
Therefore for the right understanding of Scripture, knowledge of
nature is needful. In Scripture there is a double meaning, literal
and spiritual. The first is necessary for the second : and, as we have
shown, mathematical knowledge is necessary for it. It is certain that
the patriarchs studied mathematical science and transmitted it to the
Chaldaeans and Egyptians, whence it came to the Greeks. "This is
proved by Josephus, and confirmed by Jerome and other doctors, and
also by such philosophers as Albumazar. Further, the fathers have
themselves extolled the value of mathematical science, as may be
shown by passages from Cassiodorus, Augustine, Bede and others.
The importance of mathematics to theology may be considered under
seven heads . . . . . 175-

First head. Knowledge of the heavens. Astronomy shows
the insignificance of the earth as compared with the heavens. The
smallest of the stars is larger than the earth, and the largest star is
insignificant compared with the space of the sky. The earth can
be traversed at foot pace in three years. A star moving with immense
velocity takes thirty-six thousand years to compass the heavens.
Further, it is to astronomy that we look for solution of many theo-
logical problems, as for the substance of which the heavens are made,
the position of paradise and of hell, the influence of heavenly bodies
upon the things of earth. Again many obscurities in the text of

Scripture can only be cleared up by astronomical research . 180-

The second head is that of sacred geography. By geography,
which is dependent on astronomy, we can determine the precise
position and the physical conditions of the places named in Scripture.

180

183

cx ANALYSIS OF THE ‘OPUS MAJUS.’

VOL. 1. PAGES
All these, apart from their literal importance, have a distinct spiritual
signification. The river symbolizes the world ; the Dead Sea, hell ;
Jericho, the flesh ; the Mount of Olives, spiritual life; the vailey of
Jehoshaphat, humility; Jerusalem, the soul in the enjoyment of
peace, or again the Church militant and triumphant. Minute
research will reveal numberless intermediate meanings . . 188-187
The third head relates to sacred chronology. Scripture presents
to us a succession of times, with regard to which precise knowledge
can only be given by mathematical astronomy. ‘The starting-point
is the creation of the world. Was this in the autumnal or the vernal
equinox? From what is said in the Old Testament as to the Feast
of Ingathering [Exodus xxiii. 16] we should infer the former. Yet
Jewish and Christian commentators adopt the latter view. It will be
for astronomy to decide this difficult point. Further, the question of
the longevity of the ancient patriarchs has to be considered. One
mode of accounting for it may be the more favourable position of the
sun and the planets in primitive times. Again there is the problem
of the Deluge. The right interpretation of Josephus points to
November as the month in which it. began. Lastly, did night come
before day, or the converse? The former would seem to be the true
view . . . . 187-195
The fourth head deals not with chronology in general, but with
the definition of periods. How is the beginning of a lunation
to' be fixed? by astronomical calculation, or by the moment when the
new moon is visible? The actual lunation is variable. The average
lunation must be used. The Jews use the Metonic cycle of nineteen
years, or 235 lunations. This gives twenty-nine days, twelve hours,
and 4$ of an hour for the mean lunation. They take a period of thir-
teen lunar cycles or 247 years, within which all their festivals recur at
the same moment. The lunation is considered to begin with the sun-
set immediately following the computed time. "These considerations
may be applied to the date of the Creation, of Noah's issue from the
ark, of the Passover, and finally of the Passion. The current belief
in the Latin Church is that Christ was born in the second year of
a lunar cycle. and died on March 25 (a. d. viii Kal. Aprilis', the moon
being at the fifteenth day (the Greeks holding that it was the
fourteenth day). Against this much may be urged. It implies that
it was in the thirteenth year of a cycle. From the computation of
S. Dionysius this would involve the Passion taking place on a Sunday,
which isimpossible. A table is appended showing one solution of the
difficulty. This wou.d show the date of the Passion to be April 3
(a. d. iii Non. Aprilis), on the fifteenth year of the lunar cycle, Christ
being then thirty-two years old. This view is offered to the Pope for
consideration . . . . . 2 . . 195-210

PART IV. cxi

VOL.I. PAGES

Fifth head. This relates to geometrical forms; and again it
has to be premised that the spiritual meaning of Scripture is not
to be grasped, unless the literal meaning be first understood. The
precise form of the ark, the tabernacle, the temple should be pre-
sented to us with mathematical accuracy ; it will then be possible to
interpret their mystical signification. A remarkable case in point
is the rainbow, of which we are told that it is a symbol of God's
promise as to the Deluge. The meaning of this is misunderstood
for want of understanding the geometry of the rainbow, which is
produced by the solar rays striking on the raindrops and being
refracted or reflected thence. Only by geometry can such a text
as that of the threefold burning of mountains by the sun be under-
stood. The mountains receive direct rays. The rays reflected by
them are focussed in the air and contribute to warm them. Lastly,
there are the doubly refracted rays passing from the sun into the
clouds and from the clouds into the air. Again, the rays may fall
either vertically, or obliquely, or horizontally, producing different
effects in each case. The laws as to the passage of light through
space apply equally to the passage of all other forces. Of all these
things there is a spiritual interpretation. Direct vertical rays may
be compared to the action of grace on the righteous ; they neither
reflect nor refract it. In the wicked we see the light driven away,
reflected: in the imperfect it is bent aside, refracted. It is to be
noted here that the geometrical form of the triangle is specially
adapted to symbolize the Trinity. Each angle is distinct yet each
embraces the whole space. Again, our geometrical principles as to
the action of forces may be applied to the estimation of the forces of
temptation, which act in proportion to their proximity. Hence the
need of keeping the tempted as far removed as possible from the
objects which tempt . . . . . 210-219

Sixth head. This relates to number. (a) As with geometrical
forms, so with number there is a spiritual meaning behind the literal
meaning. (^) For the understanding of chronicles it is necessary to
know the different systems of numeration, and to be able to convert
one into another. (c) There are various arithmetical operations in
the Jewish law requiring a knowledge of the subject. (Z7) There are
many corruptions in the text which only an arithmetician can unravel.
(e) The perfections inherent in the number three can only be under-
stood by arithmeticians. (/) Arithmetic is necessary in astronomy,
which we have seen to be needful to the theologian. Some instances
of its value in astronomy are here given. We have to define the
length of a line on the earth's surface corresponding to a degree.
We must take a mile as 4,000 cubits: a cubit as 1} feet. How many
miles must we walk northward from a given point to find the pole-

cxii ANALYSIS OF THE ‘OPUS MAJUS.

VOL.I. PAGES
star a degree higher in the sky? We shall find the result to be
fifty-six miles, 2,984¢, cubits. From the diameter of the earth we
obtain its circumference and its surface. The distance of the heavenly
bodies may be measured in semidiameters of the earth — 3,250 miles.
Alfraganus estimates the distance of the starry sphere to be 20,110
semidiameters ; which gives the diameter of this sphere as
130,715,000 miles. From this we can calculate the circumference
and surface. The longest distance of Saturn is the semidiameter of
this sphere, or 65,357,500 miles, of Jupiter 46,816,250 miles, of Mars
28,847,000 miles, of the Sun 3,965,000 miles, of Venus 3,640,000 miles,
of Mercury 542,750 miles, of the Moon 208,541$ miles; the shorter
distance of the preceding planet being always equal to the longer
distance of the succeeding. As to the ninth and the tenth heaven we
have no scientific knowledge. As to the height of the atmosphere there
is great uncertainty. For measuring the apparent diameters of the
Sun and the Moon recourse has been to water-clocks; the number
of drops issuing from the beginning to the end of the Sun's rising
have been compared with the number issuing during a revolution
of the heavens. But there are more accurate methods by astrolabes
or quadrants. From these, and from observations of eclipses, the
moon's diameter is estimated at 45 of the Earth's diameter. The
Earth is therefere about 31} as large as the moon. Similarly the
Sun will be found to be 170 times as large as the Earth. Mercury is
zs5bjos of the Earth. In a similar way the relative magnitude of
the other planets as compared with the Earth may be determined.
The fixed stars are 1,022 in number, and are divided into six groups
according to this magnitude. Those of the first magnitude are 107
times as large as the Earth; of the second, ninety times the Earth's
magnitude: of the third, seventy-two times, of the fourth, fifty-four
times, of the fifth, thirty-six times, of the sixth, eighteen times. But
besides these there are infinite numbers of other stars whose
magnitude cannot be determined . . . . 219-236

Seventh head. Music. The theologian ‘should be acquainted with
the theory, if not with the practice, of vocal and instrumental music.
Music covers the whole ground of recitation, punctuation, accent,
things necessary for prose as well as poetry. Of instruments again
many are spoken of in Scripture, and each has a spiritual as well as
literal meaning. Nor must dancing, which may be called visible
music, be forgotten. . . . . 236-238

We have now to consider certain objections that have been raised
with regard to mathematical science. Mathematic has been con-
founded with magic, and put on the same level as fortune-telling,
witch-craft, and the preparation of charms and incantations. It has
been credited with the doctrine that human actions are absolutely

PART IV. — cXiii

VOL. I. PAGES
determined by stellar influences. But this doctrine is explicitly |
condemned by all philosophers, both of Greece, Rome, and Arabia.
They maintain free-will against any such supposed physical necessity ;
and they reprobate utterly the use of charms and incantations. The
prejudice against mathematics was strengthened by the strife of
heathenism. against Christianity, in which magic was used by the
former, and in which Christian miracles were accounted for by magic.
The reproach of denying free-will remained, when the suspicion of
magic had passed away. But examination of Ptolemy’s works shows
clearly that he never fell into this error. He, and his principal
Arabian commentators, held that the forecasts of the future revealed
by astronomy indicated general tendencies only, and did not impose
any specific compulsion on individual actions. But this distinction
bas not been always perceived in the attacks made by Christian
wri'ers on mathematical science. They have confounded true science
with false. . . e. . 288-249

What is true is that the influences of the : stars implant certain
tendencies to good or evil action, always at the same time leaving free
scope to human will. It is evident that physical temperament is one
of the factors in human action. Temperament is itself a result of the
influence of the stars. That climate affects character is obvious to
every one. And this influence is to be traced zz: minimis. From
every part of the sky to every point of the earth's surface a cone of
forces proceeds, affecting more or less every community and every
individual, though not in such a way as to override free-will. These
things would be studied by physicians if they were better acquainted
with astronomy. In the case of a commonwealth, or of the states-
men who direct commonwealths, it is more easy to discern the
nature and degree of such influences, and to forecast their re-
sults. And great advantage will accrue: to the community from
doing so . «x . . . 249-253

We now arrive at the practical applications of mathematical science
to Church government. The first of these is the proof offered by
astrology of the superiority of Christianity to other religions, and
the insight given into the nature'of Antichrist. It must be under-
stood that the heaven is to be divided into twelve Houses; that is,
taking the quadrants formed by the intersection of the meridian
and.horizon, each may be divided into three. To five of the
seven planets two Houses are allotted; to Mercury and the Moon
one each. The association of Jupiter with each of the other
planets has a special meaning. If with Saturn, the reference is to
Judaism. With Mars, to Chaldaeism. With the Sun, to Egyptian
religion. With Venus, to the Saracen worship. With Mercury,
to Christianity . . . . m e o £3; 253-258

VOL. I. h

cxiv ANALYSIS OF THE ‘OPUS MAJUS.

VOL. I PAGES
But there is another and more essential meaning of the word
House. If we divide the ecliptic into twelve parts, and‘ through the
divisions conduct circles intersecting at the poles of the ecliptic,
the regions between any two of these circles is in the true sense
a House; bearing the name of its zodiacal sign. The principal
House of each planet is that in which it was created. Leo is the -
House of the Sun, Capricorn of Saturn, Sagittarius of Jupiter, Virgo
of Mercury. There are certain signs for each planet which are
called its Exaltation; for the Sun Aries, for Saturn Libra, for Jupiter
Cancer, for Mars Capricorn, for Venus Pisces, for Mercury Virgo.
The signs are divided iato four groups: three, Aries, Leo, Sagittarius,
are hot and dry: three, Taurus, Virgo, and Capricorn, are cold
and dry : three, Gemini, Libra, Aquarius, are hot and moist: three,
Cancer, Scorpio, and Pisces, are cold: and moist. A planet being
in any of the groups to which its House belongs is said to be in its -
Triplicity. We have further to consider Boundaries and Aspects.
With regard to Boundaries, they vary for each planet and for each
sign. With regard to Aspects, each sign is divided into three equal
portions of ten degrees, and a portion is assigned to each planet in
sequence . . . . . . 958-261
It will appear in the result that Mercury has manifold and strong
connexions with the sign of Virgo. As Mercury is connected with
Christian faith, so is the Moon, with its irregular motions, connected
with the corruption of that faith. The conjunctions of the planets,
and especially those of Jupiter and Saturn, throw light on important
epochs of history. These are of three kinds, occurring respectively
in periods of 20, of 240, and of 960 years. Judging from what took
place at previous periods, it may be inferred that the Mahometan
faith will not be of much longer duration. There yet remains the
period of Antichrist; on the date of which study of these astronomical
periods may throw light . . . . . 261-269
A second application of mathematics to the service of the Church
is the correction of the Calendar. The Julian Calendar fixed the
length of the year at 365) days. Hence the arrangement of an
additional day every fourth year. But this estimate is known to be
too great by the 43s part of a day. Therefore in every 130 years
there is an accumulated error of one day . . . . 269-271
Again, it has been assumed that the equinoxes and solstices
occurred on fixed days. These days in the beginning of the Church
were fixed thus: the winter solstice on December 25, the vernal
equinox on March 25, the summer solstice on June 24, the autumnal
equinox on September 24. Subsequently the vernal equinox was
transposed to March 21. Hence the earliest Easter, being the first
Sunday after the full moon succeeding to the vernal equinox, was

PART IV. CXV

VOL. I, PAGES
March 22. But the winter solstice and the vernal equinox are no
longer on these days. At the present time the winter solstice is
on December 13, the vernal equinox on March 13, the summer
solstice on June 15, the autumnal equinox on September 16. In
every 125 years the error of another day accumulates. The con-
sequence of this error is that Easter is observed at the wrong
time, in the third and in the fourteenth years of the lunar cycle.
The error will be far more serious in future centuries, so that
ultimately the period when Lent should be observed will be at a
time when every one is eating meat . oe . . . 271-274

Further, there is a serious error in the computation of the lunar
cycle. Successive periods of nineteen years differ in length, some
containing four, others five leap-years. The only satisfactory period
would be thirty Arab years of twelve lunations, making 10,631 days.
It is true that the Council of Nice adopted the lunar cycle; and
120 years afterwards it was confirmed by Pope Leo, The error at
this latter period was not more than a day. Since that time astro-
nomy has been in disrepute, for reasons already mentioned, and no
one has been found who could clearly indicate the error, with
sufficient authority ; although in the time of Pope Hilary some con-
sideration was given to the subject. At the present time the error
is so great as to attract the ridicule of Jewish and Arab astronomers,
and deserves the serious attention of the ruler of the Church . 275-285

GEOGRAPHY,

We now pass to the influence of the heavens upon things terrestrial.
In all things that are brought forth on earth, whether for good or evil,
the sun and the heavens are the moving cause. We have therefore
to consider the different ways in which different parts of the earth’s
surface are. affected by these agencies. Imagining that surface
divided by the equator and the equinoctial colure into four equal
portions, we have specially to consider the portion contained between
the equator and the poles, bounded east and west by the colure.
What proportion does land bear to water? Ptolemy thought one-
sixth, but other authorities think the proportion much greater.
Seneca and Pliny look on the space of ocean dividing the west of
Spain from the east of India as inconsiderable. Under the word
Spain we must include a vast tract extending westwards across the
Straits of Gibraltar, in the direction of Atlas. On the whole, it seems
probable that the land known to us from east to west extends over
more than half the earth’s circumference. Further, it seems probable

h 2

.cxvi ANALYSIS OF THE "OPUS MAJUS.

VOL. I. PAGES
that the disposition of land and water may be similar on-the other -
side of the northern hemisphere to that of this side ; and the same
may be argued of the two divisions of the southern hemisphere,
especially as the sun in its annual course comes nearer to it . 286-294

Speaking of the parts known to us, Ptolemy and others have dis-
tinguished seven cZi»ta/a — marking them by the increasing length
of the longest day. The position of each place referred to is defined
by the intersection of the line of latitude and longitude belonging
to it. The zones, or c//zta/a, of Ptolemy are marked according to the
increase of a quarter of an hour in the length of the longest day up
to the sixty-first degree of latitude; thence to the sixty-fourth degree,
by half an hour's increase ; thence to the sixty-sixth by one hour's
increase. Peyond this point we come to the region where in the
summer season the sun is always above-the horizon, in winter always
beneath it. Here the divisions must be marked according as the
longest day is one month, or two or three, up to six. As to longi-
tude, it should be measured not from any arbitrary point, but from
the true east and west on the equator. The neglect of this pre-
caution has led to much confusion in the tables of Toledo; and
generally a far more accurate determination of the latitude and longi-
tude of towns and states is needed, such as can only be instituted by
apostolical, imperial, or at least regal authority. . . . 294-301

A right understanding of locality and climate concerns alike the
interpretation of Scripture, the propagation of the faith, and the wel-
fare of commonwealths. Missionaries in particular should know the
distribution of the various religions of the world; where the lost
tribes of Judea are to be looked for, where the incursions of Anti-
christ are most to be dreaded. Our knowledge of these matters,
derived from Pliny, Ptolemy and other writers of antiquity, has been .:
recently enlarged by the travels of William Rabraquis in Central
Asia . . . . . 801-305

At the tropic of Cancer | we begin t to find regions where the sun at
the summer solstice casts no shadow. Southwards to the tropic of
Capricorn the same phenomenon occurs for each place twice in the
year. And we have knowledge of regions south of the tropic of
Capricorn where the noonday shadow is always to the south. And
though in these last the sun approaches so nearly at our winter time,
and recedes so far at our summer time, as to invo.ve great extremities
of heat and cold, yet these evils may be lessened by the configuration
of mountain and plain, so that the region is habitable, as we know
in the case of the island of Taprobane . . . 805-809

We may begin our description of the habitable world with India.
Its southern coasts are washed by a branch of the Atlantic Ocean, so
vast that from the mouth of the Red Sea to the south of India is .

PART IV. CXVil

NE VOL. I. PAGES
a year's voyage. India has a third of the habitable surface. Eastof

South India is the island of Taprobane abounding in gold and jewels,

and governed peaceably by an elected king with a council . 809-310
The south coast of India passes from the south tropic north-west,

cutting the equator at Arym, a point ninety degrees from the west,

but more than that from the east. Then the coast line proceeds

south-west, passing the opening of the Red Sea, and bounding South

Ethiopia till the Indian Sea joins the Atlantic. On the Nile, at the

latitude of sixteen degrees, we find the is:and of Saba, the royal city

of Aethiopia — called also Meroe, about 700 miles from the coast. At

the same latitude, on the Red Sea, is the city of Ptolemais. Between

these two, or more probably to the west of Meroe, is Berenice the city

of the Troglodytes, who are identified with the Garamantes. West

of these are the Hesperi . . . 810 8313
Egypt is the region included between Syene and the Mediterra-

nean: divided into upper Egypt or the Thebais, and the Delta.

' The Delta extends from Heliopolis on the Arabian frontier to

Alexandria on the confines of Africa. Africa received its name

from Affer, a descendant of Abraham. Before this it had been called

Libya. Much of the northern coast was occupied by Medes,

Persians, and Armenians brought by Hercules. The interior was

occupied by Gaetulians, afterwards called Numidians, amongst whom

the Carthaginians established their empire. Between Carthage and

Egypt are Tripolis and Cyrene . . . . . 818-318
Sonething must be said of the Nile. Its origin is in Aethiopia,

probably in the region bordering on the Red Sea. Its course is for

a long time westwards as far as Meroe. Between Meroe and Syene

it is northward, and so onward to the Delta. Its inundation is in

summer, hence the difficulty of explaining it. The opinion of Thales

that it was due to northern winds preventing the outflow, is disproved

by the fact that the inundation begins in the upper part of the river.

A more probable view is that of Anaxagoras, that it is due to the

melting of snow in the mountains of Aethiopia. Aristotle rejects

this view, but gives reasons for supposing a great rainfall to occur

n summer time in the marshy regions from which the Nile

flows . . . .. 818 825
The region from the eastern bank of the N ile i is to be regarded

as part of Arabia, which also includes the vast space eastward as

far as the Persian gulf and northward through south and east

Palestine as far as the Euphrates. We can now trace the principal

positions of the Hebrews in the Desert, and also of Edom, of Moab

and of other neighbouring tribes mentioned in the Scriptures . 825-382
The region between the Tigris and the Euphrates is Assyria or

Mesopotamia, in which were the cities of Nineveh, Aram, and

—— o ————— - -— — — -

exviii ANALYSIS OF THE ‘OPUS MAJUS.

VOL. I. PAGES
Babylon. In Babylonia dwelt Noah and his sons after the deluge.
Both the Tigris and the Euphrates rise in Armenia. The Tigris
flows for some space underground before reaching Nineveh and
joining the Euphrates. The Euphrates swells in summer as does
the Nile. To the east of the Euphrates lie North Arabia and Syria,
the southern part of which is the Holy Land. Here a more detailed
description becomes necessary . . . . 332-335
Beginning with the coast, we find Gaza on the confines of Egypt
and Palestine, then proceeding northward Ascalon, Joppa, Azotus,
Caesarea, Acon, Tyre, Sarepta, Sidon, Barut, Gibeleth, Tortosa,
Laodicea. From this last to Antioch is two days’ journey. From
Antioch to Tarsus in Cilicia three days’ journey . . . 835 836
Passing to the interior, we find Beer-sheba at the southern
boundary. Twenty miles to the north is Hebron, the place of
sepulture of the patriarchs. Near Hebron is Carmel, and a little
to the east, the town and mountain of Ziph; fourteen miles to the
north is Bethlehem, which is six miles to the south of Jerusalem.
This city is twelve leagues from Joppa, and nine leagues to the east
of it is Jericho. Tekoa, the country of Amos, is twelve miles to the
south-east, and here we come to Pentapolis, the region of the Dead
Sea, where nothing lives, where bodies that usually sink in water
float, lumps of bitumen are found on the surface ; here too are found
the apples of Sodom . . . . 836-339
The Jordan flows into the Dead Sea. [ts origin is by two
branches from Lebanon, and it passes through the lakes of
Gennesareth and Tiberias. North of Jericho is Scythopolis or
Bethsan. Westward and to the north of Jerusalem is Anathoth
the birthplace of Jeremiah. Thence northward, twelve leagues from
Jerusalem, is Samaria, now called Sebaste. North-eastward is the
plain of Megiddo; north of this and east of Acon, at seven leagues’
distance, is Nazareth. Two leagues further east is Mount Tabor,
and the city of Tiberias, and the lake of that name, containing the
purest waters of Judaea ; it is near but distinct from the lake of
Gennesareth, To the north, separated by a desert region, are
Bethsaida and Capernaum. East of Acon, and two leagues north
of Nazareth, is Cana of Galilee. Still further north is Corazaim.
We are thus brought into the region of Lebanon, whence fertilizing
waters descend to the neighbourhood of Tyre and Sidon . . 389-343
Beyond Jordan, north of the Dead Sea, is the citadel of Macheron.
Here was the tribe of Reuben. North is Pella, at the boundary of
Palestine on that side of Jordan. Eastward were the kingdoms
of Og and of Sihon. On their boundaries is Ramoth-Gilead, not
far from the range of Anti-Lebanon. In this neighbourhood is the
city of Damascus, situated four days’ journey from Jerusalem . 348-844

PART IV. cxix

VOL. I PAGES
Summing up these details, we may speak of Syria as including the
space from the Euphrates to the Mediterranean, and from Cilicia to
Egypt. It is divided into the provinces of Syria Comagena, Syria
Caele, Phoenician Syria, and the three divisions of Palestine, Galilaea,
Samaria and Judaea. Gomage is the capital city of the first,
Antioch of the second. Phoenician Syria extends from the south of
Lebanon to the north of Palestine. It -contains the cities of
Damascus, Tripolis, Tyre and Sidon; and beyond -the: Jordan,
Pella and Mount Hermon and Mount Gilead . . . 844-317
The three regions of Galilaea, Samaria, and Judaea belonged to
the Hebrews, who held the region beyond the Jordan from the
Dead Sea to Mount Hermon. In the north part of Galilee is
Decapolis. South of this Ithuraea or the tetrarchy of Trachonitis.
The northern part of Galilee contained a mixed race of Jews and
heathen. Lower Galilee begins with the lake of Tiberias. South
of Galilee is the district of Samaria, and south .of Samaria is
Judaea .. - « 941-848
We see then that the amount of territory possessed by the Jews
was but small. From Dan to Beer-sheba is but 170 miles, from
Joppa to the Jordan, not seventy. To this, their possessions -east
of the Jordan areto beadded . . . . «© . « 848-850
Passing to.other regions of the world, we find the range of Mount
Taurus extending from the Indian Ocean, separating Parthia,
Mesopotamia, and Syria, from the Scythian regions, and from
Armenia and Cappadocia, and finally reaching Cilicia. n its
course this range receives various names, as Caucasian, Caspian,
Hyrcanian and many others. Media, Persia, Parthia, lie between
the Indus and the Tigris east and west, having the Caspian Sea
and Caucasian mountains to the north, and the Persian gulf to the
south. The Parthian empire coincides with :what was once the
Persian . . . . . 950-352
India lies east of the Indus, bounded on the north by the Seric
sea and by the mountains which extend east from the Caucasian
range. Vast as the Indus is, the Ganges flowing from the Caucasus
into the Eastern Ocean is yet greater. On the Ganges live the
Brahmins, living a life of extreme temperance and chastity, and
attaining great longevity. North of India is the Scythian ocean and
the Caucasian range already spoken of . . . . . 892-353
Westward from India, at the confines of India and Parthia, we
find the Caspian gates on the south shores of the Caspian or
Hyrcanian Sea. This sea is entirely inland, formed by great rivers
flowing from the north. West of Parthia is Hyrcania, and then the
greater Armenia divided by the Euphrates from Cappadocia. The
lesser Armenia is identified with Cilicia. This region from south to

cxx ANALYSIS OF THE ‘OPUS MAJUS.

VOL. I. PAGES
north is of about four days' journey, bounded by Lycaonia, now
called Turkia, and including several ancient provinces as Lydia and
Phrygia. The whole of this country is now called by the Greeks
" Anatolia, otherwise Asia Minor. . . 853-856
Dividing this from Europe is the Arm of St. George, with Constanti-
nople on its left shore, leading to the Pontic Sea, which extends 1,400
miles from east to west. From north to south its narrowest part is
between Sinopolis and the province of Cassaria (Crimea), on the east
of which is the shallow sea of Maeotis formed by the mouth of the
Tanais (Sea of Asof). This river flows from the Riphaean mountains
in the extreme north. From the Tanais to the Danube is a vast
desert plain, which it takes the Tartar horsemen two months to
traverse. It is bounded by Poland and Hungary. To the north of it
is Great Russia—bounded to the west by the Baltic Sea, beyond
which lie Denmark, Sweden, and Norway. Then across a great
expanse of sea Scotland and England lie to the west, and beycnd
them Ireland . .. - « . 996-858
At the north of the Baltic Sea is Esthonia, eastward is Livonia,
and south of it Courlandia, then Prussia and Pomerania. On the
confines of Dacia and Saxonia is the port of Lubec. In the Baltic
hes the island of Gothland. South of Prussia is Poland; south of
this Bohemia, then Austria; west of Austria is Alemannia, France and
Spain ; eastward is Hungary bounded to the north-east by Albania,
which extends as far as the river Don, having Bulgaria, and Con-
stantinople, and the province of Cassaria to the south, and Russia
to the north. North again of Russia are the Hyperboreans, a peaceful
long-lived race, with a climate far more equable than might be ex-
pected from its position. Among these northern nations is a great
variety of religions. The Livonians, Curlandians, Prussians, Estho-
nians are pagans. The Ruscenes are Greek Christians, though in
common with the Poles, Bohemians and many others, their language
is Sclavonian. The Tartars, who have subjugated almost all nations
from the Danube to the extreme east, lead a wandering pastoral life.
Some of the tribes subject to them are pagans, others follow the
Mahometan law . . . . 9958-361
On the north-eastern border of the Pontic Sea is the land of the
Georgians, and Corasiminians, where of old Amazons used to live.
South of these are Cappadocia and Armenia. From the mountains
of Armenia flow the Euphrates and Tigris. Here Noab's ark rested.
SS. Bartholomew, Judas, and Thaddeus suffered martyrdom here ;
and at one time there were 8oo Christian churches ; though Rubruquis
found but two, and these small. The city of Naxuana, the principal
town of Armenia, now destroyed by the Tartars, was visited by him,
as he passed up the river Araxes. In the mountains to the east he

PART IV. cxxi

VOL.I. PAGES
found the Alani who are tolerant and orthodox Christians, and east
of these the Lelgi who are Saracens . . : . 861-804
This brings us to the southern shore of the Caspian Sea, where
Alexander erected the Caspian gates, as a protection against the
incursion of barbaric tribes from the north. Rubruquis passed
through these gates This being the region of Gog and Magog,
who after ravaging the world will become at last the foes of Anti-
christ, it is of the highest importance to the Church that its geo-
graphy should.be known. The Caspian Sea, extending from west
to east, is as large as the Pontic Sea, and to compass it is a four
months' journey. Rubruquis traversed its northern shore in going
to the Tartar emperor, and its western shore in returning. It has
no connexion with the ocean, being formed by the Ethilia (Volga)
and other rivers. From the Don to the Ethilia was the land of
old called Albania, till lately occupied by the Cumani. East of the
Volga also the Cumanians dwelt till dispossessed by the Tartars.
Northward is Asiatic Bulgaria, whose inhabitants are of the same
race and language as those on the Danube. East of this region is
the land of the Huns . . . . . 904-801
These regions extend as far as Caracathaia or Black Cathay.
Here it is that the emperor of Tartary dwells, changing his abode
according to the season. It has sometimes been said that Prester
John lived here, but his kingdom, formed of a Nestorian tribe, was
far more westerly. His power was established on the death of Coir
Cham. Prester John was succeeded by his brother Unc, who took
the title of Cham, and who reigned for a time in Cara Corum, the
principal Tartar city. But Unc Cham was destroyed by the Tartar
leader Chinghis. His grandson, the son of Unc's daughter, is Mangu
Cham to whom Rubruquis was sent by the King of France. The
name given to these Tartars by themselves is Moal. They have
by this time conquered nearly all Asia ; they hold Russia, Bulgaria,
and the neighbourhood of Constantinople . . . . 867-871
Eastward of Black Cathay are several tribes with peculiar habits ;
and beyond them, to the extreme east, is Great Cathay, the nation
of the Seres, whence comes silken clothing. The inhabitants of this
country are skilful workmen, and acquainted with the medical
properties of plants, and carefully study the changes of the pulse
and other symptoms of disease. They use paper-money. They are
for the most part idolaters (Buddhists) ; but Saracens are mixed with
them, and also Nestorians, who preach and practise a corrupt form of
Christianity. Their patriarch professes willingness to acknowledge
the authority of the Roman See. Of these various peoples some write
from above downwards and from right to left. Others write as we
do, and with our letters. The inhabitants of Eastern Cathay paint

cxxii ANALYSIS OF THE ‘OPUS MAJUS.

*. "4 VOL. I. PAGES
rather than write, forming groups of letters, each group representing
a sentence. The geography of Western Europe does not require any
detailed description . 4e. —. ^. 4. 811-8176

AsTROLOGY.

This geographical description should be followed by an account
which I have not been able to complete, (a) of the stars, (4) of the
planets, (c) of the way in which the climatic disposition of each place
is affected by them, (7) thus making true astrological judgements
possible, (e) with the result of promoting the safety of the state. All
that I can do is to offer a few remarks on these points. Each of the
fixed stars has properties of its own. Those of the twelve signs are
specially important to us. .À special treatise would be needed to
describe these characteristics adequately and to point out the way
in which we.are affected by them. Each planet has also its special
character, modified by the zodiacal sign in which they are situate, by
their aspects, that is by any two or more of them being in the same,
in opposite, or in intermediate directions, by the position reached in
their epicycle or eccentric, and by.the House of the heavens which
they may be occupying. This again requires a special treatise. 376-379

From this we pass to the effects produced by the.heavens on places
and things.upon the earth. The sun may be said to beget no less
than the parent: and the sun's influence endures through life. Each
spot on the earth's surface is the centre of a distinct horizon, and is
thus affected differently from every other. We have to consider its
distance from the pole and the equator, what stars are in the zenith,
and what signs are dominant there. On all these points the Hebrew
astronomers are specially instructive. Special parts of the body are
affected by different constellations, and by the position of the moon
in them. Each hour of the day is under the control of a particular
planet. On medical art especially, but also on all.other departments
of human activity, the bearing of all this is obvious. The quarters
of the moon must be of course studied, and also the daily transit of
the moon through a portion of the.Zodiac .. "e . + 879-385

Besides the revolutions of the moon and sun, .attention must be
given to those of the planets, especially to those of longer period.
The comet for.instance of 1264 was due to Mars, and was related to
the wars in England, Spain, and Italy of that time. All planetary
conjunctions are important; but of special importance to man's
welfare are the conjunctions of the Moon with stars of various nature.
Position in the orbit must always be examined. In the apsis
planetary force is greatest; weakest in the oppo:ie point. We

a— M ee — € M — — - - —— — —— — —

PART IV. cxxiii

VOL.1. PAGES
must observe too in what house each planet may be; for on this
the whole complexion of the year may largely depend. On the
foregoing data we form our judgements of events past, present, and
future. As a first step to this we must form accurate astronomical
tables exhibiting the position of the heavenly bodies at any given
date. Comparing these positions with the political events of such
a date, we obtain methods for forecasting future events. Our best
authorities on this subject are Albumazar, Ptolemy, Haly, and the
Hebrew astrologers. A work of Aristotle on celestial impressions
should also be translated . .. . . . . . 885-390

Next comes the question, How far can this knowledge guide our
action? We cannot do away with the force resulting from any
special position of the stars: but we can modify-our.own action so
as not to be adversely affected by it. If we know that great cold
is coming, we can make provision against cold. Similarly the
trained astronomer will provide against pestilence, or any other
calamity which he sees impending. ‘Of such modifying influences
Moses and Solomon have given examples recorded by Josephus.
Another instance is the advice given !by Aristotle to Alexander as
to the treatmerit.of certain perverse tribes : Change their atmosphere
and thus change their morals. .. - +» + 890-394

What deters students from the examination of this subject is fear
of the imputation of magic. Doubtless astrology may be turned to
a bad account; but so may the most useful of tools. Men do not
dispense with weapons because malefactors use them, ‘nor cease to
go to law because some lawyers are dishonest. So, again, there is
a strange force in certain words, uttered with full consciousness
of their meaning, which may co-operate with stellar forces, ‘This
too has been abused for purposes of magic and witchcraft, and dis-
credit has been thrown on such agencies, which yet in ‘wise hands
are useful. Like the stars, the human soul, which is nobler than
they, emits forces from itself, which acting in harmony with stellar
forces may produce great results. The objection often made that,
when the stars act on any object, they must act equally on other
objects in the same horizon, is of no account: for no two objects are
in the same horizon . . » » 5... 894-398

Fascination, again, is a word with a bad sound. Yet important
truth is contained in it. Influences radiate from certain persons,
which may be good or bad, and which may be concentrated by
a strong will and directed to a special object. Words used with this
concentrated purpose may have great power. The exercise of
miraculous power by the saints has been accompanied by words.
We need knowledge of all these forces to resist the coming power
of Antichrist. It is certain that the Tartar conquests have been

CXXIV ANALYSIS OF THE ‘OPUS MAJUS.

VOL, I. PAGES
largely assisted by confidence in their astrologers. Should they
make common cause with the Saracens, the results to Christendom
may be disastrous. The children’s crusade in the last century, and
the fascination exercised by the Shepherd in our own time, are
proofs of what hostile influences may do if not arrested promptly.
What is needed is that all these influences, instead of being con-
temptuously ignored, should be carefully studied, and used under the
direction of the Head of the Church as a defence against the inroads
of Antichrist . . . . . . . . . . 998-4038

ANALYSIS OF THE 'OPUS MAJUS-

PART V.
OPTIC. PART I.

VOL. U. PAGES

In this section there are three parts. The first explains the general
principles of vision. The second deals with direct vision. The

third with reflected and refracted vision . . . . . I-

In Part I there are twelve Distinctions.

First DISTINCTION, DEALING WITH THE GENERAL CHARACTER
OF OPTICAL SCIENCE, AND WITH THE ORGANS OF VISION,

166

PSYCHICAL AND CEREBRAL . . . . . . . . 1-12

CHAPTER I.

Tbe superiority of vision to other senses bas been pointed out by
Aristotle and other authors. Vision reveals the difference of things.
It supplies a knowledge of the heavenly bodies. It is the channel
of experimental knowledge. Hearing can give faith, but not proof.
Of the other senses we need not speak. Therefore the sense of
vision becomes the object of a special science . .

CHAPTER II.

The first thing is to determine the organs of the sensitive soul,
which are to be found in the brain. Others have told us that the
visual nerves issue from the brain; but the account given is defective.
The brain has two membranes— the Dura Mater, lining the cranium ;
the Pia Mater, enfolding the brain. The brain has distinct chambers,
or cells, each of which has its own function. In the anterior part of
the first cell is sensus communis. This takes cognizance of, and
distinguishes, the impressions brought by each special sense. But it
is unable to retain these impressions, being loose and slippery. In
the back part of the same cell there is therefore the organ of
Imagination, which, being neither too moist or too dry, can retain and
store up the material received by sensus communis. The combined
operation of these two organs is called Phantasia . .

1-3

4-5

cxxvi ANALYSIS OF THE ‘OPUS MAJUS.

CHAPTER III.
VOL. il. PAGES

The attributes, or properties, of which sense takes cognizance may
be reduced to twenty-nine heads. Nine of these are apprehended
by some special sense; as colour by sight, heat by touch, sound by
bearing. The other twenty may be called sensibilia communia,
because apprehended by all, or by more than one, of the special senses,
Distance, position, figure, number, motion, rest, are among these . 5-7

CHAPTER IV.

But animals, though they have not intellect, have other faculties
than those implied in the apprehension of these twenty-nine pro-
perties. First there is the instinct prompting flight from an animal
of a dangerous species, or approach to one of its own, independently
of experience. Each object in nature has its own constitution or
complexion, and radiates corresponding impressions (species) which
concur with those of like complexion, or disagree with those of unlike.
They operate on special and on common sense, but are taken
cognizance of by a higher faculty of the sensitive soul, which we may
call the estimative sense, and may locate in the posterior cell of the
brain. But as in the case of sensus communis, it does not retain its
impressions, and needs another faculty acting as its storehouse, the
memorative faculty. Midway between these two divisions or cells of
the brain is the cell devoted to the cogitative faculty, the mistress
faculty in brutes which have not true reason. By this faculty the
spider weaves its web, the bird its nest, In man the rational soul,
coming from without, uses tbis cogitative faculty as its chief in-
strument . . . . . . . . . . " . 4-9

CHAPTER V.

That we do not find this view of the threefold division of the brain
and of animal faculty in Aristotle is due to imperfect translation.
It can be got from Avicenna, who has been better translated. And
Avicenna is the greatest philosopher since Aristotle. In any case
it will not do to confound the faculty which stores sensations with the
faculty which stores judgements, under the common name of memory.
It must further be stated that while placing these faculties in the
brain, the substance of the brain is not itself sensitive, as Avicenna
points out, respectfully correcting Aristotle on this point. We must
remember however that the sensitive soul has a twofold organ—the
brain and tbe heart. The latter is the true seat of all life, as
Aristotle maintains: the former is that which first receives im-
pressions and in which the various operations of the senses are
separately manifested . . . e . . . e . 9-12

PART V. cxxvil

VOL. Il, PAGES

SECOND DISTINCTION. . . . . . . . . 12-18
CHAPTER L

On the origin of the optic nerves Clearly the function of vision
cannot be understood without a knowledge of the structure of the eye.
Most writers on Perspective have ignored this part of the subject,
or contented themselves with a bare reference to work on medicine.
I hope however to make the matter clear by reference to three
authorities — Alhazen, Constantine, and Avicenna. There are two
cavities in the fore part of the brain called ventricles, one on the
right, the other on the left. From. these the optic nerves issue.
They meet and cross ; the right nerve passing to the left eye, and
conversely. In the hollow of the eye the nerve spreads itself out
in spherical form, Each nerve consists of three coats, the innermost
derived from the pia mater; outside this is one coming from the
dura mater; these two are wrapt in a third, coming from the lining
of the skull . . 8000. 5. 5. 5. 5. 5 o. . 12-15

CHAPTER II.

Thus the eye itself consists of three coats; containing three
humours, and a structure like a spider's web (tela araneae). The inner-
most is called by Avicenna and others the retina, and is supplied with
veins, arteries, and slender nervous fibres; the second, coming from the
dura mater, is called the uvea ; it has an opening in front through
which light passes. Behind, it is highly vascular: in front it is trans-
parent and is called cornea. The third and outermost coat is the
sclerotic, which is firm and solid. It is sometimes called consolidativa ;
it does not extend so far forward as to cover the cornea . . 15 16

CHAPTER III.

The uvea contains three humours, and also a web-like structure,
arising from its anterior part. A crystalline or glacial substance fills
the greater part of the cavity of the eye; it consists of two parts.
The hinder part, in contact with the terminal expansion of the nerve
is like melted glass, thence called vitreous; the anterior part, which
has received various names, is like ice, hail, or crystal ; it is some-
what whiter than the vitreous, Anterior to the web, occupying the
space between it and the cornea, is the third humour, somewhat
like the white of egg. On the mode in which these parts receive
nourishment there is some difference of opinion. Vision is dependent
on the crystalline humour, though not so essentially as on the optic ©
merve . 2° . © o. © «© «© © «© o. o. 15-18

cxxvill ANALYSIS OF THE ‘OPUS MAJUS.'

VOL. If. PAGES
THIRD DISTINCTION. ON THE SPHERICITY AND CENTRAL :
POINTS OF THESE HUMOURS . . . . . . . 18-25

CHAPTER I.

The eye approaches the most perfect of geometrical forms, the
sphere. But between the various humours there are important
differences of form. The crystalline is a portion of a sphere of
different curvature from the vitreous. The centre of curvature of
the vitreous is situated further forward on the axis of the eye; that
of the crystalline further backward. The cornea has the same centre
as the globe of the eye. The same may be said of the liquor albugineus.

The centre of the uvea is anterior to that of the cornea “ ". 18-20

CHAPTER II.

It must be remembered that, in speaking of these bodies as spherical,
we have only to deal with sections of spheres, relating to those parts
of the eye concerned with the passage of light. In other parts these
structures are not necessarily of spherical form . . . . . 20-21

CHAPTER III.

The centre of the consolidativa is generally placed further back
than that of the other parts. The truth is that it is not of strictly
spherical form, neither is its inner surface concentric with the outer.

It is of irregular spheroid form, somewhat prolate on the forward
surface. But the central points of all these ocular structures lie on
one straight line, as the figure shows . . . . . . 21-25

FOURTH DISTINCTION. . . . . . . . 26-80

CHAPTER I.

The cornea closes the opening in the uvea, and prevents the
escape of the aqueous. Being transparent it allows the passage
of luminous impressions. It is strong enough to resist inroads of
air and of dusty particles from without, being made up of four
layers. The aqueous is also transparent: its moisture prevents
the crystalline and iris from getting too dry. The uvea is usually
black, so that feeble impressions of light and colour may produce
their full effect. It is however, from various causes, sometimes
grey. The colour of the eye depends on this structure . « 26-27

CHAPTER Il.

The anterior glacialis [lens] is connected very speciaily with the
function of vision. It is moist, for luminous impressions would not .

PART V. CXXIX

VOL. II. PAGES
affect dry surfaces so readily; it is of delicate structure, suited to
subtle influences of light. It is transparent, yet not too transparent,
so that the passage of light may leave sufficient traces to allow of the
exercise of judgement. Its surface forms part of a larger sphere than
that of the vitreous, asalready explained . . . . . 27-28

CHAPTER III.

The vitreous is denser than the crystalline, so that refraction of
the entering ray takes place towards the normal. Through it visual
impressions are continued to the expanded fibres of the optic nerve.
This nerve is the direct channel of communication with the brain.
The consolidativa (sclerotic) is moist so as to adapt itself to the
inward structures ; firm, so as to keep them in their places; and
white, so as to contribute to the beauty of the face . . . 28-29

CHAPTER IV.

The eyelids protect the eyes during sleep, and from invasion of
irritating particles; thus the eyes have rest from the toil of receiving
impressions. The lashes moderate the intensity of impressions.
Creative goodness has supplied two eyes, in case of accident to one;
and to add beauty to the face. The eyes are spherical, so as to
admit of easy and swift motion in all directions; and also, because
had their surface been plane, rays from the points of a large object
would not have been normal to the surface. As it is, perpendicular
rays impinge upon their surface from nearly a fourth part of the

horizon at once . . . . . . . . . . 29-30
FIFTH DISTINCTION . . . . . . . . 90-34
CHAPTER I.

We have now explained the instruments of vision. We pass to the
function itself; considering in the first place rectilinear vision. First,
we find that impressions must emanate from the visible object, as
Aristotle has shown to be the case in every kind of sensation. Vision
is a virtus passiva ; but the passive must resemble the active, which
i this case is the visible object. Thus the species, or impression, is
a likeness of the object. These species are thrown out as from
a centre along every possible radius. Vision then takes place by the
radiation of species, especially by those of light and colour. Colour
has much to do with vision. A strong colour impression remains
in the eye after the object has ceased to act on it. The species of
light are even more essential than those of colour . . . 90-32

VOL. I. i

CXXX ANALYSIS OF THE ‘OPUS MAJUS.

CHAPTER II.
VOL. II, PAGES

Vision is not completed in the eye, but in the commissure of the
optic nerves within the brain. Here the impressions coming from
each eye coincide, so that the object is seen as single. If one of the
eyes be forcibly misplaced, this coincidence does not take place, and
the impression of duality is produced . . . . © « 82-33

CHAPTER III.

The terminal point of the visual process would seem to be the
optic commissure: in the same way as the olfactory bulbs terminate
the olfactory process. This in no way conflicts with what has been
said as to the location of sensus communis. We are here speaking of
special sensations. The function of vision then is partially carried
on within the eye; and is completed in the point of junction of the
optic nerves . . . . . . . e; . . 98-34

SIXTH DISTINCTION, CONTAINING EXPLANATIONS OF DIFFI-
CULTIES IN THE FUNCTION OF VISION . . . . . 99-46

CHAPTER I.

A difficulty is suggested by the smallness of the pupil. Although
cones of rays come from every part of the object to every part of the
ocular surface, yet we need only consider for practical purposes one
cone, made up of those rays which are normal to this surface. As
to the oblique rays we shall see afterwards. Now it can easily be
shown by geometry that from the base of a triangle, however large,
any number of lines can be drawn to the vertex, which will all pass
through any line subtending the base however short. Matter is
infinitely divisible: as many divisions can be made in a grain of .
millet as in the diameter of the world 0. os . . 80-3

CHAPTER II.

But independently of the cone whose rays fall perpendicularly on
the eye, there is an infinity of others whose rays fall obliquely. It
would seem that confusion must result. The explanation is that the
perpendicular rays come with much greater force, and obscure
the effect of the others, as the sun's light conceals the light of the
stars. It has further to be observed that of these oblique rays many
are made to converge by refraction with those which fall per-
pendicularly on the central part of the eye. There are thus various
degrees in vision. The central rays and those which converge with
them are seen well: some rays result in imperfect vision; some in -
noneatal . . . . . e [| e . 97-39

PART V. | Cxxxi

CHAPTER III.
VOL. IL. PAGES

A third difficulty presents itself. The species from colours must
mix throughout the medium ; black and white becoming grey, and
so on; the mixture of species having the result as the mixture of
their originals. The cone reaching the eye would thus present no
distinctions of colour. The reply given by Aristotle, Averroes, and
others is that these species have only a spiritual existence, and do not
observe the laws of material forms. Any number of them therefore
may meet in the same point without being mixed. But this view is
profoundly erroneous. We shall find the true solution by recurring
to what has been said before; the preponderating force of the rays
that fall vertically over all the rest. Suppose the object to be
black in the centre, white and red at the extremities. The black in
their course will come into contact with white rays ahd red rays:
but these latter will be oblique, and will therefore not affect the
result. So with the rays from the white and the red parts of the
object . .. . . . . . . . . . . 89-4

CHAPTER IV.

Those who have spoken of species as spiritual, do not use that
word as it is used of God or the Soul : they mean imperceptible. But
such a use of the word is confusing. The species resembles that of
which it is the image; it is therefore material. It passes through
a material medium; is therefore material. It produces ‘material
results ; being related to that result as the incomplete to the com-
plete, as the embryo to the fully formed animal. Species are indeed
invisible, except it be by accident; when an opaque body intercepts
the ray of light or colour, we become sensible of it. Or again, weak-
ness of sight may make us sensible of the passage of the ray, though
we should not be so otherwise. The same principle applies to objects
perceived by the other senses. It may be asked, How is it that three
candles placed near a small opening appear as three on the other
side? There is true mixture of the species in this case, for one
illumination results. Still if the eye be applied to the opening, the
distinction of the principal rays proceeding from each will make
itself felt. . . "M . . TD SC . 43-46

SEVENTH DISTINCTION . «© .. «© . «© . . 47953

CHAPTER I.

"Importance of the difference in density between crystalline [lens]
and vitreous. If the vitreous were of the same density as the lens,
the rays passing from the latter to the former would follow their

i2

cxxxii ANALYSIS OF THE ' OPUS MAJUS.

VOL.II. PAGES
straight path. In this case a ray falling on the right side of the lens
would pass backwards to the left of the eye, and conversely. Con-
fusion as to right and left would thus result. But, the vitreous being
denser, the rays leaving the lens are refracted ; and as the diagram
shows, they converge in a way which avoids this confusion . . 41-49

CHAPTER II.

The action of the eye on the object seen. Like every other object,
the eye radiates species. But are these radiations, or those of them
which touch the object, necessary to vision? Aristotle's remarks in
his treatise on Generation seem to point to this. Ptolemy and
subsequent optical writers have asserted it. Plato maintained that
sensation was wholly active ; the Stoics that it was wholly passive.
Aristotle takes a medium course. Vision is in fact not merely
passive, but active . . . . . . . . . . 49-50

CHAPTER IIL.

Nor do Alhazen, Avicenna, and Averroes contest this view. They
only protest against the notion that the eye emits some material
substance to the thing seen. A passage in Aristotle (De Anita, ii.

12) has been understood as though he looked on sensation as wholly
passive. But it was only by way of protest against the Platonists, who
went too far in the opposite direction . . . . . . 90-52

CHAPTER IV.

As all objects in nature complete their action by emitting their own
special forces, so does the eye generate rays from itself. These meet
the rays proceeding from the object to the eye, and facilitate the
passage of these latter. As they are of different nature no confusion
arises from their meeting . . . . . . . . 02-53

EIGHTH DISTINCTION. FOUR OF THE CONDITIONS REQUIRED
FOR VISION . 5461

CHAPTER I.

The first condition is Light. Without light, colour either (a) does
not exist, or (4) sends out no emanations, or (c) what emanations it
produces do not affect vision. The third of these explanations is the
true one, The second condition is, Distance of the object. An object
placed ín immediate contact with the organ of sense is not perceived:
for the organ acts by emitting force from itself into the medium.
This is the case even with the senses of touch and taste. The
medium for these is the flesh and skin surrounding the sense
organs . . . . . . . . . . . . 54-56

PART V. cxxxiii

CHAPTER II. .
VOL.II. PAGES

The third condition is the Position of the object in respect of the
eye. They must be connected by straight lines either direct, re-
fracted, or reflected. Why is this the case with vision, and not so in
the case of hearing, or of the sensation of heat? Aristotle here fails
us. The-difficulty is obvious. A man can hear his own voice: why
cannot he see his own face? It would seem that sound generates
something more than species of sound : it must generate sound itself.
The trembling of the air following on that trembling of the object
struck which constitutes sound, is propagated in all directions, and
is therefore perceived as sound everywhere. In the same way an
odorous body not merely sends out species, but subtle material
particles, which being diffused through the air themselves emanate
in every direction. It has been already explained that there are
certain qualities capable of completing their species, by generating
fresh sources of radiation. Fire isone ofthose . . . . 56-58

CHAPTER III.

The fourth condition of vision is that the object be of suitable
Magnitude. Each point of the object must be represented on the
surface of the lens. And although that surface, like all others, is
infinitely divisible, yet, for purposes of sensation, the division must
not go so far that the points become undistinguishable. Again, the
object must not be too large. What are the limits? If the extreme
angle of vision be a right angle, an eye placed at the earth's centre
would see one fourth part of the heavens; at the earth’s surface
something less, as geometry shows. The view that the limit of the
angle of vision must be a right angle rests on no sound basis, either
of theory or experiment. Examination of the structure of the eye
furnishes geometrical proof that it is less than a right angle. And
experiment makes this certain . 2 . el; . 58-61

NINTH DISTINCTION. OTHER CONDITIONS OF VISION . . 62-74

CHAPTER I.

The fifth condition of vision is that tbe Density of the object
shall exceed that of the air and of the heaven. This is why we
see water, glass, and other transparent bodies. Air we can only see
when accumulated in great masses, which produces the same result
as density. So the most transparent water becomes opaque if the
depth be very great, shadows being cast by each particle of water
on that which succeeds to it. Further, we have to note that the

cxxxiv ANALYSIS OF THE ‘OPUS MAJUS.

VOL. II. PAGES
power of the eye to send out radiations, which we have seen to
be an essential factor in vision, is limited. And as such limitation
of penetrating power implies visibility, we have in extreme distance
a reason why extremely rare bodies become visible. The blue colour
of the sky is to be explained as in the case of deep water. Blue is
the colour which most nearly approaches blackness; it results here
from the shadows thrown by each particle of air on succeeding
particles. If the heavenly spheres were opaque, it might be supposed
that they would be visible objects. But theological reasoning shows
that they are not opaque. Beyond the eight stellar spheres is the
sphere of water, and beyond that again the tenth. It may be asked
how is it that we see a ray of light passing through a window, though
in this case the air being warmed by the sun is rarer than the air
surrounding it? The reply is that what we see is not the luminous
ray but the boundaries of the denser air which it penetrates. As to
the heavenly spheres, it has been already shown that they are
themselves transparent, the star placed in each of them being
opaque . ... . . 2 2 . . 62-66

CHAPTER 1I.

The sixth condition of vision is Rarity of the Medium. It is
objected that flame is rarer than air, and yet that a flame placed
between the object and the eye impedes vision. But it is a
mistake to suppose that flame is rarer; and Alhazen, who has been
quoted as saying this, is misinterpreted. Whether a lynx sees
through a wall or not, the human eye which we are here considering
certainly does not. On the other hand, we are not to suppose
a vacuum between heaven and earth. Radiation of species would
be impossible in that case. A vacuum is a mere mathematical
abstraction . . . . . . e; . . . 66-67

CHAPTER III.

The seventh condition is Time. Time, as Aristotle shows, is needed
for an act of memory: much more for an act of sensation. It has
been maintained that radiations from the object and the eye take
place in an indivisible instant of time, For if not, then the particles
of time, however small, would form a perceptible aggregate while the
radiation passes from the east of the heavens to the west. This
view is held by all but Alhazen, and by him is contested on in-
sufficient grounds. Some however of his arguments against it are
sound, resting as they do on Aristotle's doctrine that finite energy
requires time for its operation, the time being inversely as the
energy. Suppose the energy infinite, then, and then only, does
the time become zero. The notion that the ray is spiritual not

3*5

PART V. CXXXV

VOL. II. PAGES
material, and therefore not amenable to physical laws, has been
already disposed of. It is material, and as such cannot be in several
places at the same time . e . . . . . . 68-71

CHAPTER IV.

It may be further observed that the time occupied by a luminous
radiation may be so small as to be imperceptible to our senses even
when the distance traversed is very great. Aristotle’s supposed
denial of it was a denial of the view of Empedocles that a corporeal
body was transmitted across space. But the luminous radiation is
not a body, but a form continually renewing itself out of the particles
of the medium, as it travels. It is true, as Aristotle says, that there
is a difference between the transmission of light and that of sound
and other sensory impressions. With sound there are three distinct
displacements of material particles, viz. motion of the body struck,
tremor of the air, and rarefaction of the air. Nothing of this kind
takes place with light, for though light makes heat and rarefies the
air, yet it is transmitted through celestial spaces where rarefaction
and heat-production is impossible. In the transmission of odours,
again, there are special differences. But all need time: though not
the same time. We see the stroke of a distant hammer before we
hear it. Lightning reaches us before thunder.

The eighth condition is a healthy state of the eye. A final con-
dition, relating to the axis of vision, will be spoken of afterwards
(p.97) . . e. 9. 5. 5. 5. 5. s. o. WVl-74

TENTH DISTINCTION e . . . . . . . 414-82

CHAPTER I.

We may now inquire with greater precision of what matters vision
takes cognizance, what degree of certainty it brings, and to what
errors (limiting ourselves to direct vision) it is exposed. Knowledge
is either given to us directly and immediately by Sense, or indirectly
and fer accidens. Supposing the eight conditions described to be
present in just degree, the eye will perceive the twenty-two qualities
previously noted, with or without the help of the other special senses,
and of Sensus Communis and Imaginatio (pp. 4-5). By qualities
indirectly sensible I mean those which come under our cognizance
through sensation, but which are appreciated by other faculties, as
judgement ; as when a lamb seeing an object of the form and colour
of a wolf, knows it to be an enemy. When I see a man, I see an
animated object and a substance; thus in an indirect way substance
fnay be spoken of as sensible. Again, the sensations peculiar to one

cxxxvi ANALYSIS OF THE ‘OPUS MAJUS.

VOL. I]. PAGES
of our senses are indirectly appreciated by another, as when we see
iron to be hot, or ground to be wet. For cold, heat, moisture and
dryness cannot be directly appreciated by the eye e . 74-16

CHAPTER II,

The question arises, Do all sensible things of which the eye takes -
cognizance propagate rays to the eye, or light and colour only? The
latter is the true view. These other things are magnitudes or
properties of magnitudes, and belong to matter, which is passive, not
active. The air which is the medium of sound is itself soundless, and
the medium of colour, colourless. They are called sensible, not
because they emit species to the sense, but because the sense
appreciates them. All that is really necessary for vision are the rays
of light and colour, combined with the ray directed to the object from
theeye . . PC "M 00. 5. 5. o. 16-19

CHAPTER III.

Knowledge comes to us in three ways : (1) by sensation pure and
simple, as when a colour strikes the eye without remembrance of any
previous colour; (2) by similitude of the present sensation with
a past sensation remembered; (3) by a ratiocinative process, as
when we judge an object to be transparent because we are able to
see an opaque body behind it. But, although the process by which
our perception takes place is one of reasoning, it takes place so
instantaneously that we are not aware that we reason. We are
logicians instinctively, without having names for the various steps
which the mind takes. These three modes of knowledge have been
inappropriately named, Sensation, Science, and Syllogism . . 79-82

OPTIC, PART II.

SPECIAL CONSIDERATION OF DIRECT VISION . . . 83-129
FIRST DISTINCTION. ON VISION AS DETERMINED BY THE
STRUCTURE OF THE EYE . . . . . . e . 88-91

CHAPTER I.

Those whose eyes are deep-set see further than those whose eyes
are prominent. First, because the eye is nearer to the brain.
Secondly, because it is better preserved from external injury.
Thirdly, because the visual force being compressed within a
narrower channel issues with greater energy and directness. We
often prolong this channel by holding the hollow of the hand —

PART V. cxxxvii

VOL. II. PAGES
before the eye when we wish to see very distinctly. Eye-lashes help
in the same direction. In fishes which have none, the visual force is
dispersed. So too it is that from the depth of a well we are able to
see the stars. The amount of the aqueous humour in front of the
lens would also affect vision. Those who have little see further than
others, for deep water, though transparent, yet is a bar to the trans-
mission of light. It may be observed that old peop:e hold objects
that they wish to examine further from the eye. The reason is that
their eyes abound in moisture: and tbe object to be clearly visible
must be placed beyond the range of that moisture. . . 88-86

CHAPTER II.

Distinctness of vision does not always accompany length of vision.
It depends on the sufficient size of the lens, on the purity of all the
humours of the eye, and on the absence of that degeneration of the
cornea and the capsule of the lens which comes with age, and which
involves the casting of shadows. Why is it that some eyes see better
in the dark than others? Absence of moisture and extreme trans-
parency in the ocular structures conduce to this result; such eyes
are overpowered with light in the daytime, and see badly. Further,
the eye has a certain amount of independent luminosity ; greater in
some men and animals than in others . . . . . . 86-88

CHAPTER III.

Double vision results from disturbances in ocular structures. In
the normal condition of the eyes, the object seen appears single.
If the eyes are congenitally or forcibly displaced, this unity of the
object is lost. Extreme heat or cold may produce this result; or
anger, infirmity, or drink. Duplicity of vision may depend either
on displacement of the vitreous humour, or of the nervous spirit pro-
ceeding from the brain to the eye, or on dilatation or contraction
of the uvea. In some cases there may be an exudation covering a
portion of the lens. Another cause of duplicity has been suggested.
The radiations issuing from the eye may be so feeble as to be stopped
not merely by the object of vision, but by some one of the radiations
from this object. It is stated also that in some cases the eye has
had two pupils, though I have not myself seen this . . . 88-91

SECOND DISTINCTION. ON RADIATIONS FROM THE OBJECT
AND FROM THE EYE, AS AFFECTING DIRECT VISION . . 92-99

CHAPTER I.

How is it that we see a cloud at a distance, whereas when close to
it, or immersed in it, we do not? The answer is that the radiations

VOL. I. k

cxxxvili ANALYSIS OF THE ‘OPUS MAJUS,

VOL. II. PAGES
from the eye are strong enough to penetrate it when near; not so
when distant. We must conceive the pencil of rays from the object
and that from the eye as having a common axis drawn through the
various ocular centres; this central line being specially potent in
vision. The point at which it strikes the object is seen with
clearness ; adjacent points also, in proportion to their proximity.
The axis of the eye is directed successively to each point in the
object. The eyes act in concert, their axis being directed to the same
point . . . .6 . ^. .« . ec; . . 92-94

CHAPTER II.

When one of the eyes is pushed by the finger from its proper
position, the angle of vision ceases to be the same for both of them,
and the object appears double. So too when the eyes are fixed on a
given point, an object placed between that point and the eye, or
beyond that point, will appear double. It is easy to demonstrate this
by experiment e. 5 PC "PCT . 94-95

CHAPTER III.

Further experiments on double vision may be made. If the finger
be held between the eye and a candle, and the eyes be fixed on the
candle, the finger will appear double. If the right eye be closed, the
left image will disappear. If however the light be very distant,
the result is different. The right image vanishes on closing the right
eye . . . . . . . . . . . . . 96-97

CHAPTER IV.

Again, the axes of each eye may make such an angle with the
common axis of vision as to produce a doubleimage. Or the direction
of any point in the object of vision may make such an angle with the
axes of the eyes that the point is seen double . . . . 97-99

THIRD DISTINCTION. . . . . . . . . 99-129

CHAPTER I.

Let us consider further the three modes of perception, through sense,
through recollection, and through argument, in reference to the eight
conditions of vision. Light and colour are appreciated through sense
only : and this without error, so long as the right conditions of vision
are fulfilled without excess or defect. Starlight is not seen by day
because of excess of solar light. Diminish the latter, as by descending
to the bottom of a well, and the stars are seen. The Milky Way,

PART V. CXXX1X

VOL. II. PAGES
consisting of 2 multitude of small stars clustered, produces the
erroneous impression of a continuous light; this is due only to
distance. This luminous impression is caused by the passage of
rays from these small stars through the sphere of fire; the medium
in the stellar spaces would be too rare, that of the sphere of air too
dense. We have also to take into account the refraction of rays in
the sphere of fire; but of this afterwards. The light of dawn raises
a question. Why do we not see it earlier? Why, since outside the
earth’s shadow the whole sky is illumined, does the sky appear dark
to us? The reply is, first, that the spheres of heaven are very
distant ; also that the heaven, apart from the dense bodies contained
in it, is too rare to have fixed light ; light passes through it without
affecting the eye. When the sun's rays touch that portion of air
which is comparatively near to us, this illuminated air becomes per-
ceptible. It may happen that a luminous body of small magnitude
appears far larger than it is on account of rapid motion. Sparks
from a fire produce this effect. Shooting stars are probably bodies
of small magnitude. Colour,like light, is apprehended by pure sense ;
and correct apprehension of it depends on the conditions before men-
tioned. Extreme transparency of the object, great intensity of the
colour, too great remoteness of it, rapid succession of different
colours, will interfere with accurate perception. . . . 99-104

CHAPTER II.

Of Perception through knowledge (recollection). Under this head
are to be classed distinctions of characters, whether general or special,
in visible things. The moon’s light outside the earth’s shadow is
clear and white, in the upper part of the shadow red, in the lower
part is invisible. These differences, though perceived by sight, become
known to us only after repeated observation. The explanation is not
easy. The moon’s light, like that of other stars, comes from the sun.
When the moon is in conjunction, the hindrance to illumination of
the part of the moon turned to us is the moon itself; the solar rays
diverge widely on either side, and do not reach us, even secondarily,
by dispersion. But when the moon is in the earth’s shadow, the earth
being distant from the moon, the moon is near the vertex of the cone,
and accidental solar rays entering within it produce the reddish light
seen in a lunar eclipse. The degree of this light will vary with the
distance of the moon from the earth at the time of eclipse, which may
be greater or less. Another problem, raising a similar difficulty,
occurs with colour. If we look through a very thin piece of parti-
coloured cloth at an object of given colour, we may see that colour if
the apertures in the web are large enough; if otherwise, we see
a mixed colour. The quality of the medium will modify the result.

k 2

cx] ANALYSIS OF THE ‘OPUS MAJUS.

VOL. Il. PAGES

The rays, in this case, coming from the threads of the web are so
nearly coincident with the rays coming from the object, as to be con-

fused with them . . . . . . . . . . 104-

CHAPTER III.

Of Perception through reasoning. Many examples can be given
of this. The most striking is our perception of distance. An object
may be so distant, as to subtend so small an angle in the eye that
vision ceases. Short of that limit, the degree of distance is deter-
mined by a continuous series of objects between the object and the
eye. In a flat country we have no means of judging the height of
the clouds, which we can do when we see them on the sides or
summits of mountains. [Clouds would appear to be of no great
height, though, as we know from the fact of twilight, exhalations
other than clouds may rise fifty-one miles. Such exhalations are
not aqueous: being dry they retain the sun’s heat better, and thus
rise higher.] For judging, then, of distance, we must have an inter-
mediate series of objects, each of which shall be appreciable by the
eye with sufficient accuracy. These limits are soon exceeded.
A line of trees appears continuous, though there may be a great
interval between each of them. So planets seem to be in the same
surface as fixed stars,. though the difference of remoteness is
immense. So an equilateral figure of many sides becomes at
a distance undistinguishable from a circle. A circle may be taken
for a straight line, a sphere for a plane figure. When a circle is held
sideways before the eye, the part nearer to the eye will be recognized
as nearer if the distance is moderate: if it is very far off, the difference
of distances in the points bears so small a proportion to the whole
as not to be recognized. Thus it is that, when the moon is in her
first or third quarter, the circular line defining the light part from the
dark appears as a straight line. So too the sun and moon seem to

106

us flat, though they are spherical . 2 . . . 106-108

CHAPTER IV.

All this is exemplified in the study of the Moon's Phases. The
base of the cone of solar light occupying the moon's surface appears
to us twice in the month as a straight line; otherwise as curved :
a fact unexplained in the Latin translations of Aristotle and Averroes.
Here we have to leave the region of sense, and penetrate to the
real facts, which, but for the remoteness of the sun and moon, we
should be able to see. The boundary of rays proceeding from one
eye to the moon is a great circle of that body; that of rays proceed.
ing from the sun to the moon is also a great circle, or nearly so. At
conjunction and at full moon these circles coincide, the lunar surface

-—— -— 7 — - t - ^. - . er — a — - . . e ———————————

PART V. exli-

VOL. II. PAGES
presented to the earth being wholly concealed or wholly illuminated.
At other times the illuminated surface is represented by the space
left between the intersections of two great circles, the points of
intersection being at the extremity of a lunar diameter. Regarding
these points as the lunar poles, the inner boundary of the illuminated
part may be regarded as a meridian circle. A circle drawn through
the lunar poles so as to divide the lunar surface visible to us into
two equal parts may be called the lunar colure. The inner boundary
of the luminous portion becomes identical with the colure on the
seventh and twenty-first day, and appears to us as a straight line.
Before the fourteenth day this circle presents its convex side to the
sun, after that day its concave side. In the latter half of the month
the phases are seen reversed till complete occultation returns.

So too by a reasoning process we become convinced that though
the heaven appears to us as a plane surface, it must in reality be
spherical, or at least polyhedral, so as to be undistinguishable from
a sphere. Were it plane, the stars would all disappear below the
horizon or rise above it at the same moment . . . . . 108-114

CHAPTER V.

As distance is appreciated only through a reasoning process, so it
is with magnitude. The mere magnitude of the angle subtended by
the object does not suffice, for objects of the same magnitude at
different distances appear of different magnitude, and conversely.
As in the case of distance, there must be intermediate objects familiar
to the eye with which mental comparison can be made. Extreme
distance often renders such a comparison impossible . « 114-116

CHAPTER VI.

The eye looking at a sphere sees somewhat less than the half of
it, as the third book of the E/e»ten?s shows. Heavenly bodies look
larger at rising and setting than when at the meridian. Why is this?
When looking either to east or west, the sky seems a plane, or nearly
plane, surface stretched overhead. What is over the head seems
nearer to us, and subtending the same angle, is judged smaller.
Further, owing to the interposition of terrestrial objects between our-
selves and the rising or setting star, we are better able to appreciate
its distance, and thus are led to imagine it larger. Our perception
of motion and rest depends also on a reasoning process. Motion is
apprehended by a change in the position of a body relatively to
another, the change involving a lapse of time. Rest is the absence
of such a change. Hence illusions arise. When clouds are driven
across the moon, the moon seems to be moving through them. The
clouds must be numerous and almost continuous for this effect to be

cxlii ANALYSIS OF THE ‘OPUS MAJUS.

VOL.II. PAGES
produced. Again, while we are walking at night in any direction,
a star to the right of us will seem to move with us, since it holds
very nearly the same position relatively to us at the end of our
passage as at the beginning: the star being far off, the difference
made by our change of place is imperceptible. When the sun is
on the meridian, a long line of men extending from east to west will
all see him directly in front and the shadows of their bodies will
appear parallel; the divergence of the shadows is too small to be
perceptible. The motion of the planets is imperceptible by direct
inspection. Rapid motion in a circle, followed by rest, gives the
sensation of movement in surrounding objects. In this case when
the man stands still, the humours of the eye still continue in motion.
In a moving ship, trees and houses on the bank seem to move,
especially if distant: if the eyes converge on a near object it will seem
stationary . . . . . . . . . . . 116-119

CHAPTER VII.

One of the most difficult problems is that of the scintillation of the
fixed stars. Aristotle remarks their contrast in this respect with the
planets, and attributes it to their greater distance; the eye, being
more strained, is tremulous. Scintillation is different from the tremor
sometimes seen in the sun and other planets at rising and setting.
If distance were the sole explanation, we should expect Saturn to
scintillate, which it does not. Further, it is only the larger of the
fixed stars that do so. Therefore strength of light must be a condi-
tion. And yet, since the sun at noon does not scintillate, the light
must not be too strong. One of the causes would seem to be the
internal strain of the eye at very distant objects. The planetary
bodies are easily perceived to be near, and with them there is no
strain. Moreover, the fact of extreme distance of itself weakens the
visual rays. It may be objected that the strain is greater in the case
of small stars than of large: but here the condition of sufficiently
strong light is wanting. Again, it is objected that if ocular strain
be one of the factors, this depends upon each observer's choice and
will. But this is not so. It is one of those actions which have
become involuntary through habit. But how is this difference
of distance between the planets and the stars to be known? Its
quantity doubtless is not known. But the fact that there is a
difference is a matter of sensation. Has the density, or has the
motion of the medium, anything to do with scintillation? Perhaps
both contribute, as Averroes has suggested ; and perhaps also at
these immense distances tbe visual power is exhausted, and acting
only intermittently, produces the tremulous impression. By motion
of the medium we are to understand here, not violent motions of the

PART V. cxliii

VOL. II. PAGES
lower air like wind, but subtle motions caused by the revolutions of
the heavens and of the exhalations which pervade them. A com-
bination of the foregoing causes may sufficiently explain this
complicated problem. . . . . . . . . 120-196

CHAPTER VIII.

We may now sum up the results of our study of direct vision. We
have spoken of vision as operating by sensation, by recollection, and
by a syllogistic process. If these two last are to be interpreted as in
the schools, they would imply the intervention of Reason. But it is
evident that brutes have the power of recognizing and distinguishing
both universals and particulars. A dog recognizes a particular man,
and also recognizes men in general from dogs, trees or other objects.
Therefore this faculty must be a function of sensitive life, and cannot
imply reason in the strict sense of that word. Further, animals pass
through a train of mental processes analogous to syllogistic reasoning,
though they cannot put it into a logical figure. They have a store-
house of mental impressions. They can generalize, and they can
draw conclusions ; though they are not conscious of doing so, and
cannot give an account of what is passing within them . . 126-129

OPTIC. PART III.

FiRST DISTINCTION : ON REFLECTED VISION . . . 180-146

CHAPTER I.

It is unnecessary to repeat what has been already said of the
structure of the eye and the functions of sensation. Bodies that
impede the passage of visual radiations may be either wholly
opaque, as a stone wall; or partially opaque, as water, glass,
crystal. Opaque bodies do not destroy the radiation: they merely
alter its path. An opaque body may be rough or smooth. When
the surface is rough, the parts being unsymmetrical scatter the
radiations irregularly, and there is no image. With smooth surfaces
the parts all act alike, and the radiation comes back to the eye
uninjured, though feebler than in direct vision. Proof is subjoined
of the equality of the angles of incidence and reflexion, and this proof
will hold, whether the surface be plane or spherical: for the ray may
be regarded as falling on the tangent plane . . . . 180-182

CHAPTER II.

The mirror contains nothing. What is seen is the real object,
only the radiation from it has followed an angular course. The eye

cxliv ANALYSIS OF THE ‘ OPUS MAJUS.

VOL. II. PAGES
must be situated at the extremity of that course, whether it has been
straight or angular, in order to receive the impression. It follows
that the radiation produces no durable effect on the reflecting
surface. From this again it follows that the moon and the stars
shine with their own light, not with light reflected from the sun:
otherwise we should see the sun's image reflected in them. Neither,
again, is a comet the reflexion of solar light from the surface of
a star. The case of the rainbow will be considered afterwards. The
position in which we judge the reflected object to be is, in plane
mirrors, at the intersection behind the mirror of the prolongation of
the reflected ray with that of the perpendicular let fall on the mirror
from the object. But in mirrors other than plane the apparent
position varies very greatly . . es ~ « . 182-1844

CHAPTER III.

There are seven kinds of mirrors, spherical, conical, cylindrical,
or plane. Of the first three classes each may be either convex or
concave. Geometrical proof is given that in plane mirrors the image
and the object appear equidistant from the plane of the mirror on
opposite sides. Nothing really takes place either in the mirror or
behind it. The effect produced is a mental impression caused by
the peculiar path taken by the radiation from the object. In spheri-
cal convex mirrors, the intersection of the visual ray with a line
drawn from the object to the centre of the sphere fixes the apparent
position of the object. This intersection may be beyond the mirror,
in the mirror, or on the same side as the object. Usually the image
appears less than the reality, because the rays come from a smaller
area than in the case of the plane mirror: in the spherical most of
them are dispersed. The image is erect but distorted: the outer
rays of the cone touching points more distant from the eye than the
median rays. Only when the image of a right line crosses the centre
of the sphere is that image rectilinear. Moreover, in convex mirrors
the image is nearer to the mirror than the object is; because the inter-
section of the visual ray with the perpendicular occurs sooner in
spherical than in plane mirrors. In cylindrical mirrors the errors
are even greater than in spherical, except in the one case where
a line in the object is equidistant from the axis of the cylinder.
Only if this line has any breadth, its transverse magnitude will be
distorted. In convex conical mirrors the same errors occur as in
convex spherical. . . . . "D . . . 134-137

CHAPTER IV.

The greatest illusions are those that occur in concave mirrors, both
as to the size of the image, and the number of its repetitions ; some

PART V. cxlv

VOL. II. PAGES
of these being inverted, some erect. The two diagrams accompany-
ing this chapter illustrate these effects . . . - . 187-141

CHAPTER V.

Many observations of natural objects show the dependence of
colour on the angle at which the light falls, as for instance the
plumage of the peacock’s tail or the pigeon’s neck, and also the rain-
bow, as we shall see in dealing with experimental science. Drunken
men or those in weak health see their own image projected in front
of them. Seneca explains this by a supposed feebleness of the
radiations proceeding from their eyes, which instead of penetrating
the air are reflected back as from a mirror to their bodies; and the
eye thus perceives the body to which it belongs. It may be supposed
that the air round persons in this condition is specially charged with
morbid vapours, capable of reflecting the radiation. On this hypo-
thesis it is objected that the strongest radiations from sound eyes
would be ultimately reflected from the clouds. But their distance
and their uneven surface prevent such reflexion. In the case of
drunken or weak persons we need not accept Seneca’s view of
emanations from the eye reflected from vapour. We may suppose
the emanations from the object, i.e. from the person, to be weak and
to be easily stopped, and so to become an object of direct vision. The
rays seen projected from a candle are due to the light falling in
certain directions on the eyelashes, which being polished surfaces,
act as minute mirrors. The scintillation from a metallic surface in
an elevated position, as from a cross on a church tower, is due to the
motion of the sun or moon whose light is reflected from it . 141-144

CHAPTER VI.

If a mirror be placed in a vessel of water and the image of the sun
reflected from it, a second image will appear beside the first, which
was held to be that of a star. If it were, the sun's light would hide
it Moreover, the same effect is produced by the moon or by
a candle. There are in fact here two mirrors, the surface of the
water and that of the mirror. That from the mirror is more perfect,
the other being weakened by the loss of some of the rays through
refraction. Fracture of a mirror does not necessarily result in

multiplication of images, unless the pieces are removed from each
other e . e e. e e. LJ e . es . e 144-146

SECOND DISTINCTION: ON REFRACTION . . . . 146-159

CHAPTER I.
We now come to the question of refraction. Rays passing from
a point in the object towards the eye are refracted at the cornea,

exlvi ANALYSIS OF THE ‘OPUS MAJUS.

VOL. II, PAGES
which is denser than the air, towards the normal; with the exception
of such rays as fall vertically on the cornea. The same point may
emit a vertical ray and also an infinite number of oblique rays, these
latter co-operating in the act of vision . . es . 146-148

CHAPTER II.

The intersection of the perpendicular directed from a point in the
object with the visual ray determines the apparent position of that
point. If the eye be in the rarer medium and the object be in the
denser the point appears nearer than it really is; and conversely 148-149

CHAPTER III.

The case is complicated if the surface separating the two media
be not plane but spherical. Here we have eight distinct cases.
I. When the curved refracting surface is concave to the eye. 1. The
eye being in the rarer medium, (a) the eye is between the centre of
curvature and the object, (4) the centre of curvature is between the
eye and the object. 2. The eye being in the denser medium, cases
(a) and (4) as before. II. When the curved refracting surface is
convex to the eye. 1. The eye being in the rarer medium, (a) the
object may be between the centre of curvature and the eye, (4) the
centre between the eye and the object. 2. The eye being in the
denser medium, cases (a) and. (6) as before . . . . 150-158

CHAPTER IV.

Examples of the foregoing. The submerged part of an oar
illustrates case 1 of ch. 2. If the eye were under water the upper
part would illustrate case 2. If an object be placed in a basin, and the
observer step backwards till it becomes invisible, the object will again
become visible by pouring water into the basin. This again illustrates
case 1. The sun and moon when near the horizon, where vapours
abound, seem larger than usual. The vapours form a lens with the con-
cavity towards the eye: the eye being between the centre of curvature
and the object. The object therefore seems larger and nearer. Why
then do the sun and moon not appear larger when they are high up
and the sky is cloudy? Because in this case there is no refraction,
or but little. So there is no apparent increase of size when, the
horizon being free from vapour, there is no refraction. The angle
under which the celestial object is seen is of more importance in
forming our judgement than the apparent distance, since the absence
of intervening objects makes judgement of distance difficult. A crystal
lens if consisting of a small portion of a sphere, with the convexity
turned to the eye, will magnify small objects placed beneath it, in

--h

^ ere —_

PART V. cxlvii

; VOL, II. PAGES
accordance with the fifth rule. If it be the half of a sphere or more
than the half, then the centre of the sphere will be between the eye
and the object and the magnifying effect will be less. A candle
however held at a moderate distance will appear larger than if
placed nearer, because the refracted rays from the extremity of the
object are taken for direct rays. Moreover, rays from the nearer
position are apt to dazzle a weak vision and thus are neutralized.
From a somewhat more distant position they are better appreciated.
These are a few illustrations of the effects of refraction. They are

not intended as an exhaustive treatment of the subject. . . 153-159
THIRD AND LAST DISTINCTION . . . e . 159-166
CHAPTER I.

All these scientific truths have a spiritual signification. The prayer,
Guard us as the pupil of thine eye, cannot be understood without
knowledge of the structure of the eye and the pupil. Each of the
structures by which the Pupil is defended has an allegorical
meaning . . . . 8 . . . 159-161

CHAPTER II.

As in vision we should neither be too far from the object nor too
near, so for spiritual vision we should neither be too far from God,
nor too presumptuously near. Vision is by sense, by memory,
and by reasoning; this may be paralleled in spiritual vision. Vision
is direct, refracted, or reflected: spiritually the first is divine, the
second angelic, the third human. Or, again, the first is the perfect
vision after the resurrection; the second, before resurrection and after
death ; the third, the imperfect vision of life on earth . . 161-163

CHAPTER III.

On the practical application of this science there is much to be
said. By reflexion we can multiply the images of objects at will,
as by natural mirrors formed by vapours in the sky the image of
the sun and moon are multiplied. Mirrors may be erected in
elevated positions which may reveal the details of an enemy's camp,
as is said to have been done by Caesar from the coast of Gaul when
about to invade Britain. . "M . . . . 164-165

CHAPTER IV.

By refraction even greater wonders may be wrought; small things
may be made to seem great, distant things near . . . 165-166

cx] viii ANALYSIS OF THE ‘OPUS MAJUS.

PART VI.
VOL. II. PAGES
EXPERIMENTAL SCIENCE. . . . . .. 167-222

CHAPTER I.

Having laid down the general principles of wisdom so far as they
are found in language, in mathematics, and in optics, I pass to the
subject of experimental science. There are two modes of acquiring
knowledge—reasoning and experience. Reasoning guides us to
a sound conclusion, but does not remove doubt from the mind until
confirmed by experience. A man who has never seen fire may read
the proofs that fire burns, but will not be satisfied of it till he has been
burnt. Even in geometry the demonstration of the first proposition
of Euclid fails to carry conviction till the figure has been inspected.
When Aristotle speaks of knowledge of the cause as a higher kind
of knowledge than that gained by experience, he is speaking of mere
empiric knowledge of a fact; I am speaking of experimental know-
ledge of its cause. There are numerous beliefs commonly held in
the absence of experiment, and wholly false, such as that adamant
can be broken by goats’ blood, that the beaver when chased throws
away his testicles, that a vessel of hot water freezes more rapidly
than one of cold, and so on. Experience is of two kinds: (1) that in
which we use our bodily senses aided by. instruments, and by
evidence of trustworthy witnesses; and (2) internal experience of
things spiritual, which comes of grace, and which often leads to
knowledge of earthly things. The mind stained with vice is like
a rusty or uneven mirror, in which things seem other than they are.
Without virtue a man may repeat words like a parrot, and imitate
other men’s wisdom like an ape, and all to no purpose. The in-
tellectual effect of a stainless life is well illustrated in the young man
who is the bearer of this treatise. The degrees of spiritual experience
are seven. (1) Spiritual illumination; (2) virtue; (3) the gift of the
Holy Spirit described by Isaiah; (4) the Beatitudes ; (5) spiritual
sensibility; (6) Fruits, such as the peace of God which passes
understanding ; (7) states of Rapture . . . . . 167-172

CHAPTER II.

It is solely by the aid of this science that we shall be able to dis-
abuse men of the fraudulent tricks by which magicians have imposed
on them. As compared with other sciences, this science has three
characteristics (‘ praerogativas’). Of these the first is, that it con-

PART VI. cxlix

VOL. II. PAGES
stitutes a test to which all the conclusions of other sciences are to be
subjected. In other sciences the principles are discovered by experi-
ment, but the conclusion by reasoning. An instance of this is
afforded by the rainbow, and by other phenomena of a similar kind,
as haloes, &c. The natural philosopher forms a judgement on
these things: the experimenter proceeds to test the judgement.
He seeks for visible objects in which the co‘ours of the rainbow
appear in the same order. He finds this the case with Irish
hexagonal crystals when held in the sun's rays. This property, he
discovers, is not peculiar to these crystals, but is common to all
transparent substances of similar shape, similarly placed. He finds
these colours again on the surface of crystals when slightly roughened.
He finds them in the drops that fall from the rower's oar, when the
sun's rays strike them, or from a water-wheel, or in the morning-dew
on the grass. They may be seen again in sunshine when the eye is
half opened, and in many other cases . "TM . . 172-174

CHAPTER III.

The shape in which the colours are disposed will vary. Sometimes
it is rectangular, sometimes circular . . . . . . . 174

CHAPTER IV.

Armed with these terrestrial facts, the experimenter proceeds to
examine the celestial phenomenon. He finds, on examining the sun's
altitude and that of the summit of the bow, that the two vary inversely.
The bow is always opposite the sun. A line may be drawn from the
centre of the sun through the eye of the observer and the centre of
the circle of which the bow is an arc to the sun's nadir. As one
extremity of this line is depressed, the other is elevated. It becomes
thus possible to compute the altitude of the sun beyond which no
rainbow is possible, and also the maximum altitude of the bow. It
wiil be found both by calculation and experience that this altitude in
the latitude of Paris is forty-two degrees . . . . . 179-178

CHAPTER V.

Still further investigating the shape of the iris, and the portion of it
that can be seen, the experimenter conceives a cone of which the apex
is the eye, the base is the circle of the iris, the axis being the line
already described drawn from the sun's centre through the eye to the
sun's nadir. In cases where this cone is very short, the whole of
the base may be above the horizon, as may often be seen in the spray
of a waterfall. In the sky however the cone is too elongated to admit
of this: the base is bisected in various proportions by the plane of the

cl ANALYSIS OF THE ‘OPUS MAJUS.

VOL. 1I. PAGES

horizon. The arcs visible are not portions of the same circle. When
the sun is high, and a small arc is visible, it belongs to a larger circle
than the arc seen when the sun is rising or setting. A bow can be
seen when the sun is just below the horizon ; but owing to terrestrial

vapours, only the crown of the arch is usually seen . . « 178-181

CHAPTER VI.

In some latitudes there can be no rainbow at noon even in the
winter solstice. When the latitude (i. e. the distance from the zenith
to the equator) is 24° 25’, the sun’s altitude at noon in the winter
solstice will be 42°, therefore there can be no bow. Passing north
from this latitude, there can always be a noon rainbow till we come to
latitude 66° 25’, when at the winter solstice there is no sun. Similar

calculations can be made for other latitudes . . . , 181-185

CHAPTER VII.

We have now to inquire whether the iris comes from incident,
reflected, or refracted rays. Is the bow an image of the sun? Are
the colours on the clouds real? Why is the iris of circular form?
Here we call experiment to our aid. We find on trial that if we move
in^a direction parallel to the rainbow it follows us with a velocity
exactly equal to our own. If we approach it, it recedes: if we
recede, it follows. The same phenomenon occurs with respect to the
sun. We have seen that the sun is always opposite the rainbow; the
line between the centre of the bow and the centre of the sun passing
through the eye of the observer. If the sun were apparently
stationary, this would involve the bow moving much faster than the
observer, the latter moving through the same angle, but at less
distance from the apex. But this is not so.' Therefore there is an
apparent motion of the sun concurrently with that of the bow. The
case is analogous to what happens when a hundred men are ranged
in line facing the sun. Each sees the sun in front of him. Their
shadows seem parallel, though we know that in reality they must
diverge, yet owing to the vast distance of the sun this divergence is
imperceptible. We are thus brought to the conclusion that, supposing
a rainbow to occur, each of the hundred men, facing backwards,
would see a different rainbow, to the centre of which his own shadow
would point. The rays causing the iris are therefore not incident
rays, otherwise the colour would appear fixed in the cloud. And for
the same reason they are not refracted rays, for in refraction the
image does not follow the change of place of the observer, as is the
case here. One condition of the phenomenon is that the atmosphere
shall be more illuminated at the standpoint of the observer, and less

PART VI cli

VOL. II. PAGES
at the position of the cloud. The movement of the sun from east
to west during the appearance of the rainbow may be left out of
account . . + . 2 5. «© 5. o. 185-190

CHAPTER VIII.

The colours in the bow arise from an ocular deception. They are
analogous to those which appear when the eyes are weak or half-shut.
They are not due to the same cause as the colours produced when
light shines through a crystal, since these do not, like the colours of
the rainbow, shift with the position of the observer . .. . 190-192

CHAPTER IX.

Each drop of rain in the cloud is to be regarded as a spherical
mirror; these being small and close together, the effect is that of
a continuous image rather than of a multitude of images. The colour
is due to the distortion of the image caused by the sphericity of the
mirror ©. C . . 9 . . « 192-198

CHAPTER X.

The diversity of colours has been attributed to varieties in the
texture of the cloud, the denser parts producing violet and blue, the
lighter partsred and orange. But we see the same colours in the dew-
drops, where there can be no such differences of density ; similarly in
the crystal. Aristotle has been wrongly translated and interpreted
in this matter. Another erroneous belief is that lunar rainbows occur
only once in fifty years. They may occur at any full moon under
suitable atmospheric conditions. . . . .. . .. 193-194

CHAPTER XI.

The shape of the bow is a difficulty. It cannot be explained by
refraction. It is to be observed that the same colour is continued all
round the circle in each ring. All parts of the ring therefore preserve
the same relation of the solar ray to the eye. This implies circularity
of form. It is asked why the whole space contained by the circle is
not occupied with colour. Because from the points in this central
area rays equal to the angle of incidence are not reflected to the
eye. . . . . . . . . . . . 194-196

CHAPTER XII.

The cloud therefore is not coloured ; the appearance of colour, for
it is only an appearance, is given by rays reflected from the raindrops.
Of colours there are five, white, blue, red, green, black: though
Aristotle, dividing blue and green into other shades, speaks of seven.

clii ANALYSIS OF THE ‘OPUS MAJUS.

VOL. II, PAGES
These colours appear to have some relation to the various structures
of the eye. In addition to the problem of the rainbow, there is the
problem of haloes and coronae. On this I give the best explanation
that as yet occurs to me. I do not however pretend that it is satis-
factory. Far more careful experiments, made with properly con-
structed instruments, are needed before an adequate explanation
canbegiven' . . .. . . . . . . « 196-201 d

THE SECOND PREROGATIVE OF EXPERIMENTAL SCIENCE. 202-215

In all sciences Experiment is able to reveal truths quite un-
connected with the discussion of principles, and with regard to
which it is useless in the first instance to assign a reason. The
initial state of mind should be readiness to believe; this should be
followed by experiment: reasoning should come last. I subjoin
examples of my meaning.
I. The astronomer constructs his spherical astrolabe, by which he
can observe the precise longitude and latitude of heavenly bodies
at different times. But it is not inconceivable that experiment may |
devise means of bringing this instrument into such relation with
the revolution of the heavens that it should follow their course. The
motion of the tides, the periodic changes in certain diseases, the
diurnal opening and closing of flowers, are facts tending to belief
that such a discovery is possible. If effected it would supersede all
other astronomical instruments . ‘ ^ $ . 202-203
2. My next example relates to the act of prolonsin human life.
As yet we have nothing to rely on but ordinary rules of health.
These are observed but by few, and usually not till the close of life,
when it is too late. lf a suitable regimen were observed by all,
no doubt life would be much prolonged. But there are special
remedies unknown as yet to medicine, but to be found by experiment,
which may extend the period of life much further. Observation of
the habits of certain animals may guide us to truths on this matter
which are as yet hidden. Other indications are given in the works
of Aristotle, Pliny, Artephius, and others. A combination of gold,
pearl, flower of sea-dew, spermaceti, aloes, bone of stag's heart, flesh
of Tyrian snake and of Aethiopian dragon, properly prepared in due
proportions, might ps n to an extent hitherto un-
imagined . . .. 204-208
3. A third tarps o be found i in 1 Alchemy; The problem here
is not merely to transmute the baser into the more precious metals,
but to promote gold to its highest degree of perfection. In this
perfected gold we should guid have a further aid to the prolonga-
tion of life . , ‘ i " "E . 214-215

— À

"E es

PART VII. cliii

VOL. IIl. PAGES
THIRD PREROGATIVE OF EXPERIMENTAL SCIENCE . . 215-222

In this we leave altogether the domain of the sciences now re-
cognized, and open out entirely new departments of research. At
present the influences exerted on us by the stars can on:y be known
through difficult astronomical calculations. Experimental science
may enable us to estimate them directly. It may be possible for us
to act on the character of the inhabitants of any region by altering
their environment. Inventions of the greatest utility may be dis-
covered, as perpetual fire, or explosive substances, or modes of
counteracting dangerous poisons, and innumerable other properties
of matter as yet unknown for want of experiment. The Magnet, of
which use is already made, is but a type of other mutual attractions
exerted by bodies at a distance. For instance, if a young sapling be
longitudinally divided and the two divisions be brought near together,
held each by the middle, the extremities will bend towards each other.
In conclusion, I may point out the influence which the possessors
of this science may exercise in the promotion of Christianity among
the heathen, whether in subduing their pride, in disabusing them
of false beliefs in magic, or in overcoming their material force . 215-222

PART VII.
MORAL PHILOSOPHY. . . . . . . 228-404

FIRST PART OF MORAL PHILOSOPHY . . . . . 223-249

We have now considered Philology, Mathematics, and Experi-
mental Science, and have seen their intrinsic importance, and their
value to the Church. I come now to a fourth science, which stands
on a higher level ; that which relates to the practical conduct of life.
Other sciences relate to action of various kinds ; but this to those
actions by which we become good or bad. It is the science which
instructs Man as to his relations to God, and to his neighbour and to
himself. It deals therefore with the final purpose of all human
wisdom. It is closely related to Theology, to which it supplies
important aid, sharing therefore its dignity. Proceeding to the
divisions of the subject, tbe first point to note is that the conclusions
of the previous sciences form the principles of ethical science. The
others have prepared the way for this science as their mistress. We
find ethical principles everywhere diffused through them, which are
now by this highest of the sciences to be gathered together and find

VOL. I. l

cliv ANALYSIS OF THE ‘OPUS MAJUS.

VOL. II, PAGES
their proper place. It is called by Aristotle Moral Science; by
others Civil Science, as laying down the obligations of citizens and
States; the city standing in old times in the place of the modern
state or empire. It falls under two divisions: first, the establish-
ment of laws of conduct; secondly, exhortations towards their
fulfilment . . . , . 223-225

The first division consists of three parts: '( I) duty to God ; (2) duty
to our neighbour; (3) duty to ourselves. These three divisions are
indicated both in the Old and in the New Testament. We may
begin by laying down certain principles either held by this science in
common with Metaphysics, or reached through metaphysical methods
which here would be out of place. "These are, (1) that God exists ;
(2) that He is naturally known to man ; (3) that He is of infinite
power and wisdom; (4) that He is One; (5) that He is also Trine;
(6) that He is the author of Nature; (7) of angelic substances;
(8) of human souls ; (9) these are immortal; (10) the highest good
is in the future life; (11) man's capacity for this good; (12) the
moral government of the world; (13) future rewards and punish-
ments; (14) the worship of God ; (15) man's duty to his neighbour
and to himself; (16) the need of revelation ; (17) of mediation
between God and man e . e . . . 295-998
There are other principles of which Metaphysics can take no
cognizance—relating to the nature of God and the angels and to future
life. Of these the first is the Triune nature of God. Something of this
has been revealed to the ancient philosophers, having been received by
them from the patriarchs, as explained in the second part of this
work. Plato and Porphyrius are instances of this ; examples may be
found also in Aristotle and Avicenna . . . . 228-282
The mutual relations of the three Persons of the Trinity constitute
the first foundations of Moral Science. Next to this is the Incarna-
tion. Here too many traces of knowledge of the truth are discover-
able in the ancient philosophers, both Greek and Arabian. There are
also facts in natural history pointing in the same direction . 282-234
The coming of Antichrist is also an article of faith, of which some
knowledge is to be observed in the writings of Greek and Arabian
philosophers, and which some have thought is to be fulfilled in the
actual Tartar invasions, though this is uncertain. It will be followed
by the final punishment of the Evil ohe . . .. . .. 284-285
The creation of the world and of the human race is also a principle
laid down in the writings of Aristotle, Albumazar, and others. We
find also the doctrine of the existence of angels, good and bad. The
former direct the motions of the heavenly bodies; and one of these
is specially attached to the destiny of each human being as his
guide through life. Bad angels may tempt him to evil . . 285-288

— — ——À—— — — ——

PART VII. clv

VOL. II. PAGES
Of the immortality of the soul much is to be found in Aristotle,
Plato, Cicero, Hermes Mercurius, and Avicenna ; and they were not
ignorant that the body must be regarded as inseparable from the
soul They had knowledge also of a future state of rewards and
punishments; though, as Avicenna insists, the cares, enjoyments, and
occupations of this world hide this knowledge from us. In shaking
off these earthly trammels and receiving spiritual enlightenment true
wisdom consists, which Aristotle in the sixth and tenth book of his
Ethics holds up as identical with true happiness. Theophrastus his
successor, and Cicero, confirm what he has said. "Thus that highest
good of which Aristotle speaks consists in participation of the life of
God. Nor were the ancient philosophers unaware of the future
misery that awaited the bad, as the writings of Socrates, Cicero, and
Hermes show . . . «© «© © © . . 238-246
We now pass to the obligation to worship God, in thankfulness
for our creation, in reverence for His infinite power, in consideration
of our future bliss. On these points Avicenna, Porphyry, Plato, and
Cicero have spoken explicitly. St. Augustine has accepted Cicero’s
explanation and definition of religion. Avicenna has compared our
approach to the presence of God to our entrance into. the presence-
chamber of a great king. And Hermes has enlarged eloquently on
this subject. As to the ceremonies of heathen nations, they were for
the most part superstitious and useless, and there is no need to dwell
upon them. They were practised by these ancient writers not for
their intrinsic value, but in order to conform to popular prejudice

and custom. . . . . . . . . e . 946-249
SECOND PART: CIVIC MORALITY . . . . . 250-258
CHAPTER I.

The first subject under this head is the regulation of the propagation
of the race by the law of marriage. Next comes the subordination
of ranks, both in the state and in the family. Thirdly, the appoint-
ment of educators and judges. A definite position and function
should be allotted to each citizen. Provision should be made for the
treatment of criminals, and for the replenishment of the treasury.
Laws must be made for testamentary dispositions and for contracts of
all kinds. Occupations injurious to the state must be prohibited. The
defence of the country by an organized force must be secured . 250-252

CHAPTER II. .

It is further necessary that orderly succession in the government
should be arranged. The ruler should choose his successor with the
12

clvi ANALYSIS OF THE ‘OPUS MAJUS.

VOL. II. PAGES
consent of his nobles and of the people. Any subsequent pretender
should be outlawed. These are the principal divisions of the subject ;
which however includes the whole of Civil Law as received among
the Latins, to whom the Greeks transmitted it . . . . 252-258

THIRD PART: PERSONAL MORALITY . . . . . 954-3065

CHAPTER I.

This third division is subordinate to the two preceding. Our duty
to God occupies of course the first place. Secondly comes public
good; which takes precedence of private good, as Aristotle has
maintained. Love, Peace, Justice fall in this second division. Man
is a social animal. A hermit living by himself is neither good nor
bad. We are born to make our lives useful to others, as Cicero,
Seneca, and the Stoics have so often said. On the subject of
personal conduct and character admirable truths have been laid
down by heathen writers, which may put Christians to shame.
We will begin with those relating to virtue and vice in general;
passing afterwards to special branches. 5. 5. « 254-255

CHAPTER II.

Aristotle has defined two kinds of virtue. The first consists in the
subordination of feeling to reason ; to this the name of moral virtue
is appropriated. In his £¢%hics he has spoken of twelve moral
virtues, each regarded as the mean between two opposite vices.
These are fortitude, chastity, liberality, munificence, magnanimity,
public spirit, gentleness, friendliness, sincerity, gaiety, modesty,
justice. The second kind of which Aristotle speaks is virtue of the
Intellect. Its branches belong to the region of speculation, except
so far as they are directed to the knowledge of divine things, or of
matters useful to the state. Aristotle has distinguished innate from
acquired virtue. All the philosophers of antiquity speak of virtue as
the only real good, notably Seneca, Apuleius and Cicero, and have
also insisted on the inconsistency of those who theorize about virtue
without practising it. They have spoken of it as the beauty and the
health of the soul, and have pointed out that it is only to be acquired,
by long and arduous practice. By this means even inveterate vices
may at last be eradicated . . . . . . . « 255-262

CHAPTER III.

The ancients have spoken of vice in the same spirit as of virtue.
Algazel has said that vice acts on the soul like rust on a polished

PART VII. clvii

VOL. II. PAGES

mirror, hindering the perception of the highest truth. Sin blinds the
soul; and hence the view of Socrates that evil actions result from
ignorance. There is a natural shame at sin for its vileness ; a con-
sciousness that it lowers to the level of the beasts, each race of whom
typifies some one among human vices. We take our tone from those
around us for good or evil: hence it is of the utmost moment with
whom we associate. This truth also is illustrated by the lower
animals, as Boetius has pointed out. Much importance is attached
by Seneca and others to self-examination at the close of each day, as
to the control or the encouragement that has been given to vicious
impulse. Such control, as Aristotle and Seneca insist, should be

exercised from childhood . . . . . . . . 262-266

CHAPTER IV.

From virtue and vice in general we pass to special virtues and
vices. We find that the teaching of ancient philosophers relates to
Avarice, Pride, Lust, Gluttony, Anger, Envy, and Sloth—in other
words, to the seven mortal sins. Of these, all but one, Anger, relate
to pleasure and prosperity; Anger only has to do with adverse
circumstances. Let us begin with the former class. Disregard of
wealth was preached and practised by Aristotle and a long series of
philosophers. Seneca and Ptolemy have pointed out that this earth
is but an infinitesimal part of the universe, and that the disputes of
contending nations for its possession are like the quarrels of ants for
an anthill. Apuleius, in his study of Socrates, has insisted strongly
on the distinction between the inner man and the casual accidents of
health, strength, or wealth that surround him. Sallust and Seneca
have spoken of the general corruption that has followed the pursuit

of wealth . . . . "T . . "M . 2066-270

CHAPTER V.

As to sexual desire, Archytas and Cicero have said much of its
disturbing influence on reason. Aristotle in his exhortations to
Alexander dwelt on this, and on the degradation of man through
lust to the level of the brutes. Seneca and Cicero have dwelt on
the same subject. On Gluttony and Drunkenness, Seneca has
enlarged in his discourse to Helvia, and in his other letters. He
speaks of it as throwing the door open to lust, cruelty, and other
vices. Cicero quotes a letter of the philosopher Anacharsis upholding
the advantage of simplicity of life. Plato, Avicenna, and others have
said much of the necessity of setting the mind free from the trammels

ofthebody. . . . . . . . . . . 290-275

clviii ANALYSIS OF THE ‘OPUS MAJUS.

CHAPTER VI. | -
VOL. II. PAGES

Having spoken of the vices connected with pleasure and pros-
perity, we pass to the discomfiture of the soul in adversity by Anger.
In resisting anger, the first step is to see it as it really is, with all its
disastrous consequences to spiritual and temporal welfare. By nature
man is mild and gentle, inclined to help his fellow-man. Giving way
to anger he exhibits the physical symptoms of wild beasts, distortion
of the countenance, agitation of the limbs, swelling of the veins,foaming
at the mouth, gnashing of the teeth, spasm of the breath. The effect
on the rational faculties is no less disturbing. It has often utterly
destroyed the mental balance, and the temporary insanity caused by
it has become permanent. No less pernicious is its effect on practical
conduct. All the virtues are inter-connected, so that the loss of one
involves injury to the rest. Anger is destructive to the noblest
virtues, such as clemency, magnanimity, pity, natural affection, tran-
quillity and joy. Clemency is specially characteristic of man, and to
the rulers of men it is peculiarly appropriate. It may be noted that
among bees the king alone is without a sting. The noblest of the
Roman emperors have been distinguished for this virtue. Closely
connected with it is the virtue of magnanimity, which leads its
possessor to forgive injuries, and to be unconscious of their existence.
But this state of mind is wholly incompatible with anger. As that
part of the heavens which is nearest the stars is free from clouds, so
is the magnanimous spirit free from the disturbing influences of
anger. The swelling and exaltation of spirit which anger produces
is no sign of vital energy, but rather of morbid flatulence and weak-
ness. Besides magnanimity, other virtues are impaired by anger, as
mercy, patience, and joy. Mercy is that which lifts man nearest to the
level of God. Nothing is nobler than forgiveness and forbearance, and
readiness to find extenuating circumstances in every offence, remem-
bering how prone we are to give offence ourselves. To avenge
ourselves on brute animals is what no one thinks of: and should we
be less indulgent to men than to brutes? Readiness to forgive a
personal injury is stimulated by cultivating indulgent feelings towards
human nature. But such a state of mind as this is wholly incom-
patible with anger. The destructive effects of Anger on such virtues
as Piety and Peace are too obvious to dwell upon . . . 275-288

CHAPTER VII.

In addition to these things, anger makes a man reckless of his own
life and that of his friends, as there are many signal examples in
history to show. Under its influence a man becomes careless of
wealth or reputation, and is led to blasphemous rebellion against

PART VII. clix

VOL. II, PAGES
Providence. It differs from the other vices in the suddenness of its
access, and in its overthrow of the mental balance. Moreover it
spreads by contagion through whole populations, and vast regions
have been devastated by it . e . . .* 288-290

CHAPTER VIII.

Examples of self-restraint. In contending against this vice, it will
be useful to recall the examples of those who have succeeded in over-
coming it. Socrates is one of the most striking of these. Plato is
another. Of Archytas, Xenophon, Diogenes, Democritus, Heraclitus,
similar facts are recorded. Kings and rulers have shown the same
self-mastery. Antigonus dealt indulgently with those whom he over-
heard speaking ill of him. Philip of Macedon forbore to punish an
Athenian ambassador who had grossly insulted him. Even Alexander
could at times restrain himself. Pisistratus and Cato may also be
mentioned, and the behaviour of Augustus to Timagenes should not
be forgotten . . . . . . . . . . 290-294

‘CHAPTER 1X.

We now pass to the direct remedies against this vice. One is the
resolution to inquire into the facts of the case hefore we give way to
anger. We should wait, and we should demand sure evidence of the
injury. We should guard against the suspicious temper, against
readiness to take offence, and not allow, as so often happens, anger
to be its own evidence. We should beware of expecting too much
from our friends. To Caesar his friends were more fatal than his
enemies, on account of the unreasonable expectations which they
had founded on their friendship. The second remedy is to insist on
delay before punishing an offence, so that the angry mood may pass,
and meanwhile to restrain every external sign of anger, whether in
voice or gesture. This was always the habit of Socrates. Meanwhile
every effort should be made to find excuse for the alleged perpetrator
of the wrong. Finally, it should always be remembered that the
injurer is a fellow-citizen, or at least a member of that greatest of
communities, the human race. The offender is either an equal, an
inferior, or a superior. In each case there is a special ground for
refraining from revenge. The enormity of the ravages resulting from
this vice is my excuse for dwelling upon it at such length. . 294-298

CHAPTER X.

From the subject of Anger I pass to that of patient endurance of
misfortune. And first, since there is a moral government of the world,
why do good men suffer? Seneca in his essay on this point says

cix ANALYSIS OF THE ‘OPUS MAJUS:

VOL. II. PAGES
that God sends these sufferings to strengthen their character. In
the training of children the father has more regard for vigour of
character than the mother, and acts accordingly. So it is with God.
Those whom He loves He chastens, lest through ease and comfort
their forces should decay. There can be no proof of heroism except
wrestling with calamity, therefore those are to be pitied who have no
such trial of their force. A brave man is proud that his general sends
him to the post of danger. The sailor, the ploughman, are hardened
by their calling : and it is so with character. Brave men face their
trials willingly, and are purified by them as gold in the furnace.
Thus the true blessings of life are given; the false appearance of
happiness is seen for what it is, a superficial veneer veiling the vice
and worthlessness within . . . . . . . . 298-303

CHAPTER XI.

Seneca proves further that the wise man cannot sustain injury or
insult. That he will be attacked is certain, but he will not give way
to attack ; it will not injure him ; he will be as asbestos in the flame
or rocks in the sea-foam. We may distinguish injury from insult;
the former being the graver, though the latter is often more dreaded.
The injurer seeks to inflict hurt. But for the wise man there is no
hurt but sin. What is external, what is inflicted by fortune, cannot
touch him. He can lose nothing : for what is truly his own he carries
with him. It may be urged that such a man is impossible. Rare he
is doubtless: but Cato proves the possibility. Injury can only be
inflicted by the strong on the weak ; and how can the bad man be
stronger than the good? Obviously the bad man may intend a
wrong : but it does not follow that the wise man will suffer it. He is
beyond the reach alike of injury or benefit; he is raised to the level
of God, except that he is mortal. He bears all assaults gladly, looking
on them as trials of his strength. Insult is a smaller matter, to be
complained of rather than avenged. It implies some mistrust in the
recipient of his own worth, from which a wise man would be free.
We are not to suppose him insensible. Bodily pain, the loss of friends,
political disaster, he will feel like other men; but of mere insult he
will be simply unconscious, or will treat it as a passing dream. He
will not take offence at it any more than a mother at the petulance
of her child. For those who would insult him are but grown-up
children. If he restrains and punishes them, it is not because himself
has been hurt, but for their own welfare. The physician is not angry
with his delirious patient. If rich men pass him by unnoticed, he
reflects that they are but beggars or worse, since the beggar wants
little, they much. It would be doing them too much honour to be
offended by them. The current of opinion is nothing to him: he

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VOL. II, PAGES

passes on athwart it, as the planet moves against the revolution of
the sky. He makes no distinction of what can be tolerated and what
is intolerable. He must conquer fortune wholly or not at all. For
the wise man such a thing as injury does not exist. If he deserves
what he suffers, he takes it as a judgement: if not, let the doer

blush for it. Such was the spirit of Socrates . . . . 803-311

CHAPTER XII.

In a discourse addressed to his mother, Seneca has suggested
consolation under every kind of calamity. When misfortunes are
many, it is not worth while bewailing any one of them separately.
We are hardened by the rest, like veteran soldiers who bear their
wounds in silence. Seneca alleges his own example under trial.
Though not attaining to the level of the truly wise, he yet has followed
wise men's teaching, and so has been forewarned and forearmed
against the caprices of fortune. Take each misfortune singly. And
first of exile. What is exile but a change of place? Of the vast
multitudes in Rome is not a large proportion foreign? Again, is not
constant motion as natural to the mind as it is to the heavenly
bodies? Looking at the human race, we find each part of it constantly
migrating ; and what is migration but exile? Wherever we go we
carry our moral nature with us: we find the same universe around us.
Let us remember what Brutus tells us of the cheerful activity of
Marcellus in exile. Poverty is sometimes added. If meat and drink
and clothing are supplied, it is no cause for complaint that avarice and
gluttony are not satiated. The real necessities of life are easily
provided. For the rest, the mind is everything; jewels, gold and
silver are of small account. Violence and disease may affect the
body; the mind they cannot touch. The poor are not less happy
than the rich. But luxury has been carried so far that the travelling
money of an exile is what once would have been the patrimony of
princes. Homer had but one servant, Plato three, Zeno none. But
how if all these evils, poverty, exile and neglect, be joined together?
The answer is the same. The same reason which supplies endurance
of one will suffice for all. As for ignominy, it depends on him who
endures it: the prison was an honourable p'ace when Socrates was
its inhabitant. When a great man is cast down he is venerated
still, as when a stately temple islaid in ruins . . . . 811-817

CHAPTER XIII.

Writing to Gallio, Seneca asks, Is death an evil? All men share it.
Do men speak ill of you? What, if they are bad men? You are in
pain. If the pain is slight it is easy to bear, if severe the greater

clxii ANALYSIS OF THE ‘OPUS MAJUS'

VOL, II, PAGES
honour in bearing it. It is hard to be poor. All depends on who is
the poor man. The birds and beasts do not feel their poverty. The
rich man is but a money-chest. The crowds that follow him are
but as flies looking for honey, or wolves rounda carcass . 318-319

CHAPTER XIV.

Writing to a lady who had lost her son, Seneca continues, The
mastery of life is only to be seen when trial tests it. Your son
stood this test nobly. Natural affection has its natural limits. The
grief of animals for the loss of those dear to them lasts but a short
time. Men alone grieve long; and even with them it is the weaker
sex, or the more barbarous tribes, who are crushed by it. Was this
sorrow unexpected by you? Remember that none are exempt from
it. Of no earthly possession have we a secure hold. We have them
as actors have their stage properties ; the scene ended, they pass
back to the manager. What we have we should be ready to give
up at a moment’s call. In loving it think of it as even now passing
away. Why weep one part of life when the whole of it is sad? Man
is but a frail helpless thing that the most trivial accidents may destroy.
His longest life is but a few years, and may be cut short at any
moment. There are noble instances of constancy under such
calamities as yours, as of the priest engaged in sacrifice who, hearing
of his son’s death, went on calmly with the service. Cornelia, mother
of the Gracchi, Livia and Octavia the sister and the wife of Augustus,
bore their bereavement nobly. Reflect further that life is so un-
certain that the sudden close of it may mean avoidance of calamity
which would otherwise have followed. Nothing is sure but what has
been already done. The sooner we are disentangled from earthly
things the speedier will be our flight to the realms above . . 919-822

CHAPTER XV.

My reasons for treating this third part of Moral Philosophy at
such length are two. First, that although we are far in advance of
heathen nations in knowledge of spiritual life, we are far behind them
both in word and deed, as to public and private life in this world.
Secondly, the works of Seneca from which I quote have been hitherto
unknown to me, in spite of a long search for them, and probably to
others. . .. © . . «© . . . . . 822-28

CHAPTER XVI.

I proceed therefore with selections from his Essay on the Brevity
of Life. Men complain that life is short. It would be long enough if

PART VII. cixiii

VOL. II. PAGES
they spent it wisely. But they waste it like spendthrifts, in luxury,
vice and sloth, or at the best in restless activity. Men cherish
a dream of retirement and quiet reflection at the close of life. But
they put off realizing it till too late. We know how Augustus longed
for such a time of peace. The art of life is no easy matter to be
learnt in a moment. Life itself is not too long for it. The wise man
knowing this guards his time against the encroachments both of
pleasure and business. Thus whatever his span of life he truly lives.
For length of years is no proof of life. The shipwrecked sailor, tost
hither and thither, has not made a voyage. Men crave for life when
they see the end of it at hand. But while it lasted they lavished it
recklessly. Much too is wasted in schemes for the morrow, the
immediate work before us being left undone. Time must be seized
as it flies. Of the three parts of time, past, present and future, the
first alone is our inalienable possession. Yet how few care to look at
it The ambitious, cruel or intemperate man hates his memories.
The one part of life which is really his own he flees from ; and yet
men cling to life when it threatens to escape them. Few understand
what true leisure is. Most men’s pursuits even when harmless are
but laborious futility. Learned men occupy themselves with the
collection of trivial and useless facts: [though be it said in passing
that sometimes these facts have philological interest ;] wise men have
the whole expanse of history open to them. They can escape from
the littleness of the present to companionship with the great thinkers
and teachers of past ages. All time belongs to such men. They
recall the past: they act in the present: they arrange the future.
They see things to which other men are blind, and they escape.
other men's miserable anxieties as to what may befall them. It is
well therefore to spare a few years for quiet meditation before our
faculties are enfeebled . . . . . . . . 828-388

CHAPTER XVII.

It is well for us not to be exempt from the common lot. Great
wealth is great slavery. Life at the best is but a stormy voyage, and
the only haven is death. Life has been lent us; let us return the
loan ungrudgingly. And for the death of those dear to us, though we
must feel like men, let us also bear like men . . . . 833-335

CHAPTER XVIII.

I now pass to Seneca's discourses on the Blessed Life, and on Peace
of Mind ; forthey are well adapted to strengthen the spirit and render
it careless of outward prosperity. Men wish for happiness, but know
not where to find it. It is worse with them than with travellers who

clxiv ANALYSIS OF THE ‘OPUS MAJUS’

VOL. II. PAGES
have lost their way. These can be set right by natives of the place.
But in life it is-the broadest and most trodden road that leads
farthest astray. We must leave the crowd if we would go right. We
must look within; the mind must be a law to itself. Nature must be
our guide. If our mind is attuned to nature it will not fail us. We
shall thus substitute for the distractions of pleasure and fortune the
joy and tranquillity of inward peace. He is to be called truly blessed
to whom the only good or evil is good or evil of the soul, the only
pleasure, to be free from slavery to pleasure. Virtue is undying,
pleasure perishes in the act of fruition. Pleasure may be the lot of
good men and of bad: but for the good it is a servant, not a master;
they are undisturbed by its absence; like the universe, like the
Deity, they retain self-mastery. They live and act without strife,
without vacillation, in inward harmony and peace. Yet virtue is not
to be sought for the joy that it brings, any more than fields are tilled
for the flowers that may spring up amidst the corn. It is an end in
itself; there is nothing beyond it. With vicious pleasure virtue is
incompatible. Lawful pleasures it accepts, as using but not abusing
them. Unless raised above them, the wise man could not withstand
the trials of life. Pleasure is but an addition to his life, not the
governing principle. To confound these things, to regard pleasure and
virtue as inseparable, is a fatal error, leading inevitably to the triumph
of the baser element. There must be no compromise. The highest
good ceases to be the highest if mixed with something alien to itself.
The very foundation of virtue is undermined when it is made to
depend on outward circumstance. It will no longer inspire deeds of
heroism and self-sacrifice. When such are called for, they will be
done unwillingly, and not with the prompt obedience of the faithful
soldier. The reward of our fidelity is true freedom. Nothing can be
done to us against our will, for our will is at one with that of God.
But who, it may be asked, comes up to this standard? whose life is
not utterly inconsistent with it? Admit this, and yet we need not be
deterred from aiming at it. It is best to have high aims. If we
resolve to be fearless in the presence of death, not to be the slaves of
fortune, to acknowledge our bond to our fellow-men, to act when
alone as though the world beheld us, to set restraint on appetite, to
bow in all things before God’s will, we are at least on the upward
path, though we may not attain. Those who scoff at us will profit little.
A man may be wealthy and prosperous, yet good. He may use his
wealth to relieve the needy or to support the state. He will not
throw it away; yet, if it be taken from him he will be content. The
difference between him and others is, that his riches belong to him,
they belong to their riches. If innocently gained they cause him
neither pride nor shame. He will hold them lightly, and will use

PART VII. cixv

VOL. 1I. PAGES
them worthily. We must distinguish between those who are strug-
gling towards true wisdom, and those who have attained it. We can
at least resoive not to bow down before wealth as a blessing, not to
be the slaves of it, always to hold ourselves in readiness to abandon
it Strange indeed is the tendency in bad men to malign men better
than then;selves, instead of attacking one another; to pick out the
specks in these, heedless of their own hideous eruptions. Yet
they only bring into greater prominence the virtue which they
assault . . . . . . . . . . . 885-347

CHAPTER XIX.

We must pursue our steady course, not diverted from it by the
varying blasts of opinion. We shall incur the reproach that a philo-
sophic life involves abandonment of the duties of a citizen. But in
retirement we remain active, still working at what will be of use to
those who come after us. The turbulent politics around us are not
our only field of action . . . . "M . . 948-949

CHAPTER XX.

I conclude with extracts from Seneca's discourse on Peace of Mind,
without which there can be no happiness. We are as ready to flatter
ourselves as others. We are too timid to tell ourselves the truth.
Yet without uprooting our secret vices there can be no inward peace.
Sometimes we yield to the desire for incessant change; sometimes
we sink into inertness. Or we have not attained full mastery over our
passions, and are kept in perpetual struggle ; or again we are still tor-
mented by ungratified ambition. These disappointed hopes prey on
the mind, and we become envious of the success of others. We shift
and turn in hope that change may bring relief, we lose all power of
forbearance, and end with disgust for life and the world. The remedy
for this is not, as Athenodorus advises, to re-enter the arena of public
life, but to choose such occupations in retirement as shall make our
lives useful to others. We may serve the state by advising and
directing the young, as well as by holding public offices. We are not
to flee from men and live only for ourselves. We remain citizens;
but of the world, not merely of a single state. We act on those
around us by the influence of example. Socrates under the Thirty
Tyrants was a tower of strength to his fellow citizens. It is well
carefully to measure our own powers, which we are apt to overrate.
Defects of temper, health, fortune, often unfit us for public life, and
point to retirement as the better course. We should not begin what
we cannot carry through. Great care should be taken in the choice
of friends; not insisting on perfection, but above all avoiding the

clxvi ANALYSIS OF THE ‘OPUS MAJUS;

VOL. II. PAGES
querulous. Consider next the question of wealth, perhaps the most
fruitful source of our miseries. The less wealth we start with the less
we can lose : and the rich bear losses quite as badly as the poor. Of
this Diogenes was well aware, when he took to a life of voluntary
poverty. There can be no more doubt of his happiness than of the
happiness of God. When his one slave left him he merely remarked
that if the slave could do without him surely he could do without the
slave. Our wisdom is to reduce the number of our wants, to be
content with a moderate fortune, and to live well within it. Even in
intellectual pursuits there should be the same moderation. Vast
collections of books are of smal] avail, monuments of luxury rather
than aids to study. In all the perplexities of life courage first, then
custom, will teach us to bear the yoke. Custom is nature’s sovereign
remedy for all cares and sorrows. Life, whatever its station or
degree, is a servitude. Custom adapts us to it and we cease to com-
plain. Let us leave the unattainable, and attempt things within our
reach. The lofty are liable to the deepest fall. These counsels are
for ordinary men, not for the man of perfect wisdom. For he can walk
more boldly : to him not fortune only, but his own life, is but a tem-
porary loan, which he is ready to surrender at call and gratefully. The
test of a good life is readiness to die. Knowing that he was born into
a world of trouble, no evil can take him unawares. Let us avoid the
crowds of men who rush hither and thither like insects on the trees
in restless and purposeless activity. Idle conversation is apt to be
worse than idle. Let us refrain from too many occupations; our
disappointment will be the less. Let us take the work that comes to
us, neither too eager nor too fickle. Let us possess our souls in
patience, all else being external to us and indifferent. The behaviour
of Theodorus the philosopher, and of Canus Julius when sent to his
death by Caligula, are noble examples. Further, we must not indulge
in too much grief at the errors of mankind. Laughter is more to the
purpose than indignation ; though calm observation is a better attitude
than either. Nor need the painful death of brave men afflict us, since
they themselves endured it gladly . . . . . «. 849-802

CHAPTER XXI.

Since the body acts upon the mind, time for relaxation and
recreation must be given. Saintly men have always admitted this
and practised it, following the example set by St. Benedict. Seneca,
to whom much divine truth has been revealed, has insisted on this
point strongly. We must not always be alone, he says, nor always
in a crowd. There must be a change of occupation; occasional
amusement and gaiety. Hours of work must be limited ; exercise in
the open air, occasional change of scene, are good ; even indulgence

2o —-—- — À ——

PART VII. cixvii

VOL. II. PAGES
in wine is not to be wholly forbidden. The mind is stirred by such
influences and raised above its usual level. To these may be added
the inspiring influence of music, of which the prophet Elijah availed
himself . . . . . . e. . . . 962-365

MORAL PHILOSOPHY : FOURTH PART . . . . 966-404

The beauty of the subject, and the rarity of the books treating of it
explain the length of the preceding part. I now pass to the grounds
for accepting the Christian religion, which points the way to happiness
in a future life, and thus gives a meaning and a purpose to moral
philosophy. God has never left men without the means of salva-
tion ; hence we find ancient philosophers, and especially Aristotle,
considering what are the principles which preserve or destroy
states . . . . . . . . . . . . 866-367

The religions now existing in the world are those of Saracens,
Tartars, Pagans, Idolaters (Buddhists), Jews, Christians. They
are distinguished not merely by opinion, but also by difference
of moral aim. The Saracens permit excessive indulgence in sexual
pleasures. The Tartars err from lust of pqwer; as we learn from
the travels of William Rubruquis. Their mode of life is coarse
and rude. The Pagans live by custom rather than reason, and
suppose that their present enjoyments will be continued in a future
life. The Idolaters resemble them in this, except that their priests
practise chastity and abstinence. The Jews combined spiritual with
temporal blessings; the latter as well as the former belonging to the
future life. The Christians, while accepting temporal wealth in the
present life, are wholly independent of it in the future . . 867-370

Of these sects we may place the Pagans lowest ; they are guided
by no priesthood, and each follows his own way. The Idolaters
have a priesthood and a ritual; but they have a multiplicity of gods.
The Tartars come third ; they worship one God, though with many
superstitious and cruel observances. Next in order come the Jews,
of whom the more spiritual attained to the knowledge of the true
Christ. Fifth come the Christians, who practise the Jewish law
spiritually. Finally, there is the law of Antichrist, which for a time
overwhelms all others. And each of these has its own moral
principle— pleasure, wealth, ambition, fame, or blessedness in a future
life. In the mathematical section of this work it has been shown that
there is a connexion between these sects and the various planetary
influences, which incline men's characters in certain directions, though
without depriving them of free-will. As these influences change, each
of the sects may be modified by the others. So the Saracens, though
mainly under the influence of Venus, are modified by Jewish and

cixviii ANALYSIS OF THE ‘OPUS MAJUS.

VOL. II. PAGES
Christian law. The Tartars, though governed by Mars, in like
manner are modified by Mercury, which implies Christian influence.
The Pagans, again, and the ldolaters may differ according as the
influence of Mars or of the Sun may prevail. With the Pagans,
terrestial things as well as celestial may be objects of worship . 370-372
We have now to consider the means of showing the truth of the
Christian religion. We may appeal to miracles; or we may take
the ground of reason and philosophy common to us and the other
sects. Though the Christian should not place his chief reliance on
reason, yet he should be able to render an account of the faith that
is in him. And as the heathen do not accept this faith, we must
challenge them on philosophical ground. en losophy | is given to men
for the very purpose of leading them to truth . . . 912-878
In what follows I am appealing to the wise among them rather
than the simple. There are three kinds of knowledge : that coming
from our own study or experience; that which is learnt from
others, and that which is natüral, in the sense of being shared by
the whole species. It is no less natural to act on such truth than to
know it. Practical and speculative reason have the same source, and
are essentially the same, as Aristotle has taught . . . 373-875
The existence of God is one of these natural truths, as Cicero has
said. The necessity of demonstrating it comes from the weakening
effect of sin on our faculties. The divine unity is not known by
nature; and even those who accept it are in error as to God's
attributes. These therefore have to be explained, beginning, as the
mathematician begins, with elementary principles. That God is an
eternal first Cause of infinite wisdom, power, and goodness is accepted
by the Tartars, Saracens, Jews, and Christians. Pagans cannot deny
this truth when presented to them; as the recent conference in
Tartary between Christians, Saracens, and Buddhists has shown.
Their resistance elsewhere to Christianity is due to attempts to
impose on them a foreign yoke . . . . . 375-377
The Christian advocate may further plead that in tracing causes
we cannot go back endlessly. There must, as Aristotle has laid
down, be a first Cause, that has always existed, and must exist for
ever, unchangeably. Boethius has shown that imperfection implies
perfection, to which it is an approximation. Perfect power, as
Aristotle shows, is boundless power: and if the power of God be
infinite, a fortiori is His essence infinite. It follows that His good-
ness is infinite; and from infinite power and goodness follows the
attribute of infinite wisdom, Such a cause is capable therefore of
creating this world, and is disposed to govern it in the best way.
If it be said that the world is eternal, this is to raise it to equality
with God. If more than one Cause is asserted, then none can be

PART VII. clxix

VOL. I1. PAGES
infinite. In one world at least there can be only one. And if there
should be more worlds than one, the same infinite God is capable of
governing them. But plurality of worlds is an hypothesis which
Aristotle has dissipated ; for they would all tend to the same central
point, and lose their separate existence. . . « 871-891

God being one and infinite, man is bound to. yield Him boundless
reverence, in thankfulness for his creation and for his hopes. of future
happiness. Even the Pagans believe in a future life; so do the
Saracens, although their belief is tainted with thoughts of animal
enjoyments. The Jews have the same belief. Thus the Buddhists
have universal opinion against them. This present life is full of
misery, from which we must believe that the future life will be free.
In our glorified body and soul we shall participate in the divine
nature. So too will the punishment of the evil be infinite. This then
is the twofold motive for doing the will of God. But man cannot of
himself know that will; as the difference of his religions show,
differences which exist even within the pale of Christianity. Of the
true nature even of material things we are profoundly ignorant ;
much more of things immaterial .. . . 881-383

Therefore Revelation is necessary. Aristetle has said that in
these things the human mind is as the eye of the owl or bat to the
light of the sun, or, as Avicenna says, as the deaf man to musical
harmony, or as the untaught child to the highest truth. Man, says
Seneca, is too mortal for immortal things. And apart from intrinsic
inability to discern infinite truth he is blinded by sin. Man must
therefore be taught by divine authornty . . . . . 983-385

All sects claim such authority. We have to consider to which of
them has true revelation been made. Evidently to one only, since
God is one; there is only one world and one human race. Avicenna
and Alpharabius fully recognize this. We have therefore to choose
between the six religions of which I have spoken. The Pagans and
the Idolaters, who take creatures for God, or who assert plurality of
gods, may be at once eliminated. When confronted by the Tartar
emperor with Christians and Mahometans, they at once succumbed.
The Tartars, while accepting the unity of God, worship fire, and their
teachers are mere magicians. It is clear therefore that they are not
in possession of the authoritative truth which we seek. This they
themselves have confessed. We must therefore examine the remain-
ing three religions—Jewish, Mahommedan, and Christian . 986-358

The superiority of the Christian law is proved first by the authority
of philosophy, which as I have before shown has given its sanction
to the principal doctrines of Christianity. No such testimony has
been given to Judaism or Mahommedanism. Seneca has attacked
the Jewish creed; and Mahommedanism has been asserted by

VOL. I. tn

cixx ANALYSIS OF THE ‘OPUS MAJUS-

VOL. Il. PAGES
Avicenna and Albumazar to be imperfect and transitory. We may
add to this the testimony of the Sibyls. Coming more into detail, we
find the Jewish prophets bearing testimony for Christ, and Josephus
supplying proof that Judaism would give way to Christianity. Other
evidence is contained in the books of Esdras and of the twelve
Patriarchs. The authorship of these books is unknown, but they
are of weighty authority. Further, the Jewish religion taken by itself,
with its incessant slaughtering of cattle, is extremely repulsive ; and is
so spoken of in the Psalms and prophetical books. Similarly the
Koran uses very strong language in praise of Christ. Mahommedan
writers say much in dispraise of their. own sect, and admit that the
life of its founder was stained by many vices. Accepting then the
testimony of each sect as standing on the same level, we find none of
them, except the Christian, testifying in favour of their own founder,
to whom both Jewish and Mahommedan authorities, as well as
Christian, bear witness . R . . . . . . 988-393

The credibility of Christian writers rests on six grounds: personal
sanctity; wisdom; miraculous powers ; firmness under persecution ;
uniformity of faith ; their victory in spite of humble origin and estate.
Besides these grounds for accepting Christianity, there are the
miracles wrought by Jesus, especially the forgiveness of sins, the
surest proof of His Divine nature. For neither Moses nor for
Mahomet was divinity claimed. There is the yet further proof of
holiness of life, which both in Mahommedanism and Judaism is
found wanting. In neither is there any recommendation of poverty,
chastity, and obedience. Nor is the sanction of a future life clearly
set forth in them oe . 5. 5. . . 898-896

Having thus proved that the Christian faith is to be accepted as
true, we need not examine each one of its articles. There is however
one of them as to which much difficulty has been experienced, the
Sacrament of the Altar. I wish therefore to give reasons why it
should be willingly and ardently accepted, containing as it does the
essence of the whoie, First, it is accepted by the whole Christian
Church. Secondly, it is manifestly set forth in Scripture, as in the
Gospel of St. John, and in the Book of Wisdom, and in the Epistle of
St. Peter. Thirdly, it is confirmed by the unanimous authority of the
saints. Fourthly, we may add the testimony of innumerable miracles,
of which I here record two of undoubted authenticity and recent date.
Finally, as the Creator is omnipresent throughout the world, so by
this sacrament is the Redeemer omnipresent to those who are in
a state of grace. Without the Creator's presence the creature would
cease to exist. So without the Re-creator's presence would the
re-created fall from the state of grace. It consists with the infinite
power and goodness of Christ that this infinite good should be

PART VII. clxxi

VOL. II. PAGES

shared by those who have been re-created. This sacrament is a con-

tinual renewal of the sacrifice by which Christ has taken away the

sins of the world. He who made the original sacrifice will be willing

to renew it . . . . . . . . "M . 996-400
But it is not enough for reason to be convinced in this matter ; it

is necessary that the heart be stirred. We must feel that this sacra-

ment contains in itself the highest good, the union of man with

God. We must feel that in every Church, for each recipient who

is in the state of grace, in every part of the Sacred Host, the whole

Deity is contained. Thus humanity transcends itself, and ceases to

be bound within the limits of space and time. To the priest is

given in this Sacrament a far greater power than that of creating

a universe. The utterance of five words brings the Creator into

communion with us. Again, what would be impossible to sense, to

sustain the presence of God, is thus rendered possible. St. Dionysius

was not able to endure the sight even of the Holy Virgin. How

then could we endure the Divine presence? Even under the veil,

of this sacrament the heart is overwhelmed. Only when thus veiled

would it te possible for us to eat of Christ's flesh and drink His

blood. We are thus prepared to believe that all our truest blessings

lie in a world beyond the world of sense. We are thus made one

with God and Christ ; and to what greater good than this can man

aspire ? TM LV ef 5. « 400-404

ANALYSIS OF
"IHE MULTIPLICATION OF SPECIES.’

PART I.
CHAPTER I.

VOL. Il. PAGES
(a) As to the name and the essential meaning of species.
By species is here meant the first effect of any natural agent. Thus
light passing through space is the species of the light in the sun.
If light passes through coloured glass, the colour shed by the light
is called the species of the originating colour. Species is here used
in the sense of likeness or image. In a dream the hallucination is
a species. Intention, form, virtue, impression, passion, are other
words used to express it . . . 407 410
This first effect of the agent resembles the agent. The agent
transmutes the patient into its likeness; thus fire transmutes what it
acts on into fire, heat into heat, light into light, and so on. The
subsequent effects have not the same likeness to the agent. This
first effect is of the same specific nature as the agent, otherwise we
should be at a loss to assign its category; for it cannot belong to the
category of accidents; and there is nothing intermediate between
substance and accident. But, although of the same nature, its
essence is incomplete ; just as we should say of the embryo, only
that the incompleteness is far greater. Some agents produce more
complete species than others, as light, colour, heat. Generally
speaking, the higher the rank of agents, the more incomplete are
their species. . « 410-418
(f) There can be only one e such resembling effect for each agent.
This we call univocal; the multiple secondary effects may be called
equivocal. While the agent is acting on the patient, the effect or
virtue is called species; afterwards, when the effect is completed, it
takes the name of the agent. Fire, when it has taken hoid of the

cixxiv ANALYSIS: MULTIPLICATION OF SPECIES.

VOL. II. PAGES

wood, is called fire. This, however, is only true when the patient is

corruptible; when the patient is incorruptible, the case is otherwise.

The sun does not communicate its nature to the moon and planets

by shining on them. The species of light is completed in them, but

not the species of the sun. And generally it would be truer to say

that the patient was assimilated through the species to the nature of

the agent, than to speak of the patient losing its identity in that

of the agent ‘ "EP . . . . 413-416
(c) Natural agents produce the same species whatever be the

nature of the patient; in other words, their action is uniform. This

does not apply to agents possessing free-will, except in so far as they

may resemble natural agents. The difference in the patient may

bring about a different result, but the species is the same. — . 417-418

CHAPTER 1I.

(a) We have now to inquire what are the things which generate

species. First, all qualities that act on sense, producing some change

in the sense-organ. There may be a doubt as to sound. Here

there is a tremor in the part of the object struck: this tremor is com-

municated to the adjacent part, and so again to the next. The first

tremor makes a sound; so. does the second and the third; but the

second sound does not come from the first sound ; it comes from its

owntremor. . « . . TC . « . 418-419
(4) Do substances generate species? — Assuredly, since substances

are nobler than accidents. An accident is not generated until its

subject be first generated. Heat, the accident, is posterior to fire,

the substance. When heat appears in water, fire must pre-exist, and

the substantial nature of fire, and this we call the species of the

substance fire. Such species are not cognizable by the five senses, or

by sensus communis. But they are cognizable by a mental process,

akin to that which causes the sheep instinctively to flee from the wo:f

which it has never before seen, feeling something injurious in its

proximity. It is sometimes said that substance can have no contrary:

but there is a sense in which substances, or substantial forms act in

opposition . . . , . . . 419-423
(c) The species of substance is of the whole compound ; i.e. of

matter and form, not of form alone . . . . . 428-424
(d) Every corporeal substance can produce species, therefore also

the organs of sense. The species generated PY the organs of sense

are concerned in sensation . . e; . 424-425
(e) With regard to matter, which is passive, it may be affirmed

that it does not generate species, except in so far as compounded with

form . . . . . 425-427
(f) Light and colour generate species, but other properties of body,

PART I. cixxv

VOL. II. PAGES
such as magnitude, position, motion, &c., which are apprehended
by sexsus communis, do.not. The magnitude and figure of an object
are inferred from the species of light and colour that issue from it; not
by species of magnitude and figure. Still more obviously is this the

case with properties like proportion, relation, and position . 427-430
(g) Of things some are universals, some are particulars ; species
issue from both. Universals do.not exist apart from their particulars,
neither do their species. The species in every case is of the same

nature as the source from which itissues . . . . . 430 431

CHAPTER III.

We have considered the agent ; we are now to. consider the mode
of action. It is not correct to say that the species is something
which issues from or is emitted by the agent. Nor is it created out
of nothing. Nor again is it an impression made upon the patient as
with a seal upon wax. The true view is that the species results from
a change in the potential activity of the recipient matter. We must
distinguish between the fofentia activa and the fofentza recepliva.
The latter is that on which the Creator implants Form. But it is the
potentia activa which is here in question. The agent produces its
effect, not by union of its substance with the patient, but by stimulating
the latent activity of the matter which is acted on . : . 431-434
Action does not take place at a distance. Force is not exerted by
the agent except on the part of the patient with which it is in immediate
contact. The effect generated in the first part of the patient becomes
a force acting on the second, and so onward. Action is thus propa-
gated from particle to particle . . , . . . 434-436
lt is objected to this view that a ray of light passing through
coloured glass produces bright colours on an opaque screen; how
could such colours be evolved from the potential activity of the
intervening air, a simple substance? The reply is that the species
produced in the air is extremely feeble. 1t only becomes relatively
strong on reaching the screen which is so constituted as to develop
colour. In the same way the species of the magnet is feeble until it
reaches the iron which is better adapted to receive it. The colour on
the opaque screen is but the species of colour, and is far from being
so complete as it appears . TP . TP . 436-438

CHAPTER IV.

Six propositions have now to be considered. (a) It is not possible
to assign a minimum of quantity below which a given agent will cease
to act. In animate agents there is an augmentative power bringing

clxxvi ANALYSIS: MULTIPLICATION OF SPECIES.

VOL, II. PAGES

the agent up to a given degree of force. In inanimate agents the force

is simply proportionate to the quantity, however small the quantity

may be. It may be so small as not to be appreciable by the senses,

and yet none the Jess act. For instance, the smallest particle of

matter, all appearances to the contrary notwithstanding, possesses

gravity . . . 488-441.
(6) The whole agent acts along the whole line ofi its depth on the

patient; not merely that extremity of the agent which comes into con-

tact with the patient . . . . , . . 441-442
(c) A certain definite portion of the patient is affected by the agent,

and no more. The sun and the moon diffuse light through similar

dimensions of the medium, although with enormous differences of

intensity, corresponding to their differences of magnitude. . 442-443
(d) Will less than that definite portion suffice for the action? It

will not, unless tbat lesser portion be disunited from the rest, so as

to become a whole in itself . . . ~ 443
(e) Does half of the agent acton half of the portion affected, or does

the whole act on the whole portion ? The whole acts on the whole

portion . . . . 443-444
(f) Does the half of this portion first affected, carry on the charige

to the second half, or docs the whole change come from the agent?

The latter is the true view . . . . . . . . 444-445

CHAPTER V.

(a) With regard to the patient, how can terrene substance be
acted on by celestial, which is of different kind, since celestial is
incorruptible? The reply is that whatever the difference between
celestial and terrestrial substance, yet the Species generated by the
former are communicable to the latter . . . 445-446

(^) One celestial body may act on another ; ‘not by changing its
specific nature, but by bringing that nature to greater per-
fection. . . . . 446-441

(c) We must admit that, 3 in a certain sense, terrene things act on
celestial, since there is a sense in which all parts of the universe are
assimilable to all the rest. In vision species pass from the eye to the
object seen. Such species do not change the specific nature of the
celestial object, nor interfere with its superiority ; they do but draw
out that which it has in common with the lower . . . 447-449

CHAPTER VI.

We have, lastly, to consider what corporal agents are capable of
completing their action on patients affected by them. (The earth, as
the central point of the universe is the great region of change. The

PART Il. clxxvii

VOL. II. PAGES
heavenly bodies moved by spiritual intelligences are unchangeable.)
We shall find that the four elemental substances can carry their
action to completion, and especially the element of fire . . 449-451
But many compound substances are higher in rank than the
elemental. Why cannot they do the same? There resides in them
an aptitude for doing this, but they are practically debarred from
doing it. Were it otherwise, the higher substances would transmute
the lower into their own substance, and the lower would disappear,
and thus the order of the universe would be subverted. Consequently
spiritual and celestia] substances, while generating their species,
cannot bring them to actual completion. Such compound substances
as the heavens or as man, if their species were made complete, would
do away with all lower substances. Consequently, the carrying of
species to their complete effect is limited to very few substances, such
as the elements, and especially the element of fire. . . 451-455
The same thing is to be said of attributes or accidents. Some of
these, as hot, cold, moist, dry, can complete their species, especially
the accident of heat. Light also can do this in bodies adapted to it.
Of colour, odour, savour, and sound the same cannot be said . 455-456

PART II.

CHAPTER I.

.. We now have to consider the mode in which the radiation of
species takes place. The first part of the patient, when acted on,
becomes itself a force acting upon the second part, and so onward.
These successive parts of the patient are of equal dimension. From
the starting-point in the agent, or, which is the same thing, from the
point of the patient first affected, emanate rays in all directions in
straight lines. Those emanations, of whatever kind they be, are
called rays, by analogy with what we see emanating from a star
or any luminous point. Their rectilinear direction continues until
modified by an opaque surface which reflects them, or a change of
medium which refracts them. These lines are not merely of one
dimension: they have breadth, and depth, as well as length . 457-460

CHAPTER II.

There are five kinds of rays to be considered. (a) Rectilinear
rays, where the medium is uniform. (2) Refracted rays. The ray
passing from a rarer to a denser medium is deflected towards the
perpendicular drawn to the surface at that point ; and conversely,
when passing from denser to rarer. (c) Reflected rays. When the

-

clxxvili ANALYSIS: MULTIPLICATION OF SPECIES.

VOL. IIT. PAGES

ray meets an opaque surface, it is turned back in a direction making
with the perpendicular to the surface an angle equal to the angle of
incidence. (4) In the case of animate bodies, the ray follows
a tortuous path along: a nerve towards the centre of sensation. (e)
Secondary, or accidental, rays may be emitted, not from the luminous
point, but from the principal ray: as in the case of rays coming
through an opening into a dark room, from which secondary rays
are dispersed through the room ; although the eye placed in one
of those rays cannot see the luminous point. Rays from the sun
of this kind are of greater utility to living beings than direct

rays . à ‘ CE NE" à . " : ‘ . 460-465

CHAPTER III..

Whether the ray falls on a line or on a surface, whether the sur-
face be plane, convex or concave, the law is the same. The mode
of measuring the incident and' the reflected angle is explained else-
where. In refraction from the rarer to the denser medium the ray
is deflected towards the normal: From the denser to the rarer
away from the normal. The accompanying diagrams will illustrate
this. Perpendicular rays, coinciding with the normal, are not

deflected. ; s ; : 2 . 465-468

What is the cause of refesion and se früctiofia ? All media, however
transparent, offer a certain amount of resistance to the passage of the
ray. This is more completely overcome by the perpendicular than
by the oblique ray. The oblique ray, passing into the denser
medium, follows the course of the perpendicular ray as far as
possible, i.e. is deflected towards it, as being the path of least
resistance. On the contrary, when passing into the rarer medium,
the energy which it has been hitherto exerting in tlie denser, now
finds a vent in carrying it away from the normal, i.e. along a path

of greater resistance . , " à . 468-

That these are the respective paths followed, is shown by the
double refraction taking place when rays impinge on a globular body
filled with the denser medium. The diagram shows that the rays
issuing from the globe converge to a point, and that at this point

470

combustible substances are ignited . . «». «+ « «© 470-472

CHAPTER IV..

To what extent does refraction take place in the heavens? The
celestial orbs are of the same degree of translucency; in these there-
fore there is no refraction of rays. Rays passing from the sphere of
ether to that of air (which latter includes that of fire) are refracted ;
since ether is the more subtle medium. The proof of this is that the

PART 1H. cixxix

VOL. II. PAGES

apparent polar distance of a star is less when rising than when passing

the meridian. At the zenith, the ray, impinging on the sphere of air

perpendicularly, is unrefracted. At the horizon it is refracted. With

the circumpolar stars the polar distance appears less, when they pass

the meridian nearer the horizon, than when they pass it nearer the

zenith ; for the same reason. The precise quantity of this refraction

can be measured by astronomical instruments. Ptolemy first indicated

this source of error, and Alhazen. has verified it. It has to be taken

account of in lunar tables . . . . 472-476
There is no subsequent refraction between the sphere of fire and ;

that of air, as the one passes into the other by imperceptible

degrees . . . 476-477
Rays falling from the planets o on regions of the earth beyond the

tropics must all fall obliquely and therefore be refracted . — . 477-478

CHAPTER V.

(a) No bodies are so dense that rays may not pass through them,
though these may not always be perceptible by human organs. Some
bodies of intermediate density may partly refract, and partly reflect
the rays, as in the case of water e. . . 478-479

(^) Hardness and. solidity are to be distinguished from density.
Glass and crystal, though hard, must yet be rare, i.e. their particles
must lie somewhat far apart, since rays pass freely through them.
Hardness depends not on the number of the particles but on stability
and freedom from moisture. (c) Reflexion depends on the smooth-
ness of the surface that reflects.. A rough surface disperses the rays
in different directions . e. 0. 479

(d) We mvst.not suppose that the ray produces any effect on the
surface that reflects it. No secondary or accidental ray is generated at
the point of reflexion. Were it so, such an effect would be visible,
whatever our position might be with regard to the mirror. All that
the reflecting surface does is to change the direction of the ray.
The reflected ray.is strictly continuous with the incident ray . 479-481

CHAPTER VI.

In reflexion, the angles made by the incident and the reflected ray
with the perpendicular to the surface are equal. This may be shown
experimentally by an instrument constructed for the purpose, and
the diagrams annexed give geometrical proof of it. The rule holds,
whether the reflecting surface be plane, concave, or convex . 481-486

CHAPTER VII.

Rays reflected from a plain surface are divergent. Rays reflected
from a spherical concave surface converge at various points on

clxxx ANALYSIS: MULTIPLICATION OF SPECIES.

VOL. II. PAGES
the diameter which forms the axis of the mirror; those from the
circumference of any circle drawn on the mirror in a plane perpen-
dicular to the axis will meet in a point. The smaller the circle the
greater will be the distance of the point of convergence from the
mirror; and conversely. (Such circles are, of course, merely
imaginary ; they merely indicate a series of points similarly placed
with regard to the axis) . . . . . 486-490

But another form of concave mirror has been devised in which the
curvature is such that all the rays shall converge to a single point.
d his cannot be explained here, but it may be mentioned that the
curvature is that of a conicsection . . . .. . « 490-491

CHAPTER VIII.

Rays from the object proceed equally in all directions, as radii
from the centre of a sphere. It is objected that.rays passing through
an angular orifice illuminate an angular not a circular space. But
this depends on the distance of the illuminated surface from the
orifice. If the distance be sufficient, the illuminated surface is cir-
cular. The smaller the orifice, the less the distance required to
obtain this result. Much depends also on the strength of the rays;
those of the sun at noonday, being stronger, produce the result more
readily than the feebler rays of morning light. For the same reason,
at noon a smaller portion of the solar surface will effect the result than
in the morning ; in the latter case the illumination not being circular,
much will be dispersed and lost. That the shape of a flame is not
spherical but conical, is due to the ascending force of the particles.
In the sphere of fire, where there is no such force, the fire assumes its
natural (spherical) shape. The centre of the illuminated surface is
most strongly illuminated ; the surrounding parts being illuminated
by intersecting rays, and therefore more feebly. Since all regular
figures can be inscribed in a circle, the spherical form of emission of
rays includes all the others, and especially the conical. . 491-404

CHAPTER IX.

Species proceed from every point in the agent, not from one only.
We see this in the case of shadows. If an illuminated body be less
than the illuminating, the shadow formed is conical and limited ; if
the two are equal, it is cylindrical and unlimited. If the illuminated
body be greater, the shadow is divergent and unlimited. We are
supposing that the agent is homogeneous. If it be heterogeneous,
we must consider each homogeneous part separately. In dealing
with the cone of rays proceeding from any point, we have to remember
that it is the axis of the cone, directed vertically to the surface acted

PART Ill. clxxxi

VOL. II. PAGES
on, which is specially potent, and has the greatest penetrative power.
It is to be noted that rays proceeding from a very distant source
appear parallel, though in reality they are not so: so the walls of
a house seem parallel to each other, though in reality each is directed
to the centre of the earth . . . . . "M . 494-498

CHAPTER X.

Optical principles teach us that in looking at a sphere the visual
cone embraces less than half the surface. In considering the portion
of a convex or concave surface that can be illuminated by a source of
light, we have to determine to what portion of it rectilinear rays can
proceed from the illuminating point without impediment. In the
mutual action of two spheres, more than half the surface of the smaller
is involved, less than half of the larger . . el; . 498-501

PART III.

CHAPTER I.

We have now to consider the nature of species as existing in the
medium. Many have regarded it as body. But this is misleading.
To speak of it as body would imply that it was something which
divided the surrounding medium, having three dimensions of its own.
But the species has no dimensions other than those of the medium in
which it is generated. During the generation of species from the
medium, the medium does not lose its corporeal character, nor is any
new body created or added. The species is simply a portion of the
medium wrought on in a peculiar way by the agent. Though so
wrought on as to resemble the agent, yet the substance of which it is
formed is that of the medium . . e; . « « 9002-504

But the species moves onward in space, while the medium remains
at rest: how can the species be said to have the bodily substance of
the medium? The reply is that the species successively formed are
not numerically identical. What takes place is the successive genera-
tion from point to point of something new, as in the case of a shadow
apparently shifting its position, but which is really being constantly
renewed. It is asked why does not the movement of the air by wind
affect the direction of the species? The reply is that the force
exerted by the agent is in a definite direction and renews the species
in each portion of air as it is driven by. In the case, again, of reflex-
ion, there is no violent casting back of the species: it simply pursues
the only path possible to it. What we call species is not one identical

cixxxii ANALYSIS: MULTIPLICATION OF SPECIES.

VOL.II. PAGES
thing, but a continuous succession, each generating that which follows.
It has been said that light is body, or an emanation from body. But
Aristotle denies this, remarking that in that case we should perceive
its translation from east to west at sunrise. The remarks on the
subject in the Topics are not to be taken as conveying Aristotle's
real opinion . . . . . . . 2 . 504-507 '

CHAPTER II.

The second question is whether the species of a corporeal agent
should be regarded as corporeal or spiritual. Clearly the former:
since it is not a soul, or an intelligence, or a first cause; and these
only can be considered as spiritual. The species must be of like
nature with the agent, and of like nature with the completed effect.
It cannot be of nobler nature than that which generates it. Some hold
that, though in its essence corporeal, yet its mode of existence is
spiritual. But there cannot be this disparateness between the essence
and the mode of existence. The essence of the species has dimension,
derived as we have seen from the medium ; it is therefore corporeal.
It is said that it has not material essence (material being here taken
for corporea]). But even spiritual substances have material essence:
they are compounded of form and of matter: much more, there-
fore, are species material. It has been already shown that the
species of corporeal substance resembles the total compound. In
the medium not merely is the formal essence generated but the
material, although the essence be incomplete. I therefore conclude
that the species of a corporeal object is corporeal . . . 507-509

The contrary view has arisen from imperfect translations of Aver-
roes, Avicenna, and Aristotle. In these the word insensible has been
mistaken for immaterial. And because spiritual things are insensible,
therefore what is insensible has been taken to mean spiritual and
immaterial. It is objected that species are not always insensible, as
when a ray passes through a window or through coloured glass. But
this is only accidental. Some expressions of Avicenna as to the
reception of impressions in the brain have been wrongly interpreted.
They must be taken in connexion with what Aristotle has said on the
same subject . . . . . . . ~ » . 9809-511

CHAPTER III.

I pass to the question of the mingling of species in the medium.
The question is one of much difficulty, but Ptolemy and Alhazen
throw great light upon it. Species of the same kind melt into one,
and if opposite, then the stronger overwhelms the weaker. Those
that are contingent, i.e. have no relation to each other, co-exist

PART IV. cixxxiii

VOL.II. PAGES
separately. Species in fact act in this respect as do their agents,
and as do their completed effects. Alhazen thus explains the unity
of impression resulting from species of an object entering the two
eyes ; they are united in the brain. But if species are thus mixed,
how do we recognize various objects as distinct? Because through
the point of mixture some rays come perpendicularly from the object
to the eye, others come to this point obliquely; these latter are
eclipsed by the former. We may remark further that the various
parts of the agent are always active: the generation of the species
is therefore continuous. Species unrelated to one another do not
commingle; they exist separately and simultaneously. . 9011-516

PART IV.

CHAPTER I.

We have now to consider how and why species are weakened in
their transit. Is there resistance in the medium? There is. For
every agent produces rarefaction and condensation, as the first process
in every natural action. What is rare resists condensation, and con-
versely. Therefore every medium offers resistance. Further, there
is a practical limit to rarefaction. It may be said that resistance is
only offered by contraries, and that, to many agents generating
species, nothing is contrary, in the sense in which darkness is contrary
to light. But the resistance is not to the species themselves, but
to the processes of rarefaction or condensation which accompany
them . . . . . . . . . . . . 517-518

It is obvious that species, so long as they continue to radiate, and
are not arrested by an accumulation of such material as will intensify
their action (as in the case of fire acting on fuel), are weakened by
distance. The senses are less affected by a distant than a near
object. Two causes may be assigned. It is said to be a law that,
as the first species is weaker than the agent, so the second is weaker
than the first, and so on. This, however, is not invariable. If iron
be held at some distance from a magnet, the iron is more affected
than the air between them. So a ray, passing through coloured glass,
produces a stronger effect on a distant wall than on the intermediate
air. Another reason may be assigned. The agent radiates force in
all directions. Much force is dispersed thus. And though, for special
reasons, the force in any one line may be found not to grow weaker,
yet it will be so where the medium is ordinarily pervious. Thus both
distance and radiant dispersion account for the weakening of species.

clxxxiv ANALYSIS: MULTIPLICATION OF SPECIES.

VOL.II. PAGES
When the direction of radiation is from terrestrial to celestial, it
might be thought that the increasing rarity of the medium would
compensate the weakening of the species from dispersion; but the
second cause operates at a faster rate than the first. For radiation
in the reverse direction, from heaven to earth, there can, of course, be
no such compensation . . . . . . e . 518-521

CHAPTER II.

Supposing space were unlimited, could multiplication of species go
on indefinitely? No; for, as we have seen, the species grows con-
tinually weaker the further it is from its source. If the supply of
matter on which it could operate were infinite, then no doubt the
action would be infinite ; but this is not the case. It might be said
that, since matter is infinitely divisible, there would always remain
something on which the species, however enfeebled by distance,
could act; that therefore the duration of the action would be infinite.
But this seems a forced and unsatisfactory conclusion. Again, it
might be urged that the medium may grow continually more subtle so
as to correspond to the continual weakening of the species. But this
does not in fact take place. As a fact, the resistance, in our world,
which is finite, is always sufficient to prevent the species from
passing beyond a certain distance . . , . 021-524
Supposing the existence of a vacuum between earth and heaven,
no species could radiate ; for no natural action can take place in
a vacuum. It follows also that beyond the ninth and tenth heavens
no species from the stars can radiate. For beyond these there is
nothing, not even empty space . . . "NN . . 024-525

CHAPTER III.

The radiation of force takes place in time. For it involves change
in the medium; and change involves time. When the path of
propagation is refracted, more time is taken than when the path is
direct. Finite force cannot act instantaneously, for then it would be
equal to infinite force. As a point is to an instant, so is a line to
time. The passage of a point is instantaneous, in the passage of a line
time is occupied. Translation implies before and after . . 525-526

It is said that the transit of light is instantaneous. But all that is
meant is that the time required is insensible. Aristotle, in saying
this, is arguing against Empedocles, who regarded light as a substance
flowing from the luminous body. In this case no doubt we should be
able to see its passage from east to west in the heavens, But the
view here taken of light is not that it is a body translated, but
a movement continuously propagated. Aristotle no doubt dis-

PART V. clxxxv

VOL. If. PAGES

tinguishes the propagation of light from that of sounds or odours.
But the distinction is of degree ; light being more subtle, its motion

is morerapd . .. . « 526-528

Alkindi urges that, though through short distances the transit of
light may be imperceptible to our senses, yet that the summation of
short periods would amount, in the transit from east to west, to some-
thing that would be perceptible. But of imperceptibility there are
many degrees; and the propagation of light is so rapid that the
summation of a vast number of imperceptible periods may still not
reach the point at which perception of time by human sense is
possible . . . e " .

It is further maintained that in radiation of species, as here described,
more time would be occupied than in translation of a body through
space: because between the formation of any one species and the
formation of that which follows it, there is an interval of rest. The
fact is, however, that the resistance of the medium to a body carried
through it would be far greater than it would be to the formation
of species, which involves an exceedingly slight disturbance of the
medium ; so that the motion in this latter case will be far more rapid,

and the interposition of intervals of rest will pass unperceived . 528-529

PART V.

CHAPTER I.

In propagation of species we have to consider, first, that which we
call univocal, as when light makes light; secondly, the eguvoca/, as
when light makes heat, or any other effect of a different kind. As to
the first, we remark that the strongest are those which proceed by
direct lines, as contrasted with those which are refracted or reflected.
We may omit for the present those which proceed on tortuous paths,
as in the case of nervous action; since here a different agency, that
of life, comes into play. The species called accidental, i.e. which
proceed, not directly from the object, but secondarily from the species,

are the feeblest of all . . . . " . . . . 990-

CHAPTER II.

The path of some species falls perpendicularly on the object ; these
are the strongest ; and this whether the object be a plane surface or
curved. In either case the angles made are equal. That which
impinges on the convex surface of a sphere, is stronger than that
which falls on the concave surface, as being necessarily shorter. The.

VOL. I. n

994

cixxxvi ANALYSIS: MULTIPLICATION OF SPECIES.

VOL. II. PAGES
refracted ray is stronger than the reflected, its path lying nearer to
the direct perpendicular ray. The ray refracted by passage from
a denser to a rarer medium is less potent, for the same reason, than
the ray refracted from rarer to denser. In the case of reflected rays,
those that make an angle with the vertical line produce a greater
effect than those that fall vertically; not merely because they diverge
less from the direct ray, but because they can be accumulated by
suitably shaped mirrors. Some of these are described, though
I have not myself seen them, which bring rays to a focus both in front
and behind them . " . . . . . . . 9934-589

CHAPTER III.

Cones of rays come from the agent to each part of the surface
acted on. The shorter the cone, the stronger is the action. The
shortest cone is thus defined. Let a circle be drawn in the agent
sphere dividing its operative from its inoperative part. From any
points in the circumference of this circle let diameters of the sphere
be drawn. Tangents to the sphere at the extremities of these
diameters will form the shortest cone. Other points connected
with this subject are illustrated by the accompanying diagrams . 589-543

PART VI.

CHAPTER I.

As species are generable, so are they corruptible. And this
in two ways: (1) from exhaustion of their own strength; (2) from
tendency in the substance acted on to resort to its own natural
condition . .« + . . ^. . . (005. 5. 044-945

CHAPTER II.

When the generating agent is removed, does the species at once
disappear? Not instantaneously, but gradually, from the causes stated
in the previous chapter. The apparent permanence in some cases of
the species, after the agent has disappeared, is to be explained. The
semen retains its force in the absence of the male parent; but here
the female supplies the place. A heated stone retains its heat. Here
the species, i. e. incomplete effect, has passed into a more complete
effect. . . . « © 6 5 5 945-547

CHAPTER IIL

Are the reiterated actions of the agent on the patient to be regarded
as numerically identical, or as distinct? They must be regarded as

PART VI. clxxxvit

VOL. II, PAGES
distinct. There is no question here of anything being created. The
action and motion are not fixed and permanent things, but successory.

If a box be made and then taken to pieces, and subsequently put
together again, we consider that it has been twice made, although
out of the same material . . . . . . . . 947-549

CHAPTER IV.

In a transparent medium, does the first species continue during
the presence of the agent, or is it destroyed and renewed? The
latter is the case. There is far more rapid dispersion in a rare than
in a dense medium. In certain regions, as in the tropical zone where
the sun is vertical for a considerable time, there is less rapid and
complete dispersion. Much depends on the nature of the body
acted on. Dense bodies retain the effect for a longer time than rare.
The foregoing remarks apply to terrestrial and corporeal things.
They would need qualification if applied to things spiritual or things
celestia] . . . . e . 549-552

FRATRIS ROGERI BACON

ORDINIS MINORUM, OPUS MAJUS.

PARS PRIMA
HUJUS PERSUASIONIS,

IN qua excluduntur quatuor universales causae totius igno-
rantiae humanae, habens quatuor distinctiones. In prima sunt
quatuor capitula. In primo data totius persuasionis intentione
reprobantur illae quatuor causae universali sermone.

CAPITULUM I. |

Sapientiae perfecta consideratio consistit in duobus, vide-
licet, ut videatur quid ad eam requiritur, quatenus optime
sciatur; deinde quomodo ad omnia comparetur, ut per eam
modis congruis dirigantur. Nam per lumen sapientiae ordi-
natur Ecclesia Dei, Respublica fidelium disponitur, infidelium
conversio procuratur; et ili, qui in malitia obstinati sunt,
valent per virtutem sapientiae reprimi, ut melius a finibus
Ecclesiae longius pellantur quam per effusionem sanguinis
Christiani. Omnia vero quae indigent regimine sapientiae
ad haec quatuor reducuntur; nec pluribus potest comparari.
De hac igitur sapientia tam relate quam absolute scienda
nunc, secundum tenorem epistolae!, quicquid possim circa

! Epistolae praecedentis, Cottonian MSS., Jul D. v. (hereafter referred to as
Juk*. This was the letter of Pope Clement IV. It ran thus:

‘ Dilecto filio Fratri Rogerio dicto Baccon ordinis Fratrum Minorum.

* Tuae devotionis literas gratanter recepimus, sed et verba notavimus diligenter

VOL. I. B

Definition
of wisdom.

2 OPERIS MAJORIS PARS PRIMA.

persuasionem ad praesens Vestrae Beatitudini praesentare
conabor. Quoniam autem illa, de quibus agitur, sunt grandia
et insolita, gratiam et favorem humanae fragilitatis requirunt. |
Nam secundum Philosophum septimo Metaphysicae, ea quae
sunt maximae cognitionis secundum se, sunt minimae appre-
hensionis quoad nos. Involuta enim veritas in alto latet et in
profundo posita est, ut dicit Seneca septimo de beneficiis,
et quarto Naturalium. Et Marcus Tullius in Hortensio dicit,
quod omnis noster intellectus multis obstruitur difficultatibus,
quoniam ipse se habet ad manifestissimum in sua natura, sicut
oculus noctuae et vespertilionis ad lucem solis, ut Philosophus
dicit secundo Metaphysicae, et velut surdus a nativitate ad
delectationem harmonicam, sicut undecimo Metaphysicae dicit
Avicenna. Quapropter sufficit nobis in inquisitione veritatis
proprii intellectus imbecillitas, ut quantum possumus causas
et occasiones erroris extraneas longius a debilitate sensus
nostri relegemus.

Fourcauss — Quatuor vero sunt maxima comprehendendae veritatis

of error:
authority,
custom,
popular
prejudice,
presump-
tion of
knowledge.

offendicula, quae omnem quemcumque sapientem impediunt,
et vix aliquem permittunt ad verum titulum sapientiae
pervenire, videlicet fragilis et indignae auctoritatis exem-
plum, consuetudinis diuturnitas, vulgi sensus imperiti, et
propriae ignorantiae occultatio cum ostentatione sapientiae
apparentis. His omnis homo involvitur, omnis status occu-
patur Nam quilibet in singulis artibus vitae et studii et
omnis negotii tribus pessimis ad eandem conclusionem utitur
argumentis, scilicet, hoc exemplificatum est per majores,
hoc consuetum est, hoc vulgatum est; ergo tenendum. Sed
oppositum conclusionis longe melius sequitur ex praemissis,
sicut per auctoritatem et experientiam et rationem multi-

quae ad explanationem earum dilectus filius G. dictus Bonecor miles viva voce
nobis proposuit tam fideliter quam prudenter. Sane ut melius nobis liqueat
quid intendas volumus ct tibi per Apostolica scripta praecipiendo mandamus
quatenus, non obstante praecepto praelati cujuscunque contrario vel tui ordinis
constitutione quacunque, opus illud quod te dilecto filio Raymundo de Lauduno
communicare rogavimus in minore officio constituti scriptum de bona litera
nobis mittere quam citius poteris non omittas, et per tuas nobis declares literas
quae tibi videnter adhibenda esse remedia circa illa quae nuper esse tanti
discriminis intimasti, et hoc quanto secretius poteris facias indilate. Datum
Viterbii x Kalend Julii anno ii^ (Wadding, 7fstmales Minorum, vol. iv, p. 265^

CAUSAE ERRORIS. 3

pliciter- probabo. Si vero haec tria refellantur aliquando
magnifica rationis potentia, quartum semper in promptu est
et in ore cujuslibet, ut quilibet suam ignorantiam excuset; et
licet nihil dignum sciat, illud tamen magnificet imprudenter,
ut sic saltem suae stultitiae infelici solatio veritatem opprimat
et elidat. Ex his autem pestibus mortiferis accidunt omnia
mala humano generi; nam ignorantur utilissima et maxima
et pulcherrima sapientiae documenta, et omnium scientiarum
et artium secreta ; sed pejus est, quod homines horum quatuor
caligine excaecati non percipiunt suam ignorantiam, sed cum
omni cautela palliant et defendunt, quatenus remedium non
inveniant ; et quod pessimum est, cum sint in tenebris errorum
densissimis, aestimant se esse in plena luce veritatis; propter
quod verissima reputant esse in fine falsitatis, optima nullius
valoris, maxima nec pondus nec pretium obtinere et e con-
trario falsissima celebrant, pessima laudant, extollunt vilissima,
caecutientes,aliud esse omnem sapientiae fulgorem, fastidientes!
quae magna facilitate possunt adipisci. Et propter stultitiae
magnitudinem ponunt summos labores, consumunt tempora
multa, magnas expensas effundunt in iis, quae nullius utilitatis
vel parvae sunt, nec dignitatis alicujus secundum judicium
sapientis. Et ideo necesse est ut violentia et malitia harum
quatuor causarum omnis mali cognoscantur in principio, et
reprobentur, et longe a consideratione sapientiae relegentur.
Nam ubi haec tria dominantur, nulla ratio movet, nullum jus
judicat, nulla lex ligat, fas locum non habet, naturae dictamen
perit, facies rerum mutatur, ordo confunditur, praevalet vitium,
virtus extinguitur, falsitas regnat, veritas exsufflatur. Et
ideo nihil magis necessarium est considerationi, quam certa
damnatio istorum quatuor per sententias sapientum electas,
quibus non poterit contradici.

Quoniam vero sapientes tria prima simul collidunt et repro-
bant, et quartum propter singularem stultitiam propriam lima-
turam desiderat, ideo primo trium malitiam aperire conabor.
Sed quamvis auctoritas sit unum de istis, nulla ratione loquor
de solida et vera auctoritate, quae vel Dei judicio collata est

! Caecutientes. .. I restore the omission from B. et D., omnem sapientiae
fulgorem, fastidientes.'

B 2

4. OPERIS MAJORIS PARS PRIMA.

Ecclesiae, vel quae ex merito et dignitate proprie nascitur in
sanctis philosophis et perfectis prophetis, qui juxta humanam
possibilitatem in studio sapientiae experti sunt; sed de illa
auctoritate loquor, quam sine Dei auxilio violenter usurpave-
runt multi in hoc mundo, nec ex merito sapientiae, sed ex
propria praesumptione et desiderio famae, et quam vulgus
imperitum multis concessit in pernicionem propriam judicio
Dei justo. Nam secundum scripturas propter peccata populi
multotiens regnat hypocrita; de sophisticis enim auctori-
tatibus multitudinis insensatae loquor, quae aequivocae sunt
auctoritatis, sicut oculus lapideus aut depictus nomen habet
oculi, non virtutem.

CAPITULUM II.

The first Sed tria reprobat sacra scriptura, sacri doctores condemnant,
three re- ; : . . '«.
cognized by JUS Canonicum vetat, philosophia reprehendit ; sed propter
Cicero, — rationes prius tactas de philosophicis allegandis, et quia minus
Seneca . . . .
Adelard, "Vulgatae sunt sententiae Philosophorum circa haec tria, eas
Averrhoes principaliter introducam. Similiter vero omnes has tres pestes
and others. . .
Seneca libro secundo epistolarum prope finem uno sermone
condemnat. Dicit igitur, ‘inter causas malorum nostrorum
est, quod vivimus ad exemplar, nec ratione componimur, sed
consuetudine abducimur; quod si pauci facerent nollemus
imitari, cum plures facere ceperint, quia frequentius quam
honestius, illud facimus, et recti locum tenet apud nos error,
ubi publicus factus est! Philosophus vero per totam philo-
sophiam suam persequens auctoritatem indignam secundo
Metaphysicae causas humani erroris asserit praecipuas con-
suetudinem et populi testimonium ?. Et iterum Seneca libro
de vita beata dicit, ‘Nemo sibi solum errat, sed alieni erroris
causa et auctor est, versatque nos et praecipitat error, et
alienis perimus exemplis?. Et in secundo libro de Ira,
! The passage is in the ragrd letter (lib. xx. Ep. 8, ed. Haase). Part of the
quotation is slightly condensed from the original, which runs, * Cum plures
facere coeperunt, quasi honestius sit quia frequentius, sequimur.' In the last
sentence Jebb substitutes certi for recti.
* Met. lib. i. (minor), cap. 3 al 3° d«podcas ward rd. (0 ovpBaivovow ds ydp

elaGaper obras dfiodper Ad-yeoOa, et seq.
* Seneca, Dialog. vii. cap. 1.

CAUSAE ERRORIS. 5

* propter malitiam consuetudinis, ait, ‘difficulter reciduntur
vitia, quae nobiscum creverunt i! Et in libro de vitae beati-
tudine contra vulgi sententias refert, ‘Nulla res majoribus
malis nos implicat, quam quod ad rumorem componimur,
optima rati ea quae magno assensu recepta sunt, nec ad
rationem sed ad similitudinem vivimus. Inde est ista tanta
coacervatio aliorum supra alios ruentium. Quod enim in
strage homini magna evenit, cum se populus ipse premit,
nemo ita cadit ut non alium in se attrahat, primique sunt
exitio sequentibus. Et iterum dicit in eodem, ‘Stat contra
rationem defensor mali sui populus' ; et infra, * Non tam bene
cum rebus humanis agitur, ut meliora pluribus placeant,' et
sequitur, argumentum pessimi turba est?" Et Marcus Tullius
tertio de quaestionibus Tusculanis ait, ‘Cum magistris traditi
sumus, ita variis imbuimur erroribus, ut vanitati veritas, et
opinioni confirmatae ipsa natura cedat? Atque in Lucullo
dicit, *quidam obsecuti amico cuidam aut una cum aliquo
quem audierunt oratione capti, de rebus incognitis judicant,
et ad quamcumque sunt disciplinam quasi tempestate delati,
tanquam ad saxum inhaerescunt; plerique errare malunt,
eamque ,sententiam quam amaverunt defendere, quam sine
pertinacia perquirere quid constantissime dicant *, Et propter
pravitatem consuetudinis queritur in primo de divina natura,
*non pudet speculatorem naturae ab animis consuetudine
imbutis petere testimonium veritatis? Et contra vulgi sen-
sum dicit proemio secundi quaestionum, philosophia ‘ est
paucis contenta judicibus, multitudinem ipsam consulto fugiens,
eique suspecta et invisa 5 et in eodem libro ait, * laudabiliora
mihi videntur omnia quae sine populo teste fiunt?.' Sed alii
divisim haec tria persequuntur. Nam in libro Quaestionum
Naturalium Alardi * quaeritur de auctoritate fragili: ‘Quid est

1 Seneca, Dial. iv. 18.

* These passages are from Seneca, Dial. vii. 1 and a.

* Cic. Tusc. Disput. lib. iii. cap. 1.

* Academ. Priorum, lib. ii. 3. This is a selection of two passages from the
chapter. The quotation is not entirely accurate.

*^ De Deorum Natura, i. 30. * Tusc. Disp. lib. ii. cap. 1, § 4.

" Lib. ii. cap. 26, § 64.

® Jebb has Mardi, a mistake which, if he had had the Oxford MSS. before

They are
shown by
practical
experience.

6 OPERIS MAJORIS PARS PRIMA.

aliud auctoritas hujusmodi quam capistrum? Ut bruta quippe
animalia capistro ducuntur, nec cui nec quo ducantur dis-
cernunt, sic nos paucos bestiali crudelitate captos ligatosque
auctoritas ipsa in periculum ducit. Et in libro de Dei aeter-
nitate, *qui elegerit alteram partem quaestionis propter
amorem consuetudinis non potest recte discernere veram
opinionem! Et Averroes in fine secundi Physicorum dicit,
* Consuetudo est maxima causa impediens a pluribus rebus
manifestis. Quemadmodum enim consueto ad aliquas opi-
niones licet nocivas, erunt ei faciles, et ideo credit eas esse
utiles; similiter cum fuerit assuetus credere sermones falsos
a pueritia, erit illa consuetudo causa ad negandum veritatem,
sicut quidam tam assueti fuerint comedere venenum, quod
factum est eis cibus. Et idem Averroes vult secundo Meta-
physicae *quod opposita principiorum cum fuerint famosa
sunt magis receptibilia a multitudine consequentibus testi-
monia multorum quam ipsa principia. Atque Hieronymus
in prologo quinti libri super Jeremiam asserit, ' veritatem
paucis contentam esse, et hostium multitudine non terreri.'
Johannes quoque Chrysostomus super Matthaeum dicit, quod
a veritate nudos se esse professi sunt, qui multitudine se
armaverunt.

CAPITULUM III.

Quod per auctoritates probatum est experientia cujuslibet
certius dijudicatur. Nam experimur in nobis et in aliis quod
haec tria, ut in pluribus amplectuntur mala, frequentius falsis

him, he would have avoided. The writer referred to is Adelard of Bath, who
lived in the early part of the twelfth century. He fills an important place in
the history of mediaeval science. He was the first translator of Euclid into
Latin; not, however, from Greek but from Arabic. A more complete translation
was made in the following century by Campano. (See Weissenborn, Abhand-
lungen sur Geschichte der Mathematik, Drittes Heft, Leipsic, 1880, pp. 141-166.)
Adelard studied in the Schools of Tours and Laon; and subsequently travelled
in Greece and Asia Minor. The passage here cited is from the sixth chapter
of his Quaestiones Naturales, a work full of audacious and original speculation.
In Bacon's mathematical treatise, as yet unpublished, he is frequently men-
tioned, always under the name Alardus. (See Sloane MSS. 2156, ff. 74-95. |
! I do not know what work is here referred to.

CAUSAE ERRORIS. 7

adhaerent. Quod si aliquando bonis et veris implicentur, fere
semper sunt imperfecta, et debilem gradum continent sapien-
tiae. Matris quidem opera ut in pluribus sequitur filia, patris
natus, domini servus, regis subditus, praelati bajulus, magistri
discipulus. Quia familiare est filiis Adae sibi auctoritatem
vindicare et sua exempla spargere in lucem. Nam omnes
homines secundum Aristotelem quarto Ethicorum amant sua
opera, ut parentes natos, et poetae metra, et sic de aliis. Et
ideo multi nimia licentia scribendi usi sunt, adeo ut pravis et
bestialibus viris insinuare non dubitaverunt, cur chartas non
impletis, cur a tergo non scribitis. Et hi sunt sicut pastor
claudus et caecutiens cum ovibus multis, quas errantes per
devia falsitatis nec possunt nec sciunt ad saniora sapientiae
pascua revocare, et sunt similes avibus, qui optant sine alis
volare, prius de magisterio praesumentes, quam boni discipuli
gradum adepti sunt, quum necessario tot incidunt in errores,
quod otiosi comparatione ipsorum reputant se felices; sicut
quando -multi currunt in stadio, ille quem desperatio currere
non permittet, quantumcunque sibi videatur pernitiosum, se
tamen felicem reputat comparatione illius, qui currens cadit
in foveam invisam. Et ideo videmus fide oculata quod pro
uno exemplo veritatis tam in scientia quam in vita sunt plus
quam mille falsitates. Mundus enim plenus est hujusmodi
exemplis, atque unum exemplum verae perfectionis decem
millia imperfecta invenit de facili. Natura enim in numeris
formavit nobis perfectionis et imperfectionis documentum.
Nam tum numerus perfectus! dicitur, cujus partes aliquotae
ipsum praecise constituunt, et non est nisi unus infra denarium,
viz. senarius ; et unus inter Io et 100, ut 28 ; et unus inter 100
et 1000, ut 496; et unus inter 1000 et 10000 ut 8128; et sic
ultra; et utinam sic esset inter homines, et hoc humano
generi sufficeret. Sed nunquam fuit hoc nec in vita nec in
scientia, neque erit usquam in finalem peccati destructionem,
quoniam non solum est raritas eorum, qui in omni veritate et
scientia perfecti sunt, sed eorum qui ad perfectionem unius
veritatis vel scientiae devenerunt. Primi sunt et erunt et

! When 2*7! is a prime number, then 2?** (29-1) is a perfect number, as
6, 28, 496, 8128, &c.

8 OPERIS MAJORIS PARS PRIMA.

fuerunt semper paucissimi. Nam sunt vere perfecti, sed de
10000 hominum unus non invenitur sic perfectus nec in statu
vitae neque in professione sapientiae; utinam de secundo
genere perfectorum infra denarium unus esset, et sic ultra, ut
perfectio numerorum in hominibus conservaretur. Sed non
est ita, imo longe aliter invenitur. Similiter de consuetudine
probamus per experientiam in actibus nostris, quod nunc
datum est in exemplis. Revolvat quilibet vitam suam ab
infantia sua, et inveniet quod in pluribus ejus operibus facilius
mala et falsa duxit in consuetudinem. Nam in bonis et veris
identitas humanae fragilitati mater est satietatis, et delectatur
miser homo in varietate utilium secundum sententiam auctori-
tatum quas in principio allegavi; e contrario quidem in malis
et falsis ac nocivis sibi et aliis. Nam ut in pluribus actibus,
nisi gratia specialis et privilegium divinum in aliquibus
perfectis obtinet, humana corruptio diligenter continet ea,
quae veritati et saluti sunt contraria; nec taedio afficitur in
peccati continuatione, nec fastidium de facili invenit in rebus
variis. Quod si aliquis a juventute applicetur ad vitae et
scientiae veritatem, hic ut in pluribus actibus continet imper-
fectionem, et in ea jocundatur, perfectio enim contristat eum
frequentius ; nam paucissimos delectat, et maxime in virtutum
et scientiarum plenitudine, et ideo accidit quos aetas juvenilis
vix cavet ab errore, et senectus cum summa difficultate ad
perfectionem in aliquo transcendit. De vulgo enim idem
judicium est. Nam multitudo generis humani semper erravit
in Dei veritate, et paucitas Christianorum recepit; atque
scimus quod plebs Christianorum imperfecta est. Nam
paucitas sanctorum hoc ostendit. Similiter de philosophica
doctrina, vulgus enim semper caruit sapientia philosophiae.
Brevis enim philosophorum numerus hoc declarat. Et
vulgus quidem philosophantium imperfectum semper re-
mansit. Nam de famosis philosophus solus Aristoteles cum
sua familia vocatus est judicio omnium sapientum, quoniam
ipse omnes partes philosophiae digessit secundum possibili-
tatem sui temporis, sed tamen ad finem sapientiae non
pervenit, sicut satis manifestabitur inferius.

CAUSAE ERRORIS. 9

CAPITULUM IV.

Sed tamen quantumcunque fragilis sit auctoritas, nomen Of these
habet honoris, et consuetudo violentior est ad peccatum quam al ar
ipsa; utraque autem earum impetuosior est sensus vulgi. prejudice
Nam auctoritas solum allicit, consuetudo ligat, opinio vulgi potent s
obstinatos parit et confirmat. Consuetudo autem est altera
natura, ut dicit philosophus libro de memoria et reminiscentia !,
et in libro Problematum, et ideo majorem violentiam quam
auctoritas inducit. Unde philosophus 1o"? Ethicorum sen-
tentiae Jeremiae de pelle Aethiopum adhaeret, dicens, * quod
impossibile est vel difficile eum, qui per consuetudinem malam
induratus est, mutari ad bonum.' Et Sallustius in Jugurthino
sensum Solomonis profert, cum ait, ‘ubi adolescentiam
habuere, ibi senectutem agunt. Sententia quidem vulgi
caeteris improba magis est. Nam, ut ait Seneca tertio
Declamationum libro, * multitudo semel mota modum servare
non potest'; propter quod Johannes Chrysostomus super
Matthaeum dicit * convenerunt ut multitudine vincerent quem
ratione superare non poterant. Sic considerandum est dili-
genter quod vulgus imperitum non solum violentius est ad
persuasionem mali quam reliqua duo, sed stultum est et magis
elongatum a fine sapientiae. Nam exemplum perfectionis
trahitur ab aliquo in consuetudinem, sed vulgo sufficit ut non
erret. In nullo enim statu Ecclesiae requiritur ut ejus per-
fectionem teneat multitudo. Nam et apud religiosos paucitas
figitur in centro perfectionis suae et multitudo vagatur in
circumferentia. Sic est in statu multorum secularium, ut
cernimus ad oculum evidenter. Turba enim sicut cum Moyse
non ascendit in montem, sic nec cum Christo in transfigura-
tione Christi multitudo discipulorum assumpta est, sed tres
electi specialiter. Et cum magistrum perfectionis Christum
turba secuta est per duos annos praedicantem, postea demisit
eum, et in fine clamavit, * Crucifige.’ Nam vulgus nihil per-
fectum continuare potest, utinam enim vita, nec in studio
errasset. Et sicut nos hoc videmus in veritate fidei, sic in
professoribus philosophiae. Nam semper sapientes contra

1 De Memoria, cap. a Gc sep yap $voais bn 7d Eos.

IO OPERIS MAJORIS PARS PRIMA.

vulgus divisi sunt, et arcana sapientiae non toti mundo sed
plebi philosophantium — revelaverunt. Quoniam sapientes
Graeci nocturnis vigiliis congregati vacabant sine vulgo
collationibus sapientiae, de quibus A. Gellius scribit in libro
Noctium Atticarum, i. e. collationum sapientiae nocturnalium,
quas sapientes Attici, i.e. Athenienses celebrabant ut multi-
tudinem. vitarent. In quo etiam dicit ‘stultum est asino
praebere lactucas, cum ei sufficiant cardui, loquens de vulgo,
cui rudia et vilia et imperfecta sapientiae sufficiurit alimenta.
Nec oportet margaritas spargi inter porcos; nam rerum
majestatem minuit, qui vulgat mystica: nec manent secreta,
quorum turba est conscia, sicut in libro Gemmarum edocetur.
Atque Aristoteles in libro secretorum ! dicit, ‘ se fore fractorem
sigilli coelestis, si secreta naturae vulgaret.’ Et propter hoc
sapientes licet darent in scriptis radices arcanorum sapientiae,
tamen ramos et fructus vulgo philosophantium non dederunt.
Nam vel omiserunt scribere, vel per sermones figurativos et
multis modis, de quibus non est ad praesens dicendum,
occultaverunt. Quoniam secundum sententiam Aristotelis
libro secretorum et Socratis magistri sui, secreta scientiarum
non scribimus in pellibus caprarum et ovium, ita quod a vulgo
valeant aperiri. Sapientissimi enim et maxime experti
multotiens maximam difficultatem in libris reperiunt anti-
quorum. Et cum philosophus dividat probabile primo libro?
Topicorum, separat vulgus a sapientibus : Nam dicit probabile
esse quod videtur, vel pluribus, vel sapientibus ; sub omnibus

enim comprehenduntur vulgus et sapientes communiter, ergo

per plures vulgus designatur; quia de consortio sapientum
non est ipsum vulgusinsensatum. Et hocaccidit ei non solum
propter sui propriam stultitiam, sed quia in pluribus caput

! This work was perhaps the most widely diffused of the apocryphal writings
current in the middle ages on Aristotle and Alexander. It was translated from
the Arabic by a certain Philip, who dedicates the translation to Guido of
Valence, archbishop of Tripoli, with the remark that the treatise was addressed
by Aristotle to Alexander, who wished the philosopher to accompany him on
his Eastern expedition. It is sometimes spoken of as Aber de regimine principum,
also as liber decem scientiarum. Bacon refers to it frequently, and wrote
a copious commentary on it, which is preserved among the Tanner MSS. in
the Bodleian (116). '

* Top. lib. i. cap. a, $ 7.

= hee tant

CAUSAE ERRORIS. II

recipit languidum et infirmum, quod erroribus et proclive est
et auctor imperfectionis cujus nutu ducitur in omnem eventum.
Et ideo vulgus imperitum nunquam ad perfectionem sapientiae
potest ascendere, nam nescit uti rebus dignissimis: quas si
aliquando casu contingat omnia in malum convertit, et ideo
justo Dei consilio negatae sunt ei viae perfectionis, et optime
secum agitur quando permittitur non errare. Nam suum
nomen ostendit omnia quae praedicta sunt, et apud omnes
auctores vocatur vulgus imperitum vel insensatum. Imperitia
vero in errore et in imperfectione consistit, et ideo vulgo
familiaris est error et imperfectio. Nam multi sunt vocati,
pauci vero electi ad veritatis divinae receptionem, et similiter '
philosophicae. Quare Philosophus dicit secundo Topicorum,
quod sentiendum est ut pauci, licet loquendum sit ut plures ;
quia stultitiam vulgi aliquando simulare prudentia summa
aestimatur, praecipue cum est in furore suo. Ex his omnibus
colligitur malitia et stultitia horum trium et damnum humani
generis infinitum, et ideo suspecta sunt in omni causa, nec est
eis confidendum: et maxime vulgi sensus est negligendus
propter dictas speciales rationes, non quia aliquando cadant
supra vera, sed quia ut in pluribus falsis implicantur. Et
rarissime exemplum et consuetudo perfectionem habent,
vulgus autem nunquam pertingit ad eam, ut prius explana-
tum est.

CAPITULUM V.

Munimen vero ad defensionem contra haec habere non we are
possumus nisi mandata et consilia Dei ac scripturae suae et weet
Juris Canonici, sanctorum et philosophorum et omnium them by
sapientum antiquorum, sequamur. Et si his mandatis et aed by the
consiliis adhaereamus, non possumus errare, nec debemus wisdom
in aliquo reprobari. In praedictis igitur per philosophum ancients.
principaliter allegatum est ostendere horum pravitatem et
stultitiam, propter quas ipsa possemus et debemus evitare, sed
propter causas assignatas de inducendis philosophorum testi-
moniis silui fere in aliis; nunc autem possum invenire con-
similia testimonia, in quibus consilium vel mandatum de

obviando istis expressius habetur. Contra igitur sensum,

I2 OPERIS MAJORIS PARS PRIMA.

vulgi teneamus mandatum Exodi, * Non sequeris turbam ad
faciendum malum; nec in judicio plurimorum adquiesces
sententiae, ut a vero devies.’ Et consilium Tullii in fine! de
quaestionibus impleamus dicentis, * Tu autem etsi in oculis sis
multitudinis, tamen in ejus judicio stare noli, nec quod ipsa
putet id putare pulcherrimum. Et Seneca libro de copia
verborum invitat nos et consolatur recedentes a via multi-
tudinis, dicens, * Nondum felix es, si nondum turba te deriserit.’
Et contra consuetudinem impleamus consilium Cypriani, * Con-
suetudo sine veritate vetustas erroris est, propter quod relicto
errore, sequamur veritatem. Et Augustinus praecipit quod
veritate manifesta, cedat consuetudo veritati, quia consuetu-
dinem veritas et ratio semper excludit. Et Isidorus, ‘ Usus
auctoritati cedat ; pravum usum lex et ratio vincat. Et ideo
Tullius de immortalitate animae laudans et extollens eos, qui
fugiunt consuetudinem dicit ‘magni animi est cogitationem
a consuetudine revocare, Nomen autem auctoritatis favorabile
est. Et ideo majores nostri venerandi sunt, sive habeant
auctoritatem veram sive apparentem, quae est auctoritas ducum
vulgi. Et contra usum apparentis auctoritatis non solum
propria sunt consilia et mandata secundum vias Dei et sanc-
torum et philosophorum et omnium sapientum, sed quicquid
contra vitia humanae fragilitatis apud auctores veros dici
potest, commune est eis qui auctoritate abutuntur praesumpta.
Et ideo si consilia et mandata habemus contra defectus
verorum auctorum multo magis contra abutentes. Sed quia
auctores veridici, ut sancti et philosophi principales, juverunt
nos in consideratione veritatis, ideo regratiandum est eis, sicut
Aristoteles primo Metaphysicae regratiatur suis praedecessori-
bus, et in fine Elenchorum * de inventis multis ipsemet cupit
habere grates. Qui vero prima principia jecerunt, eis non
solum regratiandum, sed quasi totum cum quadam reverentia
ascribendum. Secundum quod Seneca vult tertio? naturalium,
‘si quid a posterioribus inventum est, nihilominus referendum

1 The word secundi seems omitted. The passage is in Tusc. Disp. ii. 26.

* De Soph. Elench. xxxiv. § 9.

* The passage is not in the third, but in the sixth book, cap. 5. It is not
very accurately quoted.

CAUSAE ERRORIS. I3

antiquis, quia magni animi fuit rerum latebras primitus dimo-
vere, et plurimum ad inveniendum contulit, qui speravit
posse reperire, et quamvis propter humanam fragilitatem in
multis defecerunt, tamen excusandi sunt. Nam in libro
memorato ait Seneca, ‘cum excusatione veteres audiendi
sunt.’

CAPITULUM VI.

Sed quoniam propter peccatum originale, et propria cujus- The wisest
libet peccata partes imaginationis laesae sunt, (nam ratio p men are
caecutiens est, memoria fragilis, ac voluntas depravata; et error.
verum et bonum uno modo sunt, falsum autem cuilibet vero
oppositum et malum cuilibet bono contrarium infinitis modis
variantur; quia ut.philosophus secundo Ethicorum exempli-
ficat, facile est diverti a signo dato propter multiformem
declinationis possibilitatem, sed veritas et virtus sunt in
puncto; infinitae etiam sunt veritates, virtutesque, atque
innumerabiles gradus in qualibet veritate et virtute, mani-
festum est quod mens humana non sufficit dare quod neces-
sarium est in omnibus, nec potest in singulis vitare falsum
nec malum. Et ideo ad auctorum dicta verorum potest
convenienter addi et corrigi in quampluribus. Et hoc egregie
docet Seneca in libro quaestionum naturalium ; quoniam libro
tertio! dicit, ‘opiniones veteres parum exactas esse; et rudes
circa verum adhuc errabant; nova erant omnia primo ten-
tantibus, postea eadem illa limata sunt; nulla res consummata
est, dum incipit, Et in quarto? libro dicit, * veniet tempus,
quo ista quae latent nunc, in lucem dies extrahet, et longioris
aevi diligentia. Ad inquisitiones tantorum una aetas non
sufhcit. Multa venientis aevi populus ignota nobis sciet, et
veniet tempus, quo posteri nostri tam aperta nos nescisse
mirentur. Et ideo dicit in prologo majoris voluminis, quod
nihil est perfectum in humanis inventionibus et infert, quanto
juniores tanto perspicaciores, quia juniores posteriores succes-
sione temporum ingrediuntur labores priorum. Et cum jam per
causam et auctoritatem verificatum est quod volo, nunc tertio

! Joc. at. vi. 5. 3 Nat. Quaest. vii. 25.

14 OPERIS MAJORIS PARS PRIMA.

per effectum probabo. Nam semper posteriores addiderunt ad
opera priorum, et multa correxerunt, et plura mutaverunt,
sicut maxime per Aristotelem patet, qui omnes sententias
praecedentium discussit. Et etiam Avicenna et Averroes
plura de dictis ejus correxerunt. Ad haec reprehenditur de
mundi aeternitate, quam nimis inexpressam reliquit; nec
mirum, cum ipsemet dicit se non omnia scivisse. Nam quadra-
turam circuli se ignorasse confitetur, quod his diebus scitur
veraciter. Et cum ignoravit hoc, multo magis majora. Ac
Avicenna, dux et princeps philosophiae post eum, ut dicit
commentator super causam de Iride in libro Metaphysicae
Aristotelis, et opera in totam philosophiam ab eo digesta,
sicut ab Aristotele, hoc manifestant, dixit se materiam Iridis
ignorasse, sicut praecedens commentator fatetur. Et in tertio
physicorum se ignorasse unum ex decem praedicamentis, viz.
praedicamentum habitus, dicere non veretur. Et proculdubio
in libro de philosophia vulgata errores et falsa continentur, ut
in undecimo Metaphysicae ponitur error de mundi produc-
tione, in quo dicitur quod Deus propter infinitam unitatem
quam habet, et ne recipiat varietatem dispositionum, non potest
creare nisi unum, scilicet, angelum primum, qui creavit secun-
dum cum coelo primo, et secundus tertium cum coelo secundo,
et ultra. Et cum in undecimo ponit omne peccatum habere fines
sue : purgationis in alia vita, et animas peccatrices redire ad
gloriam, manifeste errat, et sic in multis. Et Averroes, maximus
post eos, in multis redarguit Avicennam ; et sic sapientes nostri
eum in pluribus corrigunt et non immerito, quia proculdubio
erravit in multis locis, quamvis in aliis optime dixit. Et si
isti majores erraverunt, multo fortius juniores. — Quoniam
autem in errores inciderunt, multo magis defecerunt in neces-
sariis, superflua et inutilia cumulantes, dubia et obscura et
perplexa spargentes; et haec omnia in libris eorum manifesta
sunt, et per effectum in nobis probantur. Nam tanta difh-
cultate videndi veritatem premimur et vacillamus, quod fere
quilibet philosophorum contradicit alii, ita quod vix in una
vanissima quaestione vel in uno vilissimo sophismate vel una
operatione sapientiae, sicut in medicina, et chirurgia, et aliis
operationibus secularium, unus cum alio concordat.

CAUSAE ERRORIS. 15

Sed non solum philosophi immo sancti aliquid humanum in
hac parte passi sunt. Nam ipsimet retractaverunt dictorum
suorum quamplurima. Unde Augustinus, qui major in in-
quisitione veritatum occultarum reputatur, fecit librum de
retractatione eorum, quae non bene praedixerat. Et Hierony-
mus super Isaiam, et alii plures suam non verentur retractare
sententiam. Nam celeritate dictandi in transferendo pluries se
confitetur deceptum fuisse, et multis aliis modis; et sic omnes alii
doctores fecerunt. Sancti etiam ipsi mutuo suas correxerunt
positiones et sibi invicem fortiter resistebant. Etiam Paulus
Petro resistebat, sicut ipsemet confitetur. Et Augustinus
Hieronymi sententias reprehendit, et Hieronymus Augustino
in pluribus contradicit. Haec exempla eorum manifesta sunt,
ut inferius exponetur, et posteriores priorum dicta correxerunt.
Nam Origenem maximum doctorem secundum omnes in
multis posteriores reprobant, quia inter caetera posuit errorem
Avicennae de animabus peccatricibus, quod nulla finaliter
damnabitur. Et cum multi doctores sancti et famosi ex-
posuerunt Israel, ut dicatur vir videns Deum, venit Hieronymus
super Genesim et probat falsam esse expositionem ! per rationes
irrefragabiles, sicut inferius exponetur. Unde dicit, * quamvis
auctoritatis sint, et eorum umbra nos opprimat qui Israel
virum videntem Deum interpretati sunt, tamen magis con-
sentimus Deo vel angelo qui hoc nomen imposuit, qagm
auctoritati alicujus eloquentiae secularis, Et doctores catholici
in studiis solemnibus constituti nunc temporis in publicis multa
mutaverunt, quae sancti dixerunt, eos pie exponentes ut
possunt, salva veritate.

CAPITULUM VII.

Quoniam igitur haec ita se habent, non oportet nos ad- Plato
haerere omnibus quae audimus et legimus, sed examinare Augustine,

debemus districtissime sententias majorum, ut addamus quae preferred

eis defuerunt, et corrigamus quae errata sunt, cum omni truth to
authority.
! Nevertheless in Jerome's Commentaries on Isaiah and on Amos (vol. iv.
p. 27, and vol vi p. 1032 of Migne's ed.) the interpretation videns Deum is
accepted.

16 OPERIS MAJORIS PARS PRIMA.

tamen modestia et excusatione. Et ad hanc audaciam erigi
possumus, non solum propter necessitatem, ne deficiamus vel
erremus, sed per exempla et auctoritates, ut in nullo simus
reprehensibiles de praesumptione. Nam Plato dicit, ‘Amicus
est Socrates, magister meus, sed magis est amica veritas.'
Et Aristoteles dicit, ‘se magis velle consentire veritati, quam
amicitiae Platonis, doctoris nostri! Haec ex vita Aristotelis
ét primo Ethicorum, et libro secretorum, manifesta sunt.
Et Seneca dicit libro de quatuor virtutibus cardinalibus,
‘Non te moveat dicentis auctoritas; non quis, sed quid.’ Et
Boetius libro de disciplina scholarum, ‘stultum est magistra-
tus orationibus omnino confidere, nam primo credendum est,
donec videatur quid sentiat ; postea est fingendum eundem
in dicendo errasse, si forte reperire queat discipulus, quod
expresse objiciat sedulitati magistrali.. Et Augustinus dicit
ad Hieronymum, ‘ quod solos auctores scripturae sacrae vult
credere in scribendo non errasse, sed in scripturis aliorum,
quantumcunque sanctitate et doctrina polleant, non vult
verum putare, nisi per canonem et alios auctores vel per
rationes sufficientes possint probare quod dicunt. Et ad
Vincentium dicit * negare non possum, nec debeo, sicut in
ipsis majoribus, ita multa esse in tam multis opusculis meis,
quae possunt justo judicio et nulla temeritate culpari!' Et
in prologo libri tertii de Trinitate dicit, ‘sic meis libris nisi
certum intellexeris, noli firmum tenere. Item ad Fortunatia-
num; ‘neque quorumlibet disputationes quamvis catholicorum
et laudatorum hominum veluti scripturas canonicas habere
debemus, ut nobis non liceat, salva honorificentia quae illis
debetur hominibus, aliquid in eorum scriptis improbare atque
respuere, si forte invenerimus quod aliter senserint quam
veritas habeat, divino adjutorio vel ab aliis intellectum vel
a nobis. Talis ego sum in scriptis aliorum, quales volo esse in-
tellectores meorum ?. Si igitur propter necessitatem vitandae
falsitatis et consequendi perfectiorem statum sapientiae possu-
mus, et debemus, et consulimur per sanctos perfectos et philo-

1 Aug. de Anima, lib. iv. cap. 1.
* Aug. Ep. cxlvii. § 15, vol ii p. 628, Migne's Ed. The correspondent
was not Fortunatus the Manichaean, as Jebb has it.

=

CAUSAE ERRORIS. 17

sophos dignos, ut eorum dicta mutemus loco et tempore, et ad
eorum sententias addamus ; multo fortius licentiamur ad hoc
et cogimur in eis, quae vulgi sunt et eorum qui vulgo praesunt
imperito, praecipue cum capita multitudinis istius temporis
non attingunt ad dignitatem auctoritatis sanctorum et philo-
sophorum magnorum nec sapientum antiquorum, quorum
aliquos nostro tempore conspeximus.

CAPITULUM VIII.

Remedium vero contra haec tria non est, nisi ut tota Their ex-

virtute auctores validos fragilibus, consuetudini rationem, sen- ample we
sibus vulgi sententias sanctorum aut sapientum reponamus, imitate.
et non confidamus in argumento triplicato, scilicet, hoc exem-
plificatum est, vel consuetum, aut vulgatum, igitur tenendum.
Patet enim ex praedictis secundum sententias sanctorum et
omnium sapientum, quod longe magis sequitur oppositum
conclusionis ex eisdem praemissis. Et licet totus mundus
sit his causis erroris occupatus, tamen audiamus libenter
contraria consuetudini vulgatae. Nam hoc est magnum
remedium horum malorum, secundum quod Averroes dicit
in fine secundi physicorum, quod mala consuetudo auferri
potest per consuetudinem audiendi contraria. Nam multum
operatur in opinione, quae est per consuetudinem, audire res
extraneas, quod confirmat per effectum, dicens, quod ideo
opinio vulgi est fortior quam fides philosophantium, quia
vulgus non consuevit audire diversa, sed philosophantes multa
audiunt. Propter quod igitur Vestra Sapientia non miretur !,
si contra consuetudinem vulgi et exempla vulgata laborem.
Nam haec est via sola perveniendi ad considerationem veri-
' tatis et perfectionis.

CAPITULUM IX.

Non solum quidem hae causae generales sunt malorum in The fourth
studio et in vita, sed quarta nequior his tribus est, similiter e^" oue
communis in omni statu, et apud quamlibet personam regnare conceit of

! J. adds the words ‘nec indignetur auctoritati which are not very intel-
ligible. O. omits them.

VOL. I. C

18 OPERIS MAJORIS PARS PRIMA.

knowledge, demonstratur. Conjunxi quidem praedictas tres causas, et

is by far
the most

propter hoc quod sapientes eas saepius conjungunt et sepa-

pernicious. ravi hanc ab illis propter malitiam principalem. Haec enim

est singularis fera, quae depascit et destruit omnem rationem,
quae est apparentis sapientiae desiderium, quo fertur omnis
homo. Nam quamcunque parum sciamus et licet vile, idem
tamen extollimus; celebramus etiam multa quae ignoramus
ubi possumus occultare ignorantiam, et scienter ostendimus,
ut de nihilo gloriemur. Et quicquid nescimus, ubi scientiam
ostentare non valemus, negligimus, reprobamus, reprehendimus
et adnihilamus. ne videamur aliquid ignorare, quatenus saltem
mundo muliebri et fuco meretricio nostram ignorantiam
infami remedio coloremus, unde utilissima et maxima et omni
decore plena et sua proprietate certissima a nobis per hanc
viam et ab aliis relegemus. — Haec vero pestis propter mali-
tiam absolutam quam habet recepit cumulum suae pravitatis
in eo, qui est fons et origo causarum trium praedictarum.
Nam propter zelum nimium sensus proprii et excusandi
ignorantiam statim exoritur fragilis auctoritatis praesumptio,
qua nitimur propria extollere, et reprehendere aliena. Deinde
cum omnis homo diligat opera sua, ut dicit Aristoteles, nostra
libenter trahimus in consuetudinem. Et cum nemo sibi soli
errat, sed sententiam suam spargere gaudet in proximos, ut
dicit Seneca libro secundo epistolarum, nostris adinven-
tionibus occupamus alios et eas in vulgum quantum possumus
dilatamus. Necesse est vero causas universales hic praemitti.
ad hoc ut error vitetur et veritas relucescat. Nam in morbo
spirituali evenit sicut in morbo corporali. Medici enim per
signa causas proprias et particulares morbi cognoscunt ; sed
tam hanc quam illas praecedit causarum universalium notitia,
quas a communibus naturalium medicus habet scire; quia
dicit philosophus libro de Sensu et Sensato!, ubi terminant
principia philosophiae naturalis incipiunt principia medicinae.
Similiter igitur in cura ignorantiae et erroris, ut veritas sana
inducatur, ante ipsius propositi exhibitionem requiritur ut

! De Sensu, cap. r Tüw wepi Quaoeos ol wAcicrot wal Tüv larpüw ol duAo-
coóderrépes rv rTéxvgv uerióvres, ol pty reXevrücir els ra wept larpucijs, ol 0 ix Taw
wept pucews ápxorra: sept rijs larpucfjs.

CAUSAE ERRORIS. 19

signa et causae particulares ostendantur; sed prae omnibus
exiguntur causae universales, sine quibus nec signa aliquid
ostendunt nec causae particulares demonstrant. Nata enim
nobis est via cognoscendi ab universalibus ad particularia, sicut
dicit philosophus in principio Physicorum. Nam, ignoratis
communibus, ignorantur quae post! communia relinquuntur.

Haec autem causa quarta multum invaluit ab antiquo,
sicut nunc improba invenitur quoque in theologicis, sicut in
philosophia manifesto, per experientiam et exempla. Moyses
enim simplicissimus recepit sapientiam legis a Deo, contra Ilustra-
quem Pharao et Aegyptii, et populus Hebraeorum, et omnes [9^5 from
nationes murmurabant, ita quod vix plebs Dei electa hanc Moses,
sapientiam recipere voluit, et tamen praevaluit lex contra erate,
adversarios, qui neglexerunt et impedierunt sapientiam quam Avicenna.
didicerunt. Similiter Dominus Jesus Christus omni simpli-
Citate et sine plica falsitatis incedens, et apostoli simplicissimi
intulerunt sapientiam mundo, quibus satis contradictum erat
per ignorantiam solam tantae novitatis, et tandem, licet cum
summa difficultate, sacra veritas est recepta. Deinde sancti
doctores cum profluvia expositionum legis divinae voluerunt
dare, et magno impetu aquarum sapientiae ecclesiam irrigare,
diu reputabantur haeretict, et compositores falsitatum. Nam
sicut prologi beati Hieronymi in bibliam et alia ejus opera
probant, ipse vocabatur corruptor scripturae et falsarius et
haeresium seminator, et in tempore suo succubuit, nec potuit
sua opera in publico promovere; sed tandem post mortem
suam veritas suae translationis claruit et sua expositio, et per
omnes ecclesias dilatatae sunt, ita ut nullum vestigium trans-
lationis antiquae, scilicet LXX interpretum, qua prius usa
fuerat ecclesia, valeat reperiri. Dum etiam beatissimus Papa
Gregorius auctoritate functus est, ejus libris non fuit contra-
dictum: sed post mortem famosi in ecclesia egerunt ad hoc,
ut comburerentur, et per miraculum Dei pulcherrimum fuerunt
salvati, et apparuit mundo sapientia cum sua veritate et in
demonstratione plenissima. Et similiter cucurrit impedi-
mentum veritatis apud omnes sacrae scripturae doctores ;
nam renovantes studium semper receperunt contradictionem

! Not postes, as in J.
C 2

20 OPERIS MAJORIS PARS PRIMA.

et impedimenta, et tamen veritas invalescebat et invalescet
usque ad dies Antichristi.

Similiter de philosophia. Aristoteles enim voluit contra-
dicere prioribus et multa renovare, qui licet sapientissimus
habuit tamen repulsam, et occultationes suae sapientiae visus
est usque fere ad haec tempora recepisse. Nam primus:
Avicenna revocavit philosophiam Aristotelis apud Arabes
in lucem plenam. Vulgus enim philosophantium ipsum
ignoravit. Pauci enim et modicum philosophiae Aristo-
telis attigerunt ante tempus Avicennae, qui diu post tempus
Machometi Imperatoris philosophatus est. Avicenna vero
praecipuus Aristotelis expositor et maximus imitator multas
rebellitates passus est ab aliis: Nam Averroes major post
eos et alii condemnaverunt Avicennam ultra modum ; sed his
temporibus gratiam sapientum obtinuit quicquid dicit Aver-
roes. qui etiam diu neglectus fuit et repudiatus ac reprobatus
a sapientibus famosis in studio, donec paulatim patuit ejus
sapientia satis digna, licet in aliquibus dixit minus bene.
Scimus enim quod temporibus nostris Parisiis diu fuit contra-
dictum naturali philosophiae et metaphysicae Aristotelis per
Avicennae et Averrois expositores, et ob densam ignorantiam
fuerunt libri eorum excommunicati, et utentes eis per tempora
satis longa. Cum igitur haec ita se habent, et nos moderni
approbamus viros praedictos tam philosophos quam sanctos ;
et scimus quod omnis additio et cumulatio sapientiae quas
dederunt, sunt dignae omni favore, licet in multis aliis dimi-
nuti sint, et in pluribus superflui, et in quibusdam corrigendi,
et in aliquibus explanandi, manifestum nobis est quod illi,
qui per aetates singulas impediverunt documenta veritatis et
utilitatis quae oblata fuerunt eis per viros praedictos, nimis
erraverunt, et vitiosi plurimum fuerunt in hac parte; sed hoc
fecerunt propter scientiae extollentiam et propter ignorantiam.
Ergo in nobis ipsis debemus facere idem argumentum,
ut cum nos respuamus et vituperemus quae ignoramus,
clamemus hoc esse propter ignorantiae nostrae defen-
sionem, et ut illa modica, quae scimus, sublimius attollamus.
Permittamus igitur labores introduci congaudentes veritati,
quia proculdubio licet cum difficultate veritas semper prae-

CAUSAE ERRORIS. 2I

valebit, donec Antichristus et ejus appareant praecursores.
Nam semper bonitas Dei est parata sapientiae donum aug-
mentare per subsequentes, et subsequentium sententias in
melius transformare.

CAPITULUM X.

Caeterum duo sunt hic discutienda, videlicet, praesumptae Two heads
scientiae ostentatio, et excusatio ignorantiae infructuosa. of this ex-
Propter primum debemus advertere diligenter, quod cum aggeration
infinitae sunt veritates Domini et creaturarum, atque in qua- ledge: ]
libet sunt gradus innumerabiles, oportet quod pauca sciantur Pine
a quolibet, et ideo de multitudine scitorum non oportet quic- ance.
quam gloriari. Et cum intellectus noster se habet ad maxima,
sicut oculus vespertilionis ad lumen solis, ut prius secundum
philosophiam allegatum est, oportet quod sint parva quae
veraciter sciamus; nam pro certo ubi intellectus noster de
facili comprehendit, illud valde modicum est et vile, et quanto
cum majori difficultate intellexit, tanto est nobilius quod ad-
quiritur. Sed tamen omne id super quod potest intellectus
noster, ut intelligat et sciat, oportet quod sit indignum re-
spectu eorum, ad quae in principio credenda sua debilitate
obligetur, sicut sunt divinae veritates et multa secreta naturae.
et artis complentis naturam, de quibus nulla ratio humana
dari potest in principio; sed oportet quod per experientiam
illuminationis interioris a Deo recipiat intellectum, videlicet
in sacris veritatibus gratiae et gloriae, et per experientiam
sensibilem in areanis naturae et artis expergefactus inveniat
rationem.

Et adhuc minora sunt longe quae credimus, quam quae Perfect
ignoramus, sicut sunt secreta Dei, et arcana vitae aeternae, Knowledge
quae utcunque vidit Apostolus, ad tertium coelum raptus, able by
nesciens utrum in corpore vel extra corpus, quae tanta sunt, ^
ut non liceat homini loqui de illis. Et similiter in rebus
creatis; nam ob magnam intellectus nostri difficultatem
certum est, antequam videatur Deus facie ad faciem nunquam
homo sciet aliquid in fine certitudinis. Et si per infinita
seculorum secula viveret in hac mortalitate, nunquam ad

The simple

often sur-
ss the

earned in

wisdom.

22 OPERIS MAJORIS PARS PRIMA.

perfectionem sapientiae in multitudine scibilium et certitudine
pertingeret. Nam nullus est ita sapiens in rerum naturis,
qui sciret certificare de veritatibus omnibus quae sunt circa
naturam et proprietates unius muscae, nec sciret dare causas
proprias coloris ejus, et quare tot pedes haberet, et non plures
neque pauciores, nec rationem reddere de membris ejus. Est
igitur homo impossibilis ad perfectam sapientiam in hac vita,
et ad perfectionem veritatis nimis est difficilis, et pronus! et
proclivis ad falsa et vana quaecunque; quapropter non est
homini gloriandum de sapientia, nec debet aliquis magnificare
et extollere quae scit. Pauca enim sunt et vilia respectu
eorum quae non intelligit sed credit, et longe pauciora respectu
eorum quae ignorat. Et quoniam respectu eorum quae scit
homo, restant infinita quae ignorat, et sine omni comparatione
majora et meliora et pulchriora: insanus est qui de sapientia
se extollit, et maxime insanit qui ostentat et tanquam por-
tentum suam scientiam nititur divulgare.

Praeterea quis audet de sapientia gloriari, qui totam me-
dullam, quam unus quantumcunque studiosus addiscit per
viginti vel quadraginta annos et cum maximis expensis et
laboribus gravissimis, valet uni puero docili certo scripto et
verbo sufficienter ostendere per annum unum, vel in minori
tempore? Nam hoc probavi in puero praesenti, qui in pau-
pertate magna et modicam habens instructionem, quantitatem
anni vix ponens in addiscendo, novit tot et tanta quae omnes
mirantur qui eum cognoscunt. Nam securus dico quod licet
aliqui sciunt plus de philosophia et linguis, et in diversis
diversi ipsum excedunt, non tamen inter Latinos sunt qui
eum ex omni parte transcedunt, et ipse singulis eorum est in
aliquibus par, et in quibusdam singulos excedit. Nec est
aliquis inter Latinos quin multa bona valeat ab isto puero
auscultare. Nec aliquis tam sapiens est cui non sit necessarius
multis modis. Quamvis omnia didicit meo consilio et regi-
mine et adjutorio, et multa ipsum docui verbo et scripto,
tamen me senem in multis transcendit propter meliores ra-
dices quas recepit, ex quibus potest fructus salubres expectare,
ad quos ego nunquam pertingam. Quare igitur gloriabor de

! sic O. J. has multum parvus.

CAUSAE ERRORIS. 23

scientia? Non dico, quidam sapientes et experti potuerunt
per suam virtutem propriam facilius et citius cernere multa
secreta sapientiae, quam hic puer per seipsum, quia non est
expertus vires suas, nec percipit quantum novit nec quid
potest facere juxta fundamenta sibi tradita, sed sicut in
radicibus excedit alios, ut dictum est, sic si sano et efficaci
consilio juxta fontalem plenitudinem quam habet dirigeretur,
nullus seniorum consequeretur eum in sapientialium profluviis
rivorum. Et quoniam sapientes se sentiunt magis vacuos
quam insipientes, vel qui nolunt de ipsis confiteri, ideo vide-
mus homines quanto sapientiores sunt, tanto humilius se
inclinare ad doctrinam alterius suscipiendam, nec dedignantur
simplicitatem docentis, sed ad rusticos, et ad vetulas, et pueros
se humiliant. Quoniam simplices et idiotae aestimati sciunt
multoties magna quae latent sapientes, sicut Aristoteles docet
de somno et vigilia !, secundo libro. Nam cum simplicibus est
sermocinatio Dei secundum scripturam, et experientia reddit
nos certos in hac parte, quoniam plura secreta sapientiae
semper inventa sunt apud simplices et neglectos quam apud
famosos in vulgo. Quia homines famosi in eis occupantur,
quae vulgantur, et haec non possunt esse magnalia, sicut
patuit in prioribus ; plura etiam utilia et digna sine compara-
tione didici ab hominibus detentis magna simplicitate, nec
nominatis in studio, quam ab omnibus doctoribus meis famosis.
Proposui igitur Sapientiae Vestrae hoc exemplum, et transmisi
per eum, non solum propter duas causas superius annotatas,
sed in argumentum perfectum, ut nullus glorietur de sapientia,
nec despiciat simplices qui sciunt proponere ea quae famosis
hominibus in scientia Deus non concessit, et sciunt renovare
et revelare multa secreta, quae sapientes vulgati nondum
perceperunt.

CAPITULUM XI.

Secundum vitium, quod hic reperitur, est, quod ignorantia Ignorance
most jou

retinet locum persuasionis, sed cum veritas impugnatur, nefas when it

1 The reference seems to be to De divin. per somnum, cap. 2 sárv 4dp
evreAcis dyOpwwo wpooparixo( elo: xal eüOvóreipot, and again, TO wáÜos ToUro
cvuBaíve ros Tuxove:, kal ob Tots $poriiorrárocs.

24 OPERIS MAJORIS PARS PRIMA.

usurpsthe est et puritas malitiae, deinde ignorantiae turpitudo crescit

Pee. edge. magis et clarius revelatur. Crescit quidem, quia nititur a se

: et ab aliis excludere sapientiam ; apertius quidem revelatur,

quoniam coram Deo et hominibus! veraciter innotescit hoc

secundum judicium omnis sapientis ; ergo cum judex teneatur

habere scientiam causae, non habet homo ignorans auctori-

tatem judicandi de his quorum habet ignorantiam. Et ideo

si de illis affrmet vel neget, ejus judicio stari non debet, immo

ex hoc vehementius resistendum, quod sententia qualiscunque

feratur ex ignorantia ea auctoritatem non habet: Unde si

verum diceret, verisimile non esset. Nam, ut dicit Seneca

libro de virtutibus cardinalibus, nullam auctoritatem habet

sententia, ubi qui damnandus est damnat. Quapropter sive

sapientes apud vulgum, seu secundum veritatem, sive bonus,

sive sanctus affirmet vel reprobet quod ignoret, et maxime

in excusatione suae ignorantiae, vel ostentatione sapientiae

apparentis, approbari non debet ex hac parte, sed negligi et
contradici, quamvis ex aliis fuerit magnifice collaudandus.

CAPITULUM XII.

Knowledge Hanc vero causam malorum nostrorum cum aliis tribus ideo
of great : 4] . : . . . . .
vakeisnoy SPecialiter introduxi, ut sciamus nunc, sicut in retroactis tem-

neglected: poribus, multa quae sunt utilissima et omnino necessaria,
Matte. X studio absolute considerato et quatuor modis relate prae-
matics. — tactis, negari negligi et ex sola ignorantia reprobari. Et pro
infinitis latius explicandis posterius in singulis partibus sapien-
tiae, volo nunc aliqua extra praemittere grossiora. Cum enim
linguarum cognitio et Mathematicae est maxime necessaria
studio Latinorum, ut tactum est superius, et exponetur loco
opportuno, et fuit praecise in usu sanctorum et omnium sapi-
entum antiquorum, nos moderni negligimus, adnihilamus, et
reprobamus, quia ista et eorum utilitatem nescimus. Deinde,
si aliqui sapientes et sancti alia neglexerunt aut humana
fragilitate devicti aut ex causa rationabili, nos praesentis
temporis obstinate et pertinaciter negligimus et reprobamus,
fortificantes nostram ignorantiam propter hoc quod sancti et

! sic O. J., omnibus sanctis.

CAUSAE ERRORIS. 25

sapientes neglexerunt, non volentes considerare quod in omni
homine est multa imperfectio sapientiae, tam in sanctis quam
in sapientibus, ut prius evidenter et multipliciter probatum
est tam per eorum exempla et auctoritates, quam per rationem
et experientiae certitudinem. Praeterea non solum volumus
humanam fragilitatem considerare, sed etiam ! causas ratio-
nabiles, quas sancti et sapientes multi habuerunt, quare pro
loco et tempore multa utilia vitaverunt propter abusum homi-
num in eis, quia ea convertebant ad majoris impedimenta
utilitatis et salutis. Ne igitur nos simus causa erroris nostri
et fiat magnum sapientiae impedimentum ex eo quod vias
sanctorum et sapientum non intelligimus, ut expedit, pos-
sumus auctoritate sanctorum et sapientum antiquorum multi-
pliciter prius assignata considerare pia mente et animo
reverenti, propter veritatis dignitatem quae omnibus ante-
fertur, si sancti et sapientes aliqua quae humanam imper-
fectionem important protulerunt in quibus seu affirmatis seu
negatis non oportet quod nos imitemur ex fronte.

Scimus quidem quod non solum dederunt nobis consilium Wise men
et licentiam hoc faciendi, sed conspicimus quod ipsi multa cought to
posuerunt magna auctoritate, quae postea majori humilitate amend and
retractaverunt ; et ideo latuit in eis magna imperfectio priori- error.
bus temporibus. Quod si vixissent usque nunc, multo plura
correxissent et mutassent. Cujus signum est sicut et argu-
mentum principalis intenti, quod doctores posteriores quam-
plurima de sententiis sanctorum mutaverunt, et pie et reve-
renter interpretati sunt in sensum quem eorum litera non
praetendit. Praeterea sancti ad invicem fortiter contendebant
et mutuas positiones acriter mordebant, et reprobabant ut
taedeat nos conspicere, et supra modum miremur; quod
evidens est in epistolis beatorum Augustini et Hieronymi,
et multis aliis. Cum enim Hieronymus comparavit se bovi
lasso, qui fortius pedem figit, propter hoc quod jam in studio
Sacro senuerit, et Augustinus fuit junior eo, quamvis episcopus,
respondit monacho pontifex quod bos senex fortius figit pedes
non animi vigore sed corporis senectute. Et cum Augustinus .
multa quaereret ab Hieronymo, dicit Hieronymus, ‘ Diversas

1 MSS. have nec, but etiam seems required. .

Errors of
ancients
due to
ignorance
of foreign

languages.

26 OPERIS MAJORIS PARS PRIMA.

tu nominas quaestiones, sed ego sentio meorum opusculorum
reprehensiones continuas. Praetermitto salutationes, quibus
meum demulces caput; taceo de blanditiis, quibus reprehen-
sionem meam niteris consolari, ut ad ipsas causas veniam ;
observari legis ceremonias non potest esse indifferens, sed aut
bonum aut malum ; tu vero bonum, ego malum assero; dum
aliud vitas, ad aliud devolveris ; dum enim metuis Porphyrium
blasphemantem ! Ebionis haeretici laqueos incurris.’ Et talia
innumerabilia colliguntur ex libris sanctorum, qui tam in
rebus de quibus est contentio quam in modo reprehensionis,
multum in scientiis humanae fragilitatis ostendunt, qua affirma-
bant quod non debebant, Sed constat, non ex certa scientia
hoc fecerunt ; ergo ex apparenti, et aestimata laboraverunt in
hac parte.

CAPITULUM XIII.

Caeterum non solum ex hujus mortalitatis imperfectione
multa reprobant, quibus nos non oportet obstinate inhaerere,
immo magis ad eorum honores pie et reverenter interpretari
secundum leges veritatis ; multa etiam et maxima neglexerunt
ex causis certis. Una est, quia non fuerunt translata in
linguam latinam, nec ab aliquo Latinorum composita, et ideo
non fuit mirum si illorum non aestimabant valorem. Platonis
enim libros doctores omnes assumebant in manibus, quia
translati fuerunt ; sed libri Aristotelis non fuerunt tunc tem-
poris translati. Nam Augustinus fuit primus translator
Aristotelis et expositor, sed in minimo et in primo libellorum
suorum, videlicet in praedicamentis: nec fuit philosophia
Aristotelis tunc temporis Graecis philosophis nota, nec
Arabicis, sicut prius tactum est. Et ideo sancti, sicut et alii,
neglexerunt philosophiam Aristotelis, laudabant Platonem.
Et quia intellexerunt quod Aristoteles persecutus est senten-
tias Platonicas, Aristotelem in multis reprobant, et dicunt
rationem haereses congregasse; sicut Augustinus dicit in
libro de Civitate Dei ipsum, adhuc magistro suo Platone

! blasphemantem om. in J. The passage occurs in Ep. cxii. § 16, vol. i.
P. 927 of Migne's ed.

CAUSAE ERRORIS. 27

vivente, multos in suam haeresim congregasse. Sed tamen
omnium philosophantium testimonio Plato nullam compara-
tionem respectu Aristotelis noscitur habuisse. Si igitur
sancti philosophiam ejus vidissent, pro certo ea usi essent, et
altius extulissent, quia veritatem non negassent manifestam,
nec maxima pro minimis declinassent. Nam Augustinus
ipse transtulit librum Praedicamentorum de Graeco in Latinum
pro filio suo, et exposuit diligenter, plus laudans Aristotelem
de hoc nihilo, quam nos pro magna parte suae sapientiae.
Quoniam in principio dicit, * cum omnis scientia et disciplina
non nisi oratione tractetur, nullus tamen, o fili mi, in quovis
genere pollens inventus est, qui de ipsius orationis vellet
origine principiove tractere; idcirco miranda est Aristotelis
diligentia, qui disserendi de omnibus cupidus ab ipsius coepit
examine, quam sciret et praetermissam a cunctis! et omnibus
necessariam. Et in fine dicit, * haec sunt, fili carissime, quae
jugi labore assecuti ad utilitatem tuam de Graeco in Latinum
vertimus, scilicet, ut ex his quoque bonam frugem studii
a nobis suscipias?" Et Alcuinus de expositoribus sacrae
scripturae unus, et magister Caroli Magni, illam translationem
Augustini de Praedicamentis mire laudavit, et metrico pro-
logo decoravit in his verbis,

* Continet iste decem naturae verba libellus,

Quae jam verba tenent rerum ratione stupenda

Omne quod in nostrum poterit decurrere sensum ;

Qui legit, ingenium veterum mirabile laudet,

Atque suum studeat tali exercere labore.

Nunc Augustino placuit transferre magistro

De veterum gazis Graecorum clave Latina,

Quem tibi, Rex magne, Sophiae sectator, amator,

Munere qui tali gaudes, modo mitto legendum.

Boetius quidem fuit longe post sanctos doctores, qui primus

incepit libros Aristotelis plures transferre. Et ipse aliqua
logicalia et pauca de aliis transtulit in Latinum. Nec adhuc
medietatem, nec partem meliorem habemus. Nam Aristo-
teles quidem fuit diu ignotus et philosophantibus, nedum aliis,
et vulgo Latinorum. Caeterum sancti grammaticalia logicalia

! multis, J. * Aug. Cafegor. cap. 1 et 22.

Why the
carly
Church
neglected
philosophy.

28 OPERIS MAJORIS PARS PRIMA.

et rhetorica, et communia metaphysicae multum efferunt, et
abundanter in sacris utuntur. Unde Augustinus in libro de
doctrina christiana, 2°, 3°, 4° docet ista applicari ad divina,
et in aliis locis: nec non et sancti caeteri idem volunt. Sed
de aliis parum et raro loquuntur, imo multam negligunt et
negligi edocent aliquando, sicut per Ambrosium patet super
epistolam ad Colossenses, et per Hieronymum super illam ad
Titum, et per Rabanum de pressuris ecclesiasticis, ac etiam in
locis aliis pluribus. Sed constat omnibus philosophantibus
et theologis scientias has nullius valoris esse respectu caete-
rarum nec alicujus dignitatis. Constat omnibus! si sancti
habuissent usum scientiarum philosophiae magnarum, nun-
quam cineres philosophicos in tantum extulissent, et ad sacros
usus convertissent, quanto enim sanctae scientiae? meliores
sunt et majores, tanto sunt ad divina aptiores. Sed quia ad
manus eorum non devenerunt libri nisi grammatici, logici,
rhetorici et de communibus metaphysicae, ideo his se
juverunt secundum gratiam eis datam ; et quicquid poterant
de his laudabiliter extrahere, converterunt copiosius ad legem
Dei, ut in expositionibus eorum et tractatibus singulariter
manifestum est, et hoc suo loco planius exponetur *.

CAPITULUM XIV.

Deinde considerandum est diligenter, quod quamvis multa
habuissent de majoribus scientiis, non fuit tempus utendi eis
nisi in duobus casibus, scilicet, astronomia pro calendario, et
musica pro officio divino. X Patet enim per historias, quod
Eusebius Caesariensis, et beatus Cyrillus, et Victorius et
Dionysius Abbas Romanus, cujus doctrinam nunc sequitur
ecclesia per leges astronomiae, et alii ex mandato apostolico
laboraverunt in hac parte; sed aliae scientiae majores fuerunt
neglectae, et praecipue istae quae judicia et opera sapientiae
magnifica noscuntur continere. Et hujus causa fuit quintuplex.
Nam philosophia ante Christi adventum dedit leges mundo,

! Quapropter, J. * sanctis, J.

* The last part of the sentence is omitted in O. and D. Like many other
passages in the first thrce parts of the work, it has been supplied from Jul.

CAUSAE ERRORIS. 29

praeterquam populo Hebreorum, tam de cultu divino quam
de moribus et legibus justitiae et pacis inter cives, et belli
contra adversarios. Et quoniam hujusmodi leges fuerunt
datae, quantum potuit humana ratio, ut Aristoteles vult in
fine Ethicorum, ubi transit ad librum legum dicens, * dicamus
nunc quantum possibile est philosophiae in rebus humanis,' &c.
principes mundi noluerunt recipere legem Christi, quae fuit
supra humanam rationem, et ipsi fuerunt regulati secundum
philosophos, et ideo philosophia impedivit ingressum fidei, et
tardavit in hoc, quod mundus ea deductus legi celsiori horruit
consentire.

Caeterum non solum hoc modo philosophia tardavit fidem
Christi, sed jure legum suarum de reipublicae defensione ab
omni contrario sensu visa est per judicia futurorum et
ostensionem rerum occultarum praesentium, et per opera
mirabilia supra naturae et artis communiter operantium
potestatem, contendere cum fidei praedicatoribus, quorum
proprium fuit non per naturam et artem, sed per Dei virtutem,
prophetiam de futuris eructare, occulta producere in lucem,
miracula suscitare. Nam quod philosophiae potestas valeat
magnifica peragere, quae vulgus non solum laicorum sed etiam
clericorum duceret pro miraculis, sequentia declarabunt.
Necnon rectores rerumpublicarum ubique per consilia philo-
sophorum suas leges zelantium persecutionis et mortis judicia
sanctis Dei graviter intulerunt. Insuper ars magica per totum
orbem invalescens, occupans homines in omni superstitione et
fraude religionis, quamvis fuerat philosophis odiosa, et ab
omnibus debellata, ut certificabitur suo loco, tamen sancti
primitivi invenientes mundum occupatum in utraque pro
eodem artificio utramque reputabant, quoniam ambae fidei
fructum impediebant multis modis. Nam sicut magi Pharaonis
Moysi resistebant et populum Aegypti mandato Dei in-
obedientem faciebant, sic fuit in principio ecclesiae per artis :
magicae violentiam. Quae cum in eundem effectum, scilicet
contra opus fidei, cum philosophia concordabat, totum ejus
vituperium in philosophiam redundabat.

Praeterea Deo placuit a principio ecclesiae quod nullum testi-
monium humanum ei daretur, sed ut veritas fidei tanto vigore

The ex-
ample not
to be fol-
lowed by
later theo-
logians.

30 OPERIS MAJORIS PARS PRIMA.

mundo. radiaret, ut probaretur solum Deo auctore promulgari
per testes ab ejus imperio destinatos. His igitur de causis
philosophia fuit ab ecclesia in principio et sanctis Dei non
solum neglecta, sed eis odiosa ; non tamen propter aliquod quod
in ea continetur contrarium veritati. Nam licet imperfecta sit
respectu professionis Christianae, tamen ejus potestas non est
sectae Christi dissona, immo totaliter ad eam disposita, et
ei utilissima et omnino necessaria, sicut omnes credunt, et
certificabitur evidenter. Non igitur propter aliquid malum
philosophiae ecclesia Dei neglexit et reprobavit eam a prin-
cipio, sed propter abusores ejus, qui noluerunt eam suo fini,
qui est veritas Christiana, copulare. Et propter hanc causam
Ecclesia primitiva non fuit sollicita de translatione magnarum
scientiarum philosophiae, et ideo sancti doctores Latini copiam
philosophicorum non habent, et configurantes se principiis
Ecclesiae neglexerunt multa dignissima, sicut in principio
propter causas supradictas neglecta fuerunt, non propter
aliquid falsum vel indignum quod in philosophia reperiri
possit, ut certius suo loco per ipsos Dei sanctos patebit. Nam
ostendetur quod sancti Patriarchae et Prophetae a principio
mundi omnes scientias receperunt a Deo, quibus illam magnam
vitae longitudinem dedit, ut possent experiri quid eis fuerat
revelatum, quatenus, fide Christi introducta et evacuata artis
magicae fraudulentia, potestas philosophiae ad divina utiliter
rapiatur.

CAPITULUM XV.

Sicut vero doctores sacri magnificas scientias philosophiae
non habuerunt in usu, sic nec posteriores, scilicet Gratianus,
Magister sententiarum et historiarum, Hugo de Sancto Victore,
et Ricardus de eodem. Nam non fuerunt eorum temporibus

. translatae, nec in usu Latinorum, et ideo neglexerunt eas, nec

dignas sacris mysteriis sciverunt judicare, sed humano sensu
respuebant quorum usum non habebant, et in multis oblo-
quuntur, sumentes nihilominus occasionem ex hoc, quod
sancti doctores prius easdem neglexerunt; sed non attende-
bant causas sanctorum, scilicet, quod non sunt translatae in
eorum tempore, et etiam quia ecclesia eas jubere transferri

L———— aM TN

CAUSAE ERRORIS. 3I

propter causas quinque prius tactas neglexit. Moderni vero
doctores vulgi, licet multa de philosophia sint translata, tamen
non habent eorum usum, cum et in parvis et vilibus delectati
duos libros logicae meliores negligunt, quorum unus translatus
est cum commentario Alpharabii ! super illum, et alterius ex-
positio per Averroem facta sine textu Aristotelis est translata.
Et longe magis caetera, quae minorem obtinent dignitatem,
sicut novem scientias mathematicae, et sex scientias magnas
naturales, quae multas alias scientias sub se comprehendunt,
atque morales quatuor partes negligunt dignissimas ; et suae
ignorantiae quaerunt miserabile solatium per Gratianum et
caeteros magistros authenticos, qui non habuerunt notitiam
partium philosophiae. Nam post Christum sancti non sunt
usi dignitate philosophiae, at non propter hoc, quod ipsa sit
sacris contraria sententiis vel indigna, cum ad theologica
absolute intelligenda, et respectu ecclesiae Dei et reipublicae
fidelium ac conversionis infidelium utiliter et magnifice possit
adjuvare, sicut certificabitur suo tempore. Et tanto misera-
bilius est quod multitudo studentium modernorum magnas
negligit scientias, cum tamen fuerunt introductae post
Gratianum. Aliqui adhuc vivunt qui in studiis eas per-

legerunt.

CAPITULUM XVI.

Quamvis autem istas causas malorum omnium universales No sudden
persecutus sum, et vellem omnia reduci ad auctoritatem (8%
solidam, et sensum sapientum et expertorum, qui pauci sunt, Reform
non tamen credat Serenitas Vestra, quod ego intendo Vestriae jin the -—
clementiam Sanctitatis excitare, ut auctores fragiles et ipsam highest
multitudinem Majestas Papalis violenter invadat; nec quod
ego indignus sub umbra Gloriae Vestrae suscitem aliquam
super facto studii molestiam ; sed ut mensa Domini ferculis
sapientalibus cumulata, ego pauperculus micas mihi colligam
decidentes. Poterit enim Vestrae Potentiae magnitudo sibi et
successoribus suis providere de totius sapientiae compendiosa

plenitudine non solum absolute habenda, sed quatuor modis

! See note to p. 100.

32 OPERIS MAJORIS PARS PRIMA.

praedictis comparata. Deinde cum Vestrae Paternitatis dis-
cretio planiorem de his certitudinem reportaverit, poterit
auctoritatis vestrae judicium studiosis et sapientibus de facili
persuadere, ut quod vulgus studentium capere non potest,
cupidi sapientiae se gaudeant obtinere; insuper quantum
sufficit multitudini spes promittit. Nam Hieronymus dicit
super Isaiam, * Multitudo, accepta veritate, de facili mutat
sententiam. Et hoc verum est nisi quando captiosis malesanis
retractatur. Nam licet vulgus de se sit proclive ad malum, et
quia saepius invenitur caput languidum, tamen nisi qui praesit
impediat, satis facile est ad bonum imperfectum, quia instabilis
est, et semel mota modum servare non potest, et ideo de facili
quantum est de se vertitur ad contraria secundum regimen
praesidentis; quoniam omni vento doctrinae flectitur, velut
arundo, et quod principi ejus placet legis habet vigorem. Nos
enim hoc videmus in omni congregatione hominum, quod
secundum arbitrium capitis membra moventur. Nam si qui
praeest bonum negligit, subditi obdormiunt; si ad malum
excitati, in idem currunt cum furore; si ad bonum, similiter
sine discretione festinant. Et si vias perfectionis monet !, tunc
olfacit a longe multitudo, sed gustare non potest nec ab ea
debet requiri, ut superius ostensum est. Quod si non est
temporis vestri omnia apud vulgum consummare; poterit
Vestra Magnificentia locare fundamenta, fontes eruere, radices
figere, ut Vestrae Sanctitatis successores quod feliciter in-
ceptum fuerit valeant facilius adimplere.

! movet, J.

PARS SECUNDA

HUJUS PERSUASIONIS.
CAPITULUM I.

RELEGATIS igitur quatuor causis totius ignorantiae humanae Theology
generalibus, volo in hac secunda distinctione unam sapientiam es
esse perfectam ostendere, et hanc in sacris literis contineri ; science.
de cujus radicibus omnis veritas eruitur. Dico igitur, quod est
una scientia dominatrix aliarum, ut theologia, cui reliquae
penitus sunt necessariae, et sine quibus ad effectum pervenire
non potest; virtutem in suum jus vindicat, ad cujus nutum
et imperium caeterae jacent; una tamen est sapientia per-
fecta, quae in sacra scriptura totaliter continetur, per jus
canonicum et philosophiam explicanda, et expositio veritatis
divinae per illas scientias habetur. Nam ipsa cum eis velut
in palmam explicatur, et tamen totam sapientiam in pugnum
colligit per seipsum. Quoniam ab uno Deo data est tota
sapientia et uni mundo, et propter unum finem. Quapropter
haec sapientia ex sua triplici comparatione unitatem sortietur.
Caeterum via salutis una licet gradus multi; sed sapientia
est via in salutem. Omnis enim consideratio hominis, quae
non est salutaris, est plena caecitate, et ad finalem inferni
deducit caliginem ; propter quod multi sapientes famosi!
damnati sunt, quia veram sapientiam non habuerunt, sed

! [n his commentary on the Secretum Secreforum, Bacon, alluding to the
legend that Aristotle ascended to heaven in a column of fire, remarks: * Haec
est sententia philosophorum paganorum. Sed nobis Christianis non est licitum
hoc sentire nec firmare; quod nisi habuisset fidem Christi revelatam ei, ac
fuisset instructus a prophetis, salvari non potuit. Nescimus tamen quod Deus
fecit ei et aliis dignis prophetis et philosophis quibus dedit magnalia sapientiae.'
(Tanner MSS. 116, Sec. Secret. cap. i.]

VOL. I. D

34 OPERIS MAJORIS PARS SECUNDA.

apparentem et falsam, unde se aestimantes sapientes stulti
facti sunt secundum scripturam. Augustinus loquens de sacra
scriptura dicit libro secundo de doctrina Christiana, ‘si verum
est, hic invenitur; si contrarium, damnatur. Et vult quod
ubicunque invenerit Christianus, Domini sui intelligat veritatem
esse. Veritas Jesu Christi est sapientia sacrae scripturae.
Ergo non alibi veritas est, nisi quae in illa continetur scientia.
Et Ambrosius super epistolam ad Colossenses dicit, * Omnis
ratio supernae scientiae et terrenae creaturae in eo est, qui
est caput et auctor, ut qui hunc novit, nihil ultra quaerat,
quia hic est perfecta virtus et sapientia. Quicquid alibi
quaeritur, hic perfecte invenitur Cum ergo sacra scriptura
dat nobis hanc sapientiam, manifestum est quod hic omnis
veritas sit conclusa ; si aliqua est sapientia huic contraria, erit
erronea, nec habebit nisi nomen sapientiae; sed diversitas.
quam non faciat alibi, contrarietatem hic tamen inducit, sicut
patet per evangelicam auctoritatem, *Qui non est mecum,
contra me est. Sic de hac sapientia verum est, ut quod illi
annexum non est contra illam esse probetur, et ideo Christiano
abhorrendum.

CAPITULUM II.

In theology Haec autem manifestius patent consideranti divisionem

all studies
(including
the Canon
Law) are
rooted.

scientiarum. Nam si nitamur separare scientias ab invicem.
non possumus dicere theologiam. Sub una enim parte philo-
sophiae, scilicet morali quam Aristoteles civilem nominavit,
continetur jus civile, ut inferius innotescet. Canonicum! vero
jus a scripturis sacris nominatur, non ab aliis, sicut ipsum
nomen demonstrat; quae scripturae canonicae dicuntur libri
Veteris Testamenti, sicut Decretorum parte prima distinctione

! The first text-book on Canon Law was the Decretum of Gratian, a monk of
Bologna, completed probably in 1143. In 1234 Gregory IX published five
books of Decretals, to which a sixth book was subsequently added by Boniface
at the end of the century. Bacon, giving way to the strong prejudice felt by
himself and other theologians against the Civil Law, maintains that tbe Canon
Law is founded in the main on Scripture. But in reality the Canon Law is based
on the Civil Law. ‘Everything in the Canon Law was Roman which was not of
directly Christian or Jewish origin.’ (Rashdall, Mediaeval Unsversities, i. p. 133.)

PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 35

nona habetur, aut canones nuncupantur. Nam Canon Graece,
Regula Latine dicitur. Et tam jus canonicum quam jus
divinum regularem modum vivendi reddere comprobatur.
Caeterum jus canonicum totaliter fundatur super auctoritate
scripturae et expositore. Nam aut pro constitutionibus alle-
gantur auctores sacrae scripturae, ut Augustinus et alii, aut
summi pontifices pro suis statutis indicant auctoritates et
exempla Novi et Veteris Testamenti; et ideo hoc jus non
est nisi explicatio voluntatis Dei in scriptura. Item jus
canonicum vocatur ecclesiasticum, quo regitur in spiritualibus
Dei ecclesia, tam in capite quam in membris. Sed nihil
aliud sonat scriptura nisi hoc regimen. Praeterea jus naturale
continetur in sacra scriptura sicut docetur in principio decreti
manifeste. Jura canonica non possunt esse aliena a jure
divino, imo de fontibus illius debent derivari, et jus commune
est divinum vel humanum; divinum est quod spiritu Dei
allatum est mundo in sua scriptura; humanum quando sensu
hominis est adinventum. Sed constat ecclesiam Dei regi jure
canonico. Quapropter idem jus est divinum, de thesauro
sacrae scripturae eruendum. Et hoc manifestum est con-
sideranti partes juris canonici. Nam vel ordinat gradus
ecclesiasticorum officiorum, vel sacra Dei determinat, vel
forum conscientiae discutit, vel causas ecclesiasticas discindit.
Sed horum omnium radices et ipsa stipes erecta apud sacram
scripturam reperiuntur. Rami vero penes expositores ejusdem,
ut in canone folia, flores, fructus salutiferi capiantur. Nam
sermones canonici suavis ornatus foliis comparantur secundum
scripturam. Flores autem et fructus sunt segetum aurei
palmites et uvarum maturitio. Et ideo jus canonicum sine
potestate scripturae in uno corpore continetur, sicut unius
arboris corpus ex radicibus et stipite, ramis, floribus, et fruc-
tibus constituitur.

CAPITULUM III.

Quod autem philosophia ! non sit aliena a Dei sapientia, sed 5t. Au-

"P . - . . tine has
in ipsa conclusa, manifestandum est. Si enim a philosophis S aintained

! philosophiae, J.
D 2

that theo-
logy in-
cludes
philosophy.

36 OPERIS MAJORIS PARS SECUNDA.

tanquam injustis possessoribus rapere debent Christiani utilia
quae in libris eorum continentur, sicut dicit Augustinus, patet
quod philosophia est condigna sacrae veritati. Et iterum in
libro, scilicet de doctrina Christi, dicit quod philosophorum
aurum et argentum non ipsi instituerunt, sed de communibus
quasi metallis divinae providentiae, quae ubique est effusa,
eruitur; quod praefiguratum fuisse dicit, sicut Aegyptii
fecerant vasa atque ornamenta de auro vel argento et vestem
quam ille populus exiens de Aegypto sibi potius tanquam ad
usum meliorem vindicavit, sic doctrinae gentilium liberales
disciplinas usui veritatis aptiores et morum praecepta utilis-
sima continent, deque Deo ipso colendo multa inveniuntur
apud eos. Ulterius hoc explicat, dicens, in omnibus humanis
tractatibus, quae sunt moralia, vel historialia vel artificialia,
naturalia, logicalia vel grammaticalia, sunt nobis necessaria.
Nam pro moralibus dicit vestem, quae illorum est hominum
quidem institutio sed tamen accommodata humanae societati
qua in hac vita carere non possumus, in usum converti
christianum debet. De historialibus dicit, historia gentilium
plurimum nos adjuvat ad sanctos libros intelligendos. De
aliis vero considerationibus tam artificialibus quam naturalibus
dicit, Artium autem caeterarum, quibus adfabricatur domus, et
hujusmodi, medicinae, vel agriculturae, vel quorum omnis
effectus actio est, ut saltationum, cursionum, &c., harum autem
cognitio usurpanda est ad judicandum, ne omnino nesciamus
quid scriptura velit insinuare, cum de his artibus aliquas facit
fipuras. Pro omnibus naturalibus dicit, Benignam sane
operam faceret pro sacra scriptura, qui proprietates temporum
et locorum, lapidum, et caeterarum rerum inanimatarum,
plantarum et animalium colligeret. Et pro logicalibus dicit,
Nam de eis pro theologia possunt quaedam necessaria colligi
et condigna, sed non video, ut ait, utrum hoc possit sine eis.
Atque in libro secundo de ordine disciplinae dicit, Ad sacram

. scientiam nullus debet accedere sine scientia logicali De

mathematicis dicit Cassiodorus, Geometriam, arithmeticam,
astronomiam, musicam cum sollicita mente revolvimus, sensum
acuunt, limamque ignorantiae detergunt, et ad illam divinam
contemplationem, Deo largiente, perducunt; quas merito

PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 37

sancti patres legendas persuadent, quoniam ex magna parte
appetitus a carnalibus rebus extrahitur, et faciunt desiderare
quae solo corde possumus respicere. Et Augustinus doctos
multos sanctos fuisse commemorat, cum quaerit, Nonne aspi-
cimus quanto auro subsarcinatus exierit de Aegypto Cyprianus
doctor suavissimus et martyr beatissimus, quanto Victorinus et
alii multi innumerabiles Graeci, et Moyses quidem eruditus
omni sapientia Aegyptiorum ?

CAPITULUM IV.

Non solum autem beatus Augustinus, sed et alii sancti Corrobora-
idem asserunt Nam Hieronymus ad magnum oratorem Don bY
dicit, Si scripturas sacras legeres, quis nesciat et in Moyse ac authorities.
prophetarum libris quaedam assumpta ex gentilium libris?

Et inducit ad hujus proBationem prophetas ipsos et omnes
doctores famosos a principio ecclesiae, qui philosophorum
doctrinis fidem Christi persuaserunt principibus et infidelibus,
ac roboraverunt multipliciter. Et Beda super librum Regum
dicit, quod liberalium scientiarum sapientiam quasi suam
sumere licitum est Christianis ac divinam, alioquin Moysen et
Daniel sapientia Aegyptiorum et Chaldaeorum non paterentur
erudiri. Iterum de factura templi dicit Solomonem cum suis
servis signare Christum, et Hiram cum suis significare philo-
sophos et sapientes gentiles, ut templum Dei, hoc est ecclesia,
non solum sapientia apostolica, sed philosophorum con-
strueretur ; quia gentiles ab errore conversi atque ad veritatem
evangelii transformati, melius ipsos gentium errores noverant,
et quo certius noverunt, eo artificiosius hos expugnare atque
evacuare didicerunt. Paulus evangelium quod per revela-
tionem didicerat, melius novit; sed Dionysius melius revincere
poterat falsa dogmata, quorum cum erroribus argumenta
a puero noverat ; et ideo Salomon dicit, Scis enim quod non
est in populo meo vir, qui noverat ligna caedere, sicut Sidonii.
Haec et hujusmodi multa allegat venerabilis Beda. Sed et
Paulus Apostolus Epimenidis poetae usus est versiculo,
scribens ad Titum, ‘Cretenses semper mendaces, malae

The prin-

ciple which

stirs our

38 OPERIS MAJORIS PARS SECUNDA.

bestiae, ventres pigri! In alia quoque epistola Menandri
ponit senarium, * Corrumpunt bonos mores confabulationes
pessimae.'

CAPITULUM V.

Causae autem, quare sancti affirmant quod quaerimus, et
figuratum fuisse declarant, possunt assignari; primo propter

intellectual hoc quod ubicunque veritas invenitur, Christi judicatur se-

powers is
without us,
not within.

cundum sententias et auctoritates superius allegatas. Idcirco
quamvis aliquo modo veritas philosophiae dicatur esse eorum;
ad hanc tamen habendam primo lux divina influxit in animos
eorum, et eosdem superillustravit ; *Illuminat enim omnem
hominem venientem in hunc mundum, sicut dicit scriptura ;
cui sententiae philosophi ipsi concordant. Nam ponunt in-
tellectum agentem et possibilem ! ; anima vero humana dicitur
ab eis possibilis, quia de se est impotens ad scientias et
virtutes, et eas recipit aliunde. [Intellectus agens dicitur, qui

! This passage deals with one of the most important of mediaeval contro-
versies in which Aquinas was at issue with Averroes and his Arabian pre-
decessors. These maintained the existence of an universal reason, of which
individuals were more or less the partakers. Aquinas refutes this view in
S. T., Pars r, Quaest. Ixxvi. Art. 2: ‘Utrum intellectivum principium multipli-
cetur secundum multiplicationem corporum.’ See also his systematic treatise,
De Unitate Intellectus. It will be seen that Bacon in this passage appears to
side with the Arabians against St. Thomas. Cf. also the corresponding passage
in Opus Tertium, cap. 23. But in his more elaborate treatment of the subject in
Communia Naturalium (unpublished), Pars iv. cap. 14, he is careful to distin-
guish his doctrine from that of Averroes. That there should be a divine light
pervading the world, was one thing: that the intellect of mankind should be
one and the same substance, was quite another thesis which cut at the root
of morality. Renan (Averroes, p. 71 et seq.) shows that, though the doctrine
attacked by St. Thomas is commonly identified with Averroes, it had been
held by Alkindi, Alfarabi, and Avicenna centuries before. It may be noted,
in passing, that Jebb's error in writing repeatedly t#terius for intellectus has
gone far to make this passage unintelligible.

Aristotle can hardly be called as a witness for the Arabian side of the contro-
versy, though his distinction between intellect and the other physical facul-
ties is of course emphatic enough. Cf. De Anima, iii. 4, § 5 7d piv yàp
alaOnrixdy obx ávev cdáparos, ó 5 (vois) xopurrós. Again, ii. 2, $ 9 rovro póvov
iv M xerai xopí(ea0a1, xaÜámep 7d álfuov ToU $0aproü. The passage of the transla-
tion of which Bacon complains is De Anima, iii. 5 bre 8 howep ty dadoy rp
gvoa tori Ttc Td uy UA éxdory yéve (rovro 8 8 mávra duvdpe éxciva), Érepoy bà
70 atriov xal woinrixdy TQ woreiv navra, olov 3) Téxvg wpds ri)v DAny wéwovOer, dvayen
kal ty rp Vvxp iwepxew ravras rds kagpopas.

PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 39

influit in animas nostras illuminans ad scientiam et virtutem ;
quia licet intellectus possibilis possit dici agens ab actu intelli-
gendi, tamen sumendo intellectum agentem ut ipsi sumunt,
vocatur influens et illuminans possibilem ad cognitionem veri-
tatis. Et sic intellectus agens secundum majores philosophos
non est pars animae, sed est substantia intellectiva alia et
separata per essentiam ab intellectu possibili; et quia istud
est necessarium ad propositi persuasionem, ut ostendatur quod
philosophia sit per influentiam divinae illuminationis, volo
illud efficaciter probare; praecipue cum magnus error inva-
serit vulgus in hac parte, necnon multitudinem magnam
theologorum, quoniam qualis hic est in philosophia, talis in
theologia esse probatur. Dicit enim Alpharabius in libro de
intellectu et intellecto, * Quod intellectus agens, quem nomi-
navit Aristoteles in tertio tractatu suo de anima, non est in
materia, sed est substantia separata. Et Avicenna quinto de
anima et decimo metaphysices idem docet, necnon ipse philo-
sophus dicit,* Quod intellectus agens est separatus a possibili et
immixtus. Item vult quod intellectus agens sit incorruptibilis
secundum esse et substantiam, quoniam dicit ipsum differre
a possibili penes incorruptionem, sed possibilis est incorrupti-
bilis secundum substantiam, et corruptibilis secundum esse,
propter separationem ejus. Ergo agens secundum esse et
substantiam erit incorruptibilis; quapropter non erit pars
animae, quoniam tunc secundum esse suum in corpore cor-
rumpetur, quando separetur ; et dicit, quod se habet ad possi-
bilem, sicut artifex ad materiam, et sicut lux solis ad colores.
Artifex enim est extra materiam in quam agit, et separatus
ab ea per essentiam ; similiter lux solis expellens tenebras a cor-
poribus separata est ab eis per essentiam, et advenit aliunde.
Dicit etiam, intellectus agens scit omnia et [est] semper
in actu, quod nec animae nec angelo convenit, sed soli Deo;
item a digniore parte magis habet res denominari, ergo magis
dicetur sciens per agentem, quam ignorans per possibilem,
ante inventionem et doctrinam. Item Aristoteles! dicit quod

! Aristotle puts forward this view tentatively before he had come to a definite
conclusion as to the distinction between reason and other faculties. De Anima,
ii. 1, $ 12" A0qAor el ores irreAéx€us ToU odparos 7) yvy) dowep worr))p wAoiov.

40 OPERIS MAJORIS PARS SECUNDA.

intellectus est in corpore, sicut nauta in navi quantum ad hoc,
quod non est alligatus alicui parti, sicut nec nauta navi; sed
nauta non est profectio, sed motor tantum.

Cum igitur haec sententia sit consona veritati, ut textus philo-
sophi evidenter praetendit, et expositores declarant, ne aliquis
cavillator a latere insurgat, allegans idem quo vulgus decipitur.
dico quod Aristoteli imponuntur ista verba, * Quoniam in omni
natura est aliquid quod agat et aliud quod patiatur, ista est in
anima,’ immo respondeo quod multoties falso translatum est
et obscurum. Nam cum tertio caeli et mundi dicatur, quod
circulus et figura orbicularis replent locum !, istud est falsum ;
ut sciunt experti in naturalibus et geometricis, sicut Averroes
demonstrat ibidem. Et quod tertio Meteorologicorum dicitur
de iride est falsum etiam. Nam experientia docet, quod
quandocunque luna sit plena et pluat, nec ipsa sit nubibus
cooperta, accidit iris. Et sunt multa alia falso translata, cujus
causa patebit ex tertia parte hujus operis, et plura obscura, in
quibus quilibet alii potest contradicere. Et in hoc loco accidit
utrumque vitium vel saltem secundum, quod probo per ipsum
Aristotelem. Nam ipse dicit secundo physicorum, quod
materia non coincidit cum aliis causis in? eodem secundum
numerum, ergo in nulla natura sunt simul agens et materia,
igitur nec in anima. Si igitur ad literam teneatur textus
male translatus, tunc omnino falsus est et contra Aristotelem
alibi, et contradicit sibi tantus auctor; et qualitercunque
contingat verbum suum in secundo Physicorum est verum, et
ab omnibus concessum ; ergo sermo suus tertio de anima est
falso translatus, et indiget expositione. Nam nihil aliud in-
tendit, nisi quod in anima, videlicet, in operatione requiruntur
duo, scilicet, agens et materia; sicut in omni natura, id est
operatione naturae duo exiguntur, scilicet efficiens et materia.
Et idem est verum, sed agens semper est aliud a materia et extra

! In De Caelo, iii. 8, $ 1, Aristotle distinctly says that only three plane figures
can form a continuous surface, the triangle, square, and hexagon ; and only two
solid figures can occupy space, the pyramid and cube.

The reference to the lunar rainbow is Meteor. iii. 2, $ 9. It fully bears out
Bacon's view as to faulty translation. What Aristotle really said was that
during an experience of fifty years he had only twice observed the lunar

rainbow.
7 sic, O. cum eodem, J.

PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 41

eam secundum substantiam, licet operetur in ea. Caeterum pos-
sumus aliter hunc locum consolari. Nam Aristoteles quarto!
Physicorum dicit, quod octo modi sunt essendi in actu, quorum
unus est ut movens in moto, quia movens seu agens est se-
cundum virtutem suam in materia sua, licet non secundum
substantiam. Et sic est in omni natura in qua operatur, et ita
in anima ; et sic nullo modo sequitur quod intellectus agens
sit pars animae, ut vulgus fingit; et haec sententia est tota
fidelis et a sanctis confirmata. Et Augustinus dicit in solilo-
quiis et alibi, * Quod soli Deo est anima rationalis subjecta
in illuminationibus et influentiis omnibus principalibus. Et
quamvis angeli purgent mentes nostras et illuminent et ex-
citent multis modis, et sunt ad animas nostras tanquam stellae
respectu oculi corporalis, tamen Augustinus ascribat Deo
influentiam principalem ; soli influentia luminis cadentis per
fenestram ascribitur, et angelus aperienti fenestram compara-
tur, secundum Augustinum. Et quod plus est, vult in pluribus
locis quod non cognoscimus aliquam veritatem nisi in veritate
increata et in regulis aeternis. Cum igitur Deus illuminaverit
animas eorum in percipiendis veritatibus philosophiae, mani-
festum est quod eorum labor non est alienus a sapientia
divina.

CAPITULUM VI.

Tertia causa, propter quam sapientia philosophiae reducitur Philosophy
ad divinam, est quia non solum mentes eorum illustravit Deus ,i,, revela-
ad notitiam sapientiae adquirendam, sed ab eo ipsam habue-
runt et eam illis revelavit. Et Augustinus dicit super Johan-
nem, eis praestitit Deus sapientiam. Aristoteles in libro
secretorum asserit manifeste totam philosophiam fuisse a Deo
datam et revelatam ; et unus de maximis philosophis, scilicet
Tullius in quaestionibus Tusculanis quaerit, * Philosophia quid
est nisi donum, ut ego credo, inventum Dei?' Unde et dicit,

‘quod nec poeta grave plenumque carmen sine coelesti aliquo
instinctu effundit, Et Augustinus octavo de Civitate Dei
, docet et approbat quod Socrates pater philosophorum firma-

! Nat. Auscult. iv. 3, § 1.

42 OPERIS MAJORIS PARS SECUNDA.

vit, quod non potest-homo causas rerum scire, nisi in luce
divina, et per donum ejus. Et quilibet potest per se experiri
quod nihil primo ab homine invenitur quod sit de potestate
philosophiae. Et pono de minimo exemplum ; quoniam licet
universalia Porphyrii sunt apud eum sufficienter explicata
per logicam, metaphysicam, et naturalem philosophiam suffi-
cientissime expositam, tamen non est homo ita bene studiosus,
quin oportet ut doctores habeat et per longa tempora audiat
et studeat, antequam sciat totam veritatem universalium. Et
nullus vix ante mortem cognoscit; quod patet propter dis-
cordiam omnium !, quia aliqui ponunt ea solum in anima,
aliqui extra, aliqui medio modo. Si igitur talis ignorantia
est horum, multo magis per se nunquam perveniet homo ad
veritatem philosophorum. Quapropter veritatem horum est
necesse a principio fuisse homini revelatam. Et cum puerilis
revelatio est necessaria, multo fortius in tota sapientia philo-
sophiae, quod et a Deo est, et ille dedit et revelavit, et ideo
oportet quod suae sapientiae sit conformis.

CAPITULUM VII.

needed for — Caeterum totius philosophiae decursus, consistit in eo, ut
the ac "isi? per cognitionem suae creaturae cognoscatur creator, cui propter
divine reverentiam majestatis et beneficium creationis et conserva-
tionis et futurae felicitatis serviatur in cultu honorifico et
morum pulchritudine et legum utilium honestate; ut in pace

et honestate vivant homines in hac vita. Philosophia enim
speculativa decurrit usque ad cognitionem creatoris per
creaturas. Et moralis philosophia morum honestatem, leges

justas, et cultum Dei statuit, et persuadet de futura felicitate

utiliter et magnifice secundum quod possibile est philosophiae.

Haec sunt certa discurrentibus per omnes partes philosophiae

! Bacon's attitude in the controversy on Universals is not easy to define
with precision. ‘ Universale,' he says (Communia Naturalium), ‘non est nisi
convenientia plurium individuorum.' The universal ante vem he entirely rejected.
* Individuum est prius secundum naturam.' See Charles's monograph, pp. 239
and 383-9. A property or attribute common to several individuals (* natura aliqua
communis solis individuis’) would seem to be his definition of it. But Bacon
attached less importance to the controversy than his contemporaries.

PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 43

principales, sicut sequentia docebunt. Cum igitur haec sint
omnino necessaria christianis, et omnino consona sapientiae
Dei, manifestum est quod philosophia necessaria est legi
divinae et fidelibus in ea gloriantibus.

CAPITULUM VIII.

Item omnes sancti et sapientes antiqui in suis expositionibus Spiritual
sensum literalem colligunt ex naturis rerum et proprietatibus Uu ties
earum, ut per convenientes adaptationes et similitudines Physical.
eliciant spirituales sensus : quod declarat Augustinus libro de
doctrina Christi secundo, ponens exemplum de verbo Domini
dicentis, ‘ Estote prudentes sicut serpentes, et simplices sicut
columbae. Nam voluit Dominus per hoc, ut ad similitudinem
serpentis totum corpus exponentis pro defensione apostoli et
apostolici viri se et sua darent pro Christo capite suo et pro
fide sua. Et propter hoc omnis creatura in se vel in suo
simili, vel in universali vel in particulari, a summis coelorum
usque ad terminos eorum ponitur in scriptura, ut sicut Deus
fecit creaturas et scripturam, sic voluit ipsas res factas ponere
in scriptura ad intellectum ipsius tam sensus literalis quam
spiritualis. Sed tota philosophiae intentio non est nisi rerum
naturas et proprietates evolvere, quapropter totius philosophiae
potestas in sacris literis continetur; et hoc maxime patet,
quia longe certius ac melius et verius accipit scriptura
creaturas, quam labor philosophicus sciat eruere. Quod pro
infinitis exemplis pateat ad praesens in Iride. Philosophus
Aristoteles suis obscuritatibus nos perturbat ut nec aliquid
quod dignum sit valeamus per eum intelligere. Nec mirum,
cum Avicenna dux et princeps philosophiae fateatur se
naturam lridis ignorasse; et causa hujus est, quia philosophi
causam Iridis finalem ignoraverunt ; et ignorato fine ignorantur
ea quae sunt ad finem ; quia finis imponit necessitatem iis
quae ad finem ordinantur, ut Aristoteles vult secundo Physi-
corum. Causa vero finalis Iridis est dissipatio humiditatis
aqueae, sicut patet ex libro Geneseos; unde semper in
apparitione Iridis est nubium resolutio in stillicidia infinita, ut
consumantur aqueae humiditates tam in aere, quam in mari

44 OPERIS MAJORIS PARS SECUNDA.

et terra, quia una pars Iridis cadit in sphaeras aquae et terrae.
Consumptio vero aquae non potest esse per Iridem, nisi
propter radios solis facientis eam. Nam per varias reflec-
tiones et fractiones congregantur radii infiniti, et congregatio
radiorum est causa resolutionis et consumptionis aquarum, et
ideo Iris generatur per reflectiones multiplices. Non enim
possunt radii congregari, nisi per fractionem et reflectionem,
ut postea patebit. Ex scriptura igitur Geneseos cum dicitur
* Ponam arcum meum in nubibus coeli, ut non sit amplius
diluvium super terram,' accipitur causa finalis ipsius Iridis.
Ex quo investigari potest causa efficiens, et modus generandi
Iridem, qui modus non fuit notus philosophis sufficienter
secundum quod libri eorum manifestant nobis. Et ita est de
omni creatura. Impossibile enim est quod homo sciret
veritatem creaturae ultimam secundum quam accipitur in
scriptura, nisi fuerit specialiter a Deo illustratus. Nam
creaturae accipiuntur ibi propter veritates gratiae et gloriae
eliciendas, quas philosophi nescierunt, et ideo ad potestatem
ultimam sapientiae creaturarum non venerunt, sicut sacra
scriptura eam in suis continet visceribus. Unde tota philo-
sophia jacet in sensu literali sacris mysteriis gratiae et gloriae
decorata, tamquam quibusdam picturis et coloribus nobilissimis
redimita.

CAPITULUM IX.

Philosophy — Distinctio finalis! hujus partis, in qua ad confirmationem
reveale’ omnium praedictorum et dicendorum ostenditur quod tota
patriarchs. sapientia revelata est primo sanctis ; et ostenditur propositum

in universali.

Et hoc ultimo confirmari potest per hoc, quod eisdem
personis data est philosophiae plenitudo quibus et lex Dei,
scilicet, sanctis patriarchis et prophetis a principio mundi,
Et non solum est necessarium propter articulum qui hic trac-

! [n the MSS. this is called Distinctio tertia, but as no first and second
Distinctions are noted, ] have substituted the word *finalis! This concluding
portion of Part II, which is of great importance, seems to have been added

by Bacon as an appendix. The MS. has no division into chapters; I have
supplied this,

PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 45

tatur, sed propter totum negotium sapientiae certificandum.
Nam impossibile fuit homini ad magnalia scientiarum et
artium devenire per se, sed oportet quod habuerit revelationem,
qua probata nihil debet apud nos dubitari de arcanis sapientiae
repertis apud auctores. Sed nullum capitulum sapientiale
est tanti laboris sicut est certificatio hujus rei, eo quod est
magnum fundamentum totius comprehensionis humanae.
Atqui contrarietates et dubia multipliciter intercurrerunt, et
oportet auctores et volumina abundantius revolvi quam pro
aliquo alio articulo, qui in toto sapientiae studio valeat
reperiri. Dico igitur quod eisdem personis a Deo data est
philosophiae potestas quibus et sacra scriptura, videlicet,
sanctis ab initio, ut sic appareat una sapientia esse completa
et omnibus necessaria. Soli enim patriarchae et prophetae
fuerunt veri philosophi qui omnia sciverunt, non solum legem
Dei, sed omnes partes philosophiae. Hoc enim nostra scrip-
tura satis nobis ostendit, quae Joseph erudivisse principes
Pharaonis et senes Aegypti prudentiam docet; et Moysen
fuisse peritum in omni sapientia Aegyptiorum. Et Bezaleel et
Eliab hoc demonstrant, qui omni intellectu et sapientia rerum
naturalium fuerunt illustrati ; uno enim flatu Spiritus Sanctus
eos illuminavit et docuit totam potestatem naturae in rebus
metallicis et caeteris mineralibus. Sed et Solomon sapientior
omnibus praecedentibus et subsequentibus secundum testi-
monium scripturae plenam obtinuit philosophiae potestatem.
Et Josephus primo antiquitatum libro, capite secundo, dicit,
quod cum filii Adae per Seth fuerunt viri religiosi et ab ipso
Deo dilecti, Deus dedit eis sexcentos annos vivere propter
gloriosas partes philosophiae in quibus studuerunt, ut, quod
Deus eis revelavit, possent experiri per vitae longitudinem ;
et addit, quod Noe et filii ejus docuerunt Chaldaeos partes
philosophiae, et quod Abraham intravit Aegyptum et
docuit Aegyptios. Et postea in octavo libro, quod nullam
naturam inexaminatam Solomon praeteriit, sed de omnibus
philosophatus est, et disciplinam proprietatum earum evidenter
exposuit, et tangit quomodo descendens ad singula com-
posuerit quatuor millia librorum et quinque.

Et maximus Aristoteles ipsa veritate coactus dicit in libro

By these
thethinkers
of Greece
were in-
structed.

46 OPERIS MAJORIS PARS SECUNDA.

secretorum ; ' Omnem sapientiam Deus revelavit suis prophetis
et justis et quibusdam aliis, quos praeelegit et illustravit spiritu
divinae sapientiae, et dotavit eos dotibus scientiae. Ab istis
enim sequentes philosophi philosophiae principium et originem
habuerunt et scripserunt artium et scientiarum principia et
secreta, quia in scriptis eorum nihil falsum nihil reproban-
dum invenitur, sed a sapientibus approbatum. Et Averroes
dicit super partem coeli et mundi, *quod in tempore anti-
quorum ante Aristotelem et alios philosophos fuit philosophia
completa, ad cujus completionem Aristoteles suo tempore
aspirabat' Et apud Albumazar in majori introductorio et
alibi, et penes aliquos habetur multipliciter, quod Noe et filii
ejus multiplicaverunt philosophiam ; et praecipue Sem prae-
valuit in hac parte. Deinde post istos fuerunt viri! ... nomine
vulgato. Omnes philosophi et poetae majores et juniores
fuerunt post Noe et filios suos, et Abraham. Nam et Aristo-
teles et omnes consentiunt in hoc, quod primi philosophantes *
fuerunt Chaldaei et Aegyptii, unde adhaeret sententiis patrum
Chaldaeorum in undecimo Metaphysicae. Quia licet Noe et
filii ejus docuerunt Chaldaeos, antequam Abraham docuit
Aegyptios, tamen non fuit studium more scholastico ita cito
institutum, sed paulatim crevit ordo ejus et exercitium.
Quatenus omnis igitur dubitatio tollatur in hac parte, vide-
amus decursum et seriem infidelium philosophorum, et poeta-
rum, et omnium sollicitantium de studio sapientiali, et per-
cipiemus quod post Abraham et decessores suos, quibus a Deo
sapientia revelata est, inventi sunt singuli qui aliquem titulum
adepti sunt. Nam quantumcunque volumus strictius compu-
tare Zoroastres invenit artes Magicas, secundum Augustinum
vicesimo primo de civitate Dei; et secundum omnes auctores
hoc vulgatum est ; sed hic fuit Cham filius Noe, ut Clemens,
libro suo, et magister historiarum, et speculum historiale con-
scribunt. Deinde Io, quae postea Isis dicta est, dedit literas
Aegyptiis, ut Augustinus dicit libro de civitate Dei octavo

! There is a hiatus here in O. & D. It may have been supplied by Jul.
But fire has rendered the passage illegible.

3 There is a reference of this kind in a fragment of an apocryphal work
attributed to Aristotle entitled Mayuós, quoted by Diog. Laert. i. 1.

PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 47

t

tlecimo. Ante hujus tempora non fuit secundum Augustinum
sapientiae studium literis et scriptis pertractatum, quamvis
doctrinis Abraham instructi fuerunt. Et Isis, ut Augustinus
ait, dicitur fuisse filia Machi, qui fuit primus rex Argivorum,
qui regnavit primo anno Jacob et Esau nepotum Abrahae,
sicut Augustinus et historiae confitentur. Quanquam et alii
voluerunt, quod Isis veniret de Aethiopia in Aegyptum, et eis
literas dedit, et multa beneficia contulit, sicut recitat Augus-
tinus. Sed tamen ante tempus Machi non fuit, ut in ordine
regum Aegypti in chronicis reperitur. Eodem tempore fuit
Minerva aetate virginali apparens, multorum, ut ait Augustinus
libro praedicto, inventrix, quae Pallas dicitur, et apud poetas
Dea sapientiae nuncupatur, et Athena vocatur, atque Tritonia,
ut dicit Augustinus. Et Isidorus hunc locum esse in Africa,
qui Trito vocatur, recitat octavo libro etymologiarum, et Plinius
quinto libro, a quo Pallas dicitur Tritonia et fuit tempore
diluvii Ogygis regis, quod illi ascribitur, quia in Achaia accidit
tempore ejus, qui secundum Augustinum, Eusebium et Hiero-
nymum, et Solinum libro de mirabilibus mundi, fuit tempore
Phoronei filii Machi. Regnavit autem Machus quinquaginta
annis, et Phoroneus filius ejus sexaginta, cujus tempore facta
est repromissio Jacob, sicut patri suo, ut dicit Augustinus. Et
ideo Ogyges fuit tempore Jacob; unde Solinus dicit, diluvium
primum in Achaia fuisse tempore Ogygis et Jacob patriarchae.
Quod diluvium fuit ante diluvium Deucalionis per 600 annos, ut
idem narrat Solinus. Nam ut Hieronymus et Eusebius narrant,
regnante Cecrope primo rege Atheniensium, sub quo Moyses
eduxit filios Israel de Aegypto, fuit Deucalionis diluvium.

Et sub Phoroneo moralis philosophia incepit apud infideles.
Nam Augustinus dicit, quod sub legum et judiciorum
institutis Graecia clarior facta est!. Sed post fuerunt mores
et jura vivendi; quod patet per inhibitionem sanguinis et
licentiam de usu carnium post diluvium, et de emptione et
venditione apud Abraham pro spelunca; atque ex sanctitate
Abrahae et patrum suorum leges honestas et sacras vivendi
concludit ab eis fuisse edoctos. Et cum minus utiles scientias
perfecerunt, non debuit tantorum virorum sapientia scientiam

1 De Civitate Des, lib. xviii. cap. 3.

Pro-
metheus.

Aescula-
pius.

48 OPERIS MAJORIS PARS SECUNDA.

morum utilissimam negligere. Deinde primus inter viros
titulo majoris sapientiae doctor fuisse perhibetur, quia optimus
sapientiae investigator fuit, Prometheus !, quem poetae ferunt
de luto formasse homines, cujus frater, ut dicit Augustinus,
fuit Atlas magnus astrologus ; unde occasionem, ut Augustinus
refert, fabula invenit, quod eum portare coelum finxerit, quam-
vis mons ejus nomine nuncupatur cujus altitudine potius coeli
portatio vulgo videatur, qui in extremis Africae maritimis
prope Gades Herculis attollitur velut in caelum. Sed priores
fuerunt filii Noe et Abraham qui fuerunt periti astronomi, ut
Josephus narrat et Isidorus tertio libro, et Clemens libro
primo. Nam hi secundum Augustinum floruerunt, quando
Moyses natus est. Et Isidorus concordat libro quinto dicens,
quod Atlas fuit sub servitute filiorum Israel. Atlas vero, ut
dicit Augustinus, fuit avus maternus Hermetis Mercurii
majoris, qui magnarum artium peritus floruit et eas hominibus
tradidit, propter quod eum tanquam Deum post mortem
venerati sunt. Et hic, ut dicit Augustinus octavo decimo
libro, fuit tempore quo Moyses eduxit filios Israel ; cujus nepos
fuit Hermes Mercurius, qui ad doctrinam alterius est dictus
Trismegistus, qui famosus fuit philosophus Aegypti, maxime
in moralibus, sicut Augustinüs docet octavo de Civitate Dei.

Et hic scripsit ad Asclepium, sicut patet in libro de divinitate,

qui satis habetur, cujus Asclepii avus fuit Aesculapius primus
medicinae auctor apud infideles. Sed tamen Isidorus dicit in
tertio libro etymologiarum, quod Apollo fuit pater Aesculapii,
qui primus inter philosophos infideles dicitur docuisse artem
medicinae. Nam et patri ascribitur medicina quantum ad
prima documenta ; sed filio magis, qui hanc artem applicavit
et certiori modo docuit. Nam Apollo per carmina et hujus-
modi remedia processit, Aesculapius per veritatem experientiae,

Isidorus dicit, et creditur esse Apollo magnus, qui a poetis

fingitur esse inter Deos et dare responsa in templo Apollinis
in Delphis, unde vocatur Apollo Delphicus. Et tamen ante
istos fuit inaestimabilis gloria medicinae, secundum quod
Aristoteles tangit in libro de regimine vitae?, quam Adae et

1 De Civitate Dei, lib. xviii. cap. 8.
3 Another title for the Secrelum Secretorum.

PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 49

Enoch magis ascribit quam sequentibus philosophis. Et cum
medicina magis sit necessaria homini quam multae aliae
scientiae, non est dubium quin filii Adae ct Noe illam
invenerunt, quibus sapientiae plenitudo data fuit, et quibus
concessum est tam diu vivere propter studium sapientiae
perficiendum.

CAPITULUM X.

Post hoc, tempore Othonielis Judicis Israel, regnavit Cadmus.
Cadmus Thebaeus, qui primus dedit literas Graecis, ut in
chronicis Cluniacensibus edocetur. Et Beda in libro tem-
porum juniori et caeteri concordant, quod sub Aoth judice
Amphion musicus floruit, qui Aoth fuit proximus post
Othonielem. Et sub Barach fuit alius Apollo philosophus
secundum Chronicam Cluniacensem, auctor medicinae, tem-
poraneus Herculi secundo, cujus facta celebrantur; sicut dicit
Augustinus decimo octavo libro de Civitate Dei'. Qui Her-
cules in tempore Abimelech judicis Trojam devastavit, et pilas Hercules.
suas in India statuit, et in Gadibus columnas erexit, et dolorem
morbi non ferens seipsum tempore Jepthae judicis cremavit,
ut per Augustinum decimo octavo libro, et dicta chronica con-
firmatur. De hoc Hercule secundo propter hoc narravi, quia
alius fuit Hercules prope tempus Mercurii majoris, qui parum
post eum fuit, ut narrat Augustinus, et post eum fuit tertius,
qui certamen Olympiacum constituit, quod intermissum filius
ejus instauravit post excidium Trojae anno 408, ut Solinus
scribit. Unde multi decepti fuerunt, unum esse Herculem
aestimantes, qui omnia fecerit, quae de pluribus scripta sunt.

Similiter erratum est de hoc philosopho Apolline. Nam Apollo.
omnes, ut dicit Augustinus, aestimant ipsum fuisse illum, qui °
pro Deo in Delos insula colebatur, tanquam unus et idem
esset; cujus contrarium ostenditur multis testimoniis. Nam
ille Apollo, qui in templis dabat testimonia, invenitur saltem
respondisse quando primo facta est civitas Athenarum, ut
Athena, quae est Minerva, pro Dea coleretur; et hic philo-
sophus non potest esse, qui pro Deo Delphico colebatur. Sed

! omitted in J.
VOL. I. E

Orpheus.

Erythraean
Sibyl.

50 OPERIS MAJORIS PARS SECUNDA.

iste, de quo dicit Augustinus, fuit filius Latonae, cujus soror
Diana. Et Isidorus tertio libro idem dicit. Similiter non
videtur esse ille, de quo Hieronymus scribit in epistola ad
Paulinum, quae bibliis praeponitur Latinorum; nam ille
Hiarcum invenit in aureo throno sedentem et docentem, qui
Hiarcus dicitur esse Abrachis! astronomus, qui post mortem
Alexandri magni fuit, sicut docet Ptolemaeus in Almagesti.
Et ideo secundum hoc tres fuerunt Apollines, sicut Hercules.
Deinde sub Gideone fuerunt Orpheus et Linus, secundum
quod Beda refert. Et hi, scilicet Amphion, Orpheus, et
Linus, suo tempore dicti sunt poetae theologi, secundum
quod Augustinus dicit?, eo quod Diis carmina faciebant ;
secundum autem Solinum Nicostrates mater Evandri regis
Romani dicta est a vaticinio Carmentis, quae in Capitolino
monte Romae habitavit, et Latinis primo literas dedit. Et
haec, ut Beda refert, fuit tempore Jair judicis Israel; secun-
dum tamen chronicam Cluniacensem fuit tempore Judicis
post Jair, transactis septemdecim annis. Sed de hoc non
est cura quantum ad praesentem intentionem.

Propter Sibyllas vero et maxime Erythraeam, quae omnes
praedictos et praedictas philosophantes infideles longe super-
gressa est, oportet etiam nos aliqua certificare. Nam
Augustinus refert octavo decimo de Civitate Dei, quod
multi auctores scripserunt eam fuisse tempore Trojani
belli, et alii voluerunt eam fuisse tempore Romuli, et Achaz
vel Ezechiae regis Judae. Et excidium Trojae fuit ante
Romulum per quadringeutos triginta annos. Nam Solinus
probat Romam fuisse conditam Olympiade septima quadrin-
gentesimo tricesimo tertio anno post bellum Trojanum,
sicut docet evidenter per Herculem et Picum filium suum
et per alios. Et secundum Augustinum, octavo decimo de
Civitate Dei, vult quod Troja capta sit judicante Hebraeos
Abdon. Deinde Hesiodus philosophus successit Homero
ante Romam conditam, ut ait Tullius in quaestionibus Tus-
culanis. Et postea Archilochus, regnante Romulo, sicut ibi
describitur, et tempore Achaz vel Ezechiae regis Judae. Et

! Abrachis or Abraxis was the Arabian spelling of Hipparchus.
? De Civitate Dei, lib. xviii. cap. 14.

PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 5t

similiter regnaverunt Numitor et ejus nepos Romulus, et tunc
cessavit regnum et nomen Albanorum, et vocati sunt Romani
reges. Et rex tunc erat in Judaea Achaz, vel sicut alii
putant, Ezechias; et sub eodem Romulo Thales Milesius
fuisse perhibetur, qui fuit unus de septem sapientibus, et
primus secundum Augustinum !.

CAPITULUM XI.

Nam post poetas theologos crevit sapientia, et auctores Seven wise
sapientiae vocati sunt Sophi, i.e. sapientes; secundum tamen men of
Bedam in libro temporum, et secundum Isidorum quinto
Etymologiarum, Thales fuit sub Josia, qui rerum naturas
scrutatus est, et fuit astrologus. Tempore quo populus
Hebraeorum, ut Augustinus refert, ductus est in captivitatem,
alius de septem sapientibus apparuit, scilicet, Pittacus nomine,
et alii quinque fuerunt tempore captivitatis, quorum nomina
sunt haec, Solon Atheniensis, Chilon Lacedaemonius, Peri-
ander Corinthius, Cleobulus Lydius, Bias Pierius. De his
Solon dedit leges Atheniensibus, ad quas transferendas decem
viros populus Romanus misit, et vocantur leges duodecim tabu- Pytha-
larum, sicut scribit Isidorus quinto libro. Aliud vero genus goras, and
hominum sapientiae deditum post eos exortum est in lingua school.
Graeca, quae tamen vocatur Italica, scilicet ex ea parte, quae
Italia dicebatur, antiquitus Magna Graecia, et hi studuerunt in
Italia licet Graeci, etiam in lingua Graeca. Et isti non
voluerunt se vocari sapientes sed amatores sapientiae, quorum
princeps fuit Pythagoras Samius a Samo insula; a quo cum
quaereretur, Quis esset, respondit, philosophus, i.e. amator
sapientiae: sicut dicit Augustinus? octavo de Civitate Dei.

Sed octavo decimo libro dicit, quod Pythagoras apparuit eo
tempore quo Judaeorum soluta est captivitas, et secundum
Tullium in libro primo quaestionum Tusculanarum, Tarquinio
Superbo regnante Romanis, qui fuit septimus a Romulo, et
ultimus rex Romanorum. Postquam consules exorti sunt,
venit in Italiam Pythagoras, et illam Magnam Graeciam tenuit

! De Civitate Det, lib, xviii. cap. 24.

Ibid. lib. viii. cap. 2. Cf. lib. xviii. cap. 25.

E 2

52 OPERIS MAJORIS PARS SECUNDA.

cum honore, cum disciplina, cum auctoritate, et postea sic
viguit Pythagoreorum nomen, ut nulli alii docti viderentur.
Et Tarquinius, ut scribit Beda, tempore Cyri regis Persarum,
qui laxavit captivitatem Judaeorum, incepit, regnare. Ac
regnavit tempore Cambysis filii ejus, et duorum fratrum
magorum, et Darii, in cujus anno secundo templum aedi-
ficatum est. Et tunc clarus Pythagoras, ut dicit Beda,
habebatur, et Zorobabel. Aggaeus, Zacharias, et Malachias
prophetae claruerunt. Pythagoras quidem edoctus fuit a
Pherecide Syro, ut dicit Tullius libro praedicto, qui Phere-
cides primus animas hominum posuit immortales, cujus tem-
pora non certificantur nisi per tempus Pythagorae discipuli
sui; quamvis et Isidorus libro primo dicat, quod Pherecides
scripsit historias tempore Esdrae, qui potuit forte esse versus
finem vitae ipsius Pherecidis et in juventute Esdrae. Nam
a tempore, quo dictus Pythagoras dicitur floruisse, fluxerunt
triginta sex anni quibus regnavit Darius, et decem quibus
Xerxes, et septem menses quibus Arthabas, et sex anni
quibus Artaxerxes Longimanus, antequam Esdras ascendit
de Babylonia in Jerusalem. Nam septimo anno regni ejus,
primo die mensis primi, Esdras secundum Scripturas et
chronicas profectus est.

CAPITULUM XII.

Thelonc Haec autem duo genera philosophantium, scilicet Ionicum
ino ta lead- et Italicum, ramificati sunt per multas sectas et varios succes-
pocrates, sores usque ad doctrinam Aristotelis, qui correxit et mutavit
Aristotle. Omnium praecedentium positiones, et philosophiam perficere
conatus est. Successerunt vero Pythagoras, Archytas Taren-
tinus, et Timaeus, inter alios maxime nominati. Sed prae-
cipui philosophi, ut Socrates et Plato et Aristoteles, non
descenderunt ex hac linea, immo vero Ionici et veri Graeci
fuerunt; quorum primus fuit Thales Milesius. Quomodo
autem huic caeteri successerunt, ostendit Augustinus octavo!
libro de civitate Dei. Nam post Thaletem fuit primus

Anaximander ejus discipulus, cujus successor fuit Anaximenes,

! Cap. a.

Hes ge I AAA, o n dee APT. CiU as p PRU P RR gU... REIR EU. BUR. ER e I, gin sam

PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 53

et hi duo fuerunt tempore Judaicae captivitatis. Augustinus
et alii similiter concordant in hoc. Anaxagoras vero et
Diogenes Anaximenis auditores fuerunt, et eidem succes-
serunt sub Dario Hydaspis, cujus anno secundo templum
coepit aedificari. Anaxagorae, ut dicit Augustinus, successit
Archelaus ejus discipulus, cujus auditor fuit Democritus
secundum Isidorum octavo libro. Et Socrates, secundum
Augustinum octavo libro, Archelai fuisse discipulus perhi-
betur. Socrates autem secundum Bedam natus est sub
Arthaba, qui Persis regnavit mensibus septem, cui in idem
regnum successit Artaxerxes Longimanus, in cujus anno
septimo Esdras descendit de Babylone, et ideo simul fuerunt
Esdras et Socrates. Sed prior natu fuit Esdras, sicut ex nunc
dictis claret. Et ideo dicit Augustinus decimo octavo libro
de Civitate Dei, quod post Esdram fuit Socrates, i.e. posterior
natu. Nam quando floruit Esdras apud regem Persarum et
Judaeos, tunc Socrates exortus est. Hic Socrates dicitur
pater philosophorum magnorum, quoniam Platonis et Aris-
totelis magister fuit, a quibus omnes sectae philosophantium
descenderunt. Plato quidem, secundum Bedam in tractatu
majori de temporibus, natus est sub Sogdiano, qui mensibus
septem regnavit, cui successit Darius cognomine Nothus,
quanquam sub eodem Dario Beda in eodem tractatu de
temporibus scribat natum esse Platonem. Sed in illo tractatu
tempus Sogdiani, quia modicum fuit, computat sub regno
Dari. Nam continuat eum cum Artaxerxe Longimano.
. Nascente vero Platone, Hippocrates medicus, ut dicit Beda,
habetur insignis, et hoc tempore Empedocles et Parmenides
inventi sunt ; sed Plato Socratica primo addiscens, et ea quae
Graeca fuerunt, Aegyptum petiit, ad Archytam Tarentinum,
et Timaeum laboriosissime peragravit, ut dicit Hieronymus
ad Paulinum. Et contra Rufinum scribit Hieronymus, quod
Plato post Academiam et innumerabiles discipulos sentiens
multum deesse suae doctrinae, venit ad Magnam Graeciam,
ibique ab Archyta Tarentino eruditus, elegantiam et leporem
cum hujusmodi miscuit discipulis. Et iste Plato omnibus
philosophis antefertur secundum sanctos, quoniam ejus libri
ad eorum manus devenerunt, et quia sententias de Deo

Aristotle,
Avicenna,
Averrhoes.

54 OPERIS MAJORIS PARS SECUNDA.

pulchras, et de moribus et de vita futura multa conscripsit quae
sacrae Dei sapientiae multum concordant, ut in morali Philo-
sophia explanabo; et ab hoc aestimaverunt multi Catholici
viri quod audiverat Jeremiam prophetam in Aegypto. Nam
Aegyptum petiit propter sapientiam, et a barbaris sacerdo-
tibus instructus est, ut scribit Tullius libro Academicorum
quinto. Sed tamen Augustinus dicit quod non fuit tempore
Jeremiae. Nam Jeremias ut dicit nono de Civitate Dei,
primo prophetavit tempore quarti regis a Romulo qui vocatus
est Ancus Martius!, et in tempore quinti regis scilicet
Tarquinii Prisci. Sed Plato tunc non fuit; immo post tempus
Jeremiae fere per annos centunt, ut dicit Augustinus octavo
libro, natus est Plato. Sed ut alii aestimabant invenit LXX
interpretes a quibus instrueretur, sicut Augustinus dicit octavo
libro. Et Tullius libro de Senectute dicit quod Plato mortuus
est LXXXI? anno vitae suae, id est in fine Artaxerxis qui
Ochus dicebatur, ut scribit Beda.

CAPITULUM XIII.

Ante? vero mortem Socratis natus est Aristoteles, quoniam
per tres annos auditor ejus fuit, sicut in vita Aristotelis
legitur. Et secundum Bedam natus est sub Artaxerxe, qui
successit Dario Notho. Et in decimo septimo anno vitae
suae fuit auditor Socratis, et ipsum per tres annos audivit, et
post mortem Socratis factus est auditor Platonis secundum
Bedam, et ipsum audivit, viginti annis, ut in vita sua legitur.
Et post mortem Platonis vixit quadraginta tres annis, unde
in universo non vixit nisi sexaginta sex annis, sicut ex
dictis patet. Et hoc similiter patet in libro Censorini de
die natali, quoniam ipse Censorinus refert contra passionem
mortalem per tres annos eum magnitudine animi magis

! The remaining part of this paragraph is omitted in Jebb's ed.

* What follows, as far as the last sentence but one in cap. 15, is omitted by O.
from this second part, and interpolated in Part II] between Tertio and Quarto;
as also is the last paragraph of Part II. Further, the order in which these para-
graphs are placed in Part III is not the same as in J. O. proceeds: ‘ Hoc
Domino Alexandro notum ; et multis aliis potest hoc idem adhuc etiam ostendi
per proprietates duas Metaphysicae,’ &c.

-—— Qn rr —

PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 55

quam medicinae virtute luctatum fuisse. Hic Aristoteles
magister Alexandri magni effectus duo millia hominum
misit per mundi regiones, ut naturas rerum exquirerent,
sicut Plinius narrat in Naturalibus octavo libro et mille
libros composuit, ut in ejus vita legitur. Hic enim prae-
cedentium philosophorum errores evacuavit, et augmen-
tavit philosophiam aspirans ad ejus complementum quod
habuerint antiqui patriarchae, quamvis non potuit singula
perficere. Nam posteriores ipsum in aliquibus correxerunt,
et multa ad ejus opera addiderunt, et adhuc addentur usque
ad finem mundi ; quia nihil est perfectum in humanis inven-
tionibus, ut in prioribus est expositum. Hunc natura firmavit,
ut dicit Averroes in tertio de Anima, ut ultimam perfectionem
hominis inveniret. Hic omnium philosophorum magnorum
testimonio praefertur philosophis, et philosophiae ascriben-
dum est id quod ipse affirmavit; unde nunc temporis auto-
nomatice Philosophus nominatur, in auctoritate philosophiae,
sicut Paulus in doctrina sapientiae sacrae apostoli nomine
intelligitur!! Quievit autem et siluit philosophia Aristotelis,
pro majori parte aut propter occultationem exemplarium
et raritatem, aut propter difficultatem, aut propter invidiam,
aut propter guerras Orientis *, usque post tempora Mahometi,
quando Avicenna et Averroes et caeteri revocaverunt philo-
sophiam Aristotelis in lucem plenam expositionis. Et licet
alia Logicalia et quaedam alia translata fuerunt per Boetium
de Graeco, tamen tempore Michael Scoti, qui annis Domini
1230 transactis apparuit deferens librorum Aristotelis partes
aliquas de Naturalibus et Metaphysicis? cum expositoribus
authenticis, magnificata est philosophia Aristotelis apud
Latinos. Sed respectu multitudinis et magnitudinis suae
sapientiae in mille tractatibus comprehensae, valde * modicum
adhuc in linguam Latinam est translatum, et minus est in usu
vulgi studentium. Avicenna quidem praecipuus imitator et
expositor Aristotelis, ct complens philosophiam secundum
quod ei fuerit possibile, triplex volumen condidit philo-
sophiae, ut ipse dicit in prologo libri Sufficientiae; unum
! Om. in Jebb. 3 Om. in Jebb.
3 Jebb has Mathematicis. ! vel, Jebb.

It is for
Christian
theologians
to carry on
their work.

56 OPERIS MAJORIS PARS SECUNDA.

vulgatum juxta communes sententias philosophorum Peri-
pateticorum, qui sunt de secta Aristotelis; aliud vero se-
cundum puram veritatem Philosophiae, quae non timet ictus
lancearum contradicentium, ut ipse asserit ; tertium vero fuit
cum termino vitae suae, in quo exposuit priora!, secretiora
naturae et artis recolligens. Sed de his voluminibus duo non
sunt translata; primum autem secundum aliquas. partes
habent Latini, quod vocatur Assephae, i.e. liber sufficientiae.
Post hunc venit Averroes, homo solidae sapientiae, corrigens
dicta priorum et addens multa, quamvis corrigendus sit in
aliquibus, et in multis complendus*.

CAPITULUM XIV.

Ex his sequitur necessario, quod nos Christiani debemus
uti philosophia in divinis, et in philosophicis multa assumere
theologica, ut appareat quod una sit sapientia in utraque
relucens. Quam necessitatem voluero certificare, non solum
propter unitatem sapientiae, sed propter quod inferius tangam,
oportet nos in philosophia revolvere sententias fidei et theo-
logiae magnificas quas reperimus in libris philosophorum et
in partibus philosophiae; ut non sit mirum quod in philo-
sophia tangam sacratissimas veritates, quoniam philosophis
Deus concessit multas sapientiae suae veritates. X Oportet
igitur ut trahatur philosophiae potestas ad sacram veritatem
quantum possumus ; nam valor philosophiae aliter non lucescit 3.
Nam philosophia secundum se considerata nullius utilitatis
est. Philosophi vero infideles damnati sunt, *et cum cogno-
verunt Dominum, non sicut Dominum glorificaverunt et ideo
stultificati sunt et evanuerunt a cogitationibus suis. Et
ideo philosophia non potest aliquid dignitatis habere, nisi
quantum de ea requirit Dei sapientia. Totum enim residuum

1 This is the reading of Jul.

3 Jul. here adds a passage which fire has rendered illegible. The succeeding
paragraph is headed, * Quarta Distinctio; in qua ostenditur necessitas utendi
philosophia in divinis, non solum propter unitatem sapientiae perfectae sed quia
in sequentibus partibus hujus persuasionis adductae sunt veritates divinae quae
de pluribus philosophorum extrahuntur.'

> ‘nam... lucescit,’ supplied from Jul.

PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 573

est erroneum et inane, et propter hoc dicit Alpharabius in libro
de scientiis, quod sicut puer indoctus se habet ad hominem
sapientissimum in philosophia sic homo talis ad sapientiam
Dei. Praeterea semper crescere potest in hac vita studium
sapientiae, quia nihil est perfectum in humanis inventionibus.
Quapropter antiquorum defectus deberemus nos posteriores
supplere, quia introivimus in labores eorum, per quos, nisi
simus asini, possumus ad meliora excitari ; quia miserrimum
est semper uti inventis, et nunquam inveniendis, ut dicit
Boetius, et probatum est efficaciter superius suo loco. Item
Christiani debent ad suam professionem quae sapientia Dei
est caetera pertractare, et vias philosophorum infidelium com-
plere; non solum quia posteriores sumus, et debemus addere
ad eorum opera, sed ut cogamus sapientiam philosophorum
nostrae deservire. Nam hoc philosophi infideles faciunt ipsa
veritate coacti in quantum eis datum est; nam totam philo-
sophiam reducunt ad divina ; ut ex libris Avicennae in Meta-
physicae et Moralibus, et per Alpharabium et Senecam et
Tullium, et per Aristotelem patet; nam omnia reducunt ad
Deum, sicut exercitus ad principem, inferentes de angelis et
aliis multis, quoniam principales articuli fidei reperiuntur in eis.

Nam ut in Moralibus exponetur, Deum esse docent, et They had
quod sit unus in esse, infinitae potentiae et sapientiae et glim

bonitatis, trinis in personis, Pater, et Filius et Spiritus Sanctus, of ean

qui omnia creavit ex nihilo; et de Domino Jesu Christo et de
beata virgine multa tangunt. Similiter de Antichristo, atque
de angelis et.custodia hominum per eos !, necnon de resurrec-
tione mortuorum, et de judicio futuro, et de vita futurae
felicitatis quam Deus promisit obedientibus sibi, et de miseria
futura, quam proponit inferre his qui mandata ejus non obser-
vant. Scribuntque innumerabilia de morum honestate, de
legum gloria, de legislatore qui debet accipere legem a Deo per
revelationem, qui sit mediator Dei et hominum, et vicarius
Dei in terra, et Dominus terreni mundi, de quo cum pro-
batum fuerit quod recepit legem a Deo, ei credendum sit in
omnibus, exclusa omni dubitatione et haesitatione, qui debet
totum genus humanum ordinare in cultu Dei et legibus jus-

1 ‘per eos,’ om. in O.

58 OPERIS MAJORIS PARS SECUNDA.

titiae et pacis, et in virtutum exercitio propter reverentiam
Dei ac futuram felicitatem ; et quod idolorum cultura destrui
debet. Haec et his similia! habuerunt philosophi. In libris
enim eorum hujusmodi reperimus, sicut probatio certa doce-
bit in sequentibus, et quilibet potest experiri qui vult libros
philosophorum perlegere; et negare non possumus quin
scripta sunt ab eis, undecunque hujusmodi receperunt. Nec
mirandum est quod philosophi talia scribant ; nam omnes
philosophi fuerunt post patriarchas et prophetas, sicut prius
de hoc facta est consideratio in suo loco; et legerunt libros
prophetarum et patriarcharum qui sunt in sacro textu, et
similiter alios libros, quos fecerunt tangentes Christi mys-
teria ut in libro Enoch et in testamento patriarcharum
in libro Esdrae, 3°, 4°, 5°, et in multis aliis libris de quorum
aliquibus sit mentio in sacro textu ut de libris Nathan,
Samuelis, et Abdon prophetarum. In hujusmodi enim libris
tanguntur expresse articuli fidei, et longe expressius quam
in Canone Scripturae. Nam praeter caeteros libros liber
de testamentis patriarcharum ostendit omnia, quae de Christo
impleta sunt. Quilibet enim patriarcha in morte praedicavit
filiis suis et tribui suae, et praedixit eis ea quae de Christo
tenenda sunt, sicut manifestum est ex libro suo. Et hi libri
licet non sint in Canone, tamen sancti et sapientes Graeci
et Latini usi sunt eis a principio Ecclesiae. Nam beatus
Judas de hoc Enoch accepit auctoritatem, et Augustinus
decimo de Civitate Dei, multum fundatur super illum librum,
ut ostendatur quod primo fuit sapientia apud sanctos quam
apud philosophos, et ait quod jam propter nimiam anti-
quitatem ille liber non est in auctoritate, quam propter
aliquid aliud. De libris autem aliis manifestum est quod
in usu sanctorum et sapientum antiquorum sunt propter
hoc quod planas veritates de Christo continere noscimus.
Philosophi igitur curiosi et diligentes in studio sapientiae
peragrarunt regiones diversas, ut sapientiam inquirerent, et
libros sanctorum perlegerunt, et didicerunt ab Hebraeis
multa. Nam Avicenna in radicibus moralis philosophiae

! After * similia! O. has ' nunquam, which is omitted in Jul., and which spoils
the sense.

PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 59

recitat verba Esaiae de vita aeterna, dicens illam esse quam
oculus non vidit, nec auris audivit, et recitat, Eleemosyna tollit
peccatum, sicut propheta veritatis.dicit, scilicet Tobias. Et
Augustinus vult decimo octavo de Civitate Dei, quod Plato
legerat librum Geneseos, propter creationem mundi quam
posuit similem ei quae ibi describitur. Et quod legis librum
legit, videlicet Exodi, propter nomen Dei quod ibi ponitur,
scilicet, Ego sum qui sum. Nam hoc usus est Plato, et alibi
non potuit invenire, ut dicit Augustinus. Et praeter sacros
libros prophetales composuerunt libros philosophiae; immo
totam philosophiam his perfecerunt. Et quod philosophi non
habuerunt nisi ab eis, ostensum est in praecedentibus evi-
denter, et quia una est sapientia, quae sufficit humano generi ;
ideo sancti in libris philosophicis miscuerunt divina multa cum
alis, quantum potuit philosophia recipere. Et propterea
propter istos libros philosophicos sanctorum multa percepe-
runt philosophi de divinis veritatibus.

CAPITULUM XV.

Praeterea cum philosophi fuerunt dediti veritatibus et omni which in
vitae bonitati, contemnentes divitias, delicias, et honores, ode
aspirantes ad futuram felicitatem quantum potuit humana Sibyls were
fragilitas, immo victores effecti humanae naturae, sicut Hiero- explicit. T
nymus scribit de Diogene in libro contra Jovinianum, non
est mirum, si Deus, qui in his minoribus illuminavit, daret eis
alia lumina veritatum majorum. Et si non principaliter
propter eos, tamen propter nos, ut eorum persuasionibus
mundus disponeretur ad fidem. Et ad hoc facit quod Sibyllae
multae inventae sunt, scilicet decem ; sicut omnes sancti
concordant, et Augustinus decimo octavo de Civitate Dei !, et
Isidorus libro Etymologicorum septimo. Necnon historiae
et philosophiae et poetae concordant universaliter in his
Sibyllis. Sed certum est eas recitasse divina, et ea quae de
Christo habentur et de judicio futuro, et hujusmodi. Ergo
multo magis probabile est quod philosophi sapientissimi et
optimi a Deo receperunt hujusmodi veritates. Quod vero

! De Civitate Dei, lib. xviii. cap. 23.

60 OPERIS MAJORIS PARS SECUNDA.

Sibyllae locutae sunt praeclare veritates divinas, manifestum
est per sanctos et alios, et sufficit recitare quod Augustinus
dicit decimo octavo de Civitate Dei!. * Dixerunt igitur istae
mulieres hujusmodi sermones; dabunt Deo alapas manibus
incestis, imputato ore exspuent venenatos sputus; dabit
vero ad verbera simpliciter suum dorsum, colaphos accipiens
tacebit, et corona spinea coronabitur. Ad cibum autem fel,
et ad potum acetum dederunt. Insipiens gens, Dominum
tuum non intellexisti ludentem mortalium mentibus, sed
spinis coronasti, et horridum fel miscuisti. Templi vero
velum scinditur, et medio die -nox erit tenebrosa tribus
horis, et morte morietur tribus diebus, somno suscepto.
Et iterum metrice dixit Sibylla,

* Judicii signum, tellus sudore madescet,

Ex coelo rex adveniet per secla futurus,

Scilicet in carne praesens ut judicet orbem.

Unde Deum cernent incredulus atque fidelis,

Celsum cum sanctis ejus jam termino in ipso.

Sic animae cum carne aderunt, quas judicet ipse.

Exuret terras ignis pontumque polumque ;

Sanctorum sed enim cunctae lux libera carni

Tradetur, sontes aeternum flamma cremabit.

Actus occultos retegens tunc quisque loquetur

Secreta, atque Deus reserabit pectora luci.

Eripitur solis jubar et chorus interit astris:

Solvetur coelum, lunaris splendor abibit.

Dejiciet colles, valles extollet ab imo.

Sic pariter fontes torrentur, fluminaque igni,

Tartareumque Chaos monstrabit terra dehiscens,

Excidet e coelis ignisque et sulphuris amnis 2.’

Si igitur mulierculae fragiles hujusmodi dixerunt, longe
magis credendum philosophos sapientissimos hujusmodi gus-
tasse veritates. Et Augustinus vult decimo octavo de Civi-
tate Dei, alios percepisse Dei veritatem, quam illi qui de linea
Abraham usque ad Christum et deinceps descenderunt. Nam

! Quoted by St. Augustine from Lactantius.

* This passage from the Sibylline poem is given most incorrectly in the MSS.
I have corrected it from De Civitate Dei, lib. xviii. cap. 23.

PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 61

Job scivit resurrectionem et Dei veritates. Et in chronicis
Eusebii legitur, quod Irene et Constantino imperantibus fuit
cadaver effossum, in quo inveniebatur scriptura haec, ‘ Credo
in Christum ; sub Irene et Constantino iterum videbit me
Sol' Et nunc tempore Domini Alexandri Papae quarti
Saracenus in Borea mundum contemnens, vacans in lege sua
Deo et virtuti et contemplationi alterius vitae, recepit visita-
tionem angelicam et consilium ut converteretur ad fidem
Christi, et baptizatus est. Hoc Domino Alexandro notum
est et multis aliis, et adhuc recolunt quamplures.

CAPITULUM XVI.

Potest hoc idem adhuc etiam ostendi per proprietates duas Philosophy
metaphysicae. Nam haec scientia est de illis, quae omnibus i 0877 7E
rebus et scientiis conveniunt, et ideo ostendit numerum perfection

scientiarum, et quod oportet esse aliam scientiam ultra philoso- higher” the
phiam, cujus proprietates tangit in universali; licet in baths 2.
particulari non posset eam assignare. Scit enim philosophia
suas imperfectiones, et quod deficit a plena cognitione eorum
quae maxime sunt cognoscenda, sicut Aristoteles docet in
Metaphysica ; et Avicenna similiter, ut tactum est superius.
Et propter hoc devenit philosophia ad inveniendam scientiam
altiorem, quam dicit esse scientiam divinorum, quam Theolo-
giam perfectam vocant philosophi, et ideo philosophia elevat
se ad scientiam divinorum. Item solliciti fuerunt philosophi
super omnia inquirere sectam in qua esset salus hominis, et
dant modos probandi hic praeclaros, sicut ex moralibus
manifestum est. Et invenerunt certitudinaliter, quod aliqua
debet esse secta fidelis et sufficiens mundo, cujus proprietates
assignant, quae non possunt reperiri nisi in secta Christi, ut
probatur suis locis, et ostenditur quod de bonitate Dei est de
necessitate humana quod sciatur haec secta fidelis. Sed non
potest hoc probari infidelibus per legem Christi, nec per
auctores sacros, quia ex lege disputationis possunt negari
omnia quae in lege Christi sunt, sicut Christiani negant ea
quae in aliis legibus continentur. Et etiam quia Christum
negant, non est mirum, si auctores Christianorum negent.

62 OPERIS MAJORIS PARS SECUNDA.

Persuasio autem fidei necessaria est ; sed non potest hoc esse
nisi duobus modis, aut per miracula quae sunt supra fideles
et infideles, de quibus nullus potest praesumere ; aut per viam
communem fidelibus et infidelibus! ; sed hoc non est nisi per
philosophiam. Ergo philosophia habet dare probationes fidei
Christianae. Articuli vero hujus fidei sunt principia propria
theologiae ; ergo philosophia habet descendere ad probationes
principiorum theologiae, licet minus profunde quam ad
principia aliarum scientiarum. Et hoc modo supponatur ex
hac ratione, donec veniatur ad probationem sectarum. Nam
ibi ostendetur quod moralis philosophia efficacius theologia?
deservit in hac parte, et ideo licet secundum veritatem hujus-
modi sunt theologica, nihilominus tamen sunt philosophica, sed
propter theologiam.

CAPITULUM XVII.

Moral Praeterea tota philosophia speculativa ordinatur in finem
philosePhy suum, qui est philosophia moralis Et quia finis imponit
necting necessitatem eis, quae sunt ad finem ut Aristoteles dicit
secundo Physicorum, ideo philosophia speculativa semper
aspirat ad finem suum, et erigit se ad eum, et quaerit vias
utiles in ipsum, et propter hoc potest philosophia speculativa
praeparare principia moralis philosophiae. Sic igitur se
habent duae partes sapientiae apud infideles philosophos: sed
apud Christianos philosophantes scientia moralis proprie et
perfecte est theologia, quae super majorem philosophiam
infidelium addit fidem Christi, et veritates quae sunt proprie
divinae?. Et hic finis habet suam speculationem praecedentem,
sicut moralis philosophia infidelium habet suam ; quae igitur
est proportio finis ad finem, est proportio speculationis ad
speculationem : sed finis ut lex Christiana supra legem philoso-
phorum addit articulos fidei expressos, per quos complet legem
moralis philosophiae ‘, ut fiat una lex completa. Nam lex
Christi leges et mores philosophiae sumit et assumit, ut certum
est per sanctos, ct in usu theologiae et ecclesiae. Ergo
! Thus in Jul. Jebb's reading here is confused and inaccurate.
* Sic Jul Jebb's reading, * in homine,’ is unintelligible.
3 This passage has been corrected from Jul.
* This is the reading of Jul.

LL — —— DNE. Qo —

PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 63

speculatio Christianorum praecedens legem suam debet super
speculationem alterius legis addere ea quae valent ad legem
Christi docendam et probandam, ut surgat una speculatio
completa, cujus initium erit speculativa philosophorum in-
fidelium, et complementum ejus erit superinductum theologiae,
et secundum proprietatem legis Christianae. Et ideo philo-
sophia apud Christianos debet sapere multum de divinis, plus
quam apud philosophos infideles, et propter hoc debent
philosophi considerare philosophiam, ac si modo esset de
novo inventa, ut eam facerent aptam fini suo. Et ideo debent
multa addi in philosophia Christianorum ; quae philosophi
infideles scire non potuerant. Et hujusmodi sunt rationes
exsurgentes in nobis ex fide et auctoribus legis et sanctorum
qui sapiunt philosophiam ; et possunt esse communia philo-
sophiae completae et theologiae. Et haec cognoscuntur per
hoc quod debent esse communia fidelibus et infidelibus, ut
sint ita nota cum proferuntur et probantur, quod negari non
possunt a sapientibus et instructis in philosophia infidelium.
Nam philosophi infideles multa ignorant in praesenti! de
divinis quae proponerentur eis, ut probarentur per principia
philosophia completae, hoc est, per vivacitates rationis quae
sumunt originem a philosophia infidelium ; licet complementum
a fide Christi reciperent sine contradictione, et gauderent de
proposita sibi veritate, quia avidi sunt sapientiae et magis
studiosi quam Christiani. Non tamen dico, quod aliquid de
spiritualibus articulis idei Christianae reciperetur in probatione,
sed multae veritates sunt communes rationales, quas omnis
sapiens de facili reciperet ab alio, quamvis secundum se
ignoraret.

Non igitur mirentur philosophantes, si habeant elevare
philosophiam ad divina et ad theologiae veritates et sanctorum
auctoritates, et uti eis abundanter cum fuerit opportunum ?,
et probare eas cum necesse est, et per illas alias probare;
quoniam proculdubio philosophia et theologia communicant
in multis. Et sancti non solum loquuntur theologice, sed
philosophice, et philosophica multipliciter introducunt. Et
ideo Christiani, philosophiam volentes complere, debent in

! Sic O. ; J. has particulari. 2 Sic Jul; O. has optimum.

Summary.

64 OPERIS MAJORIS PARS SECUNDA.

suis tractatibus non solum dicta philosophorum de divinis
veritatibus colligere, sed longe ulterius progredi, usquequo
potestas philosophiae totius compleatur. . Et propter hoc
complens philosophiam per hujusmodi veritates non debet
dici theologicus nec transcendere metas philosophiae ; quoniam
ista quae sunt communia philosophiae et theologiae potest
secure tractare et ea quae communiter habent recipi a fidelibus
et infidelibus. Ettalia multa sunt praeter dicta philosophorum.
infidelium, quae tanquam propria infra limites philosophiae
debet recte philosophans colligere, ubicunque ea invenit, et
tanquam sua habet congregare, sive in libris sanctorum, sive
philosophorum, sive in sacra scriptura, sive in historiis, sive
alibi. Nullus enim auctor est quin praeter principalem inten-
tionem aliqua incidenter recitet quae sunt alibi magis propria ;
et hujus causa est annexio scientiarum, quia quaelibet ab alia
quodam modo dependet; sed omnis, qui debito modo tractat,
debet quae sunt propria ei assignare, et quae necessaria et
suae competentia dignitati, et ideo ubicunque ea inveniat velut
sua cognoscere, et tanquam propria habet rapere, et in locis
propriis collocare. Propter quod philosophans Christianus
potest multas auctoritates et rationes et sententias quam-
plurimas de scriptis aliis, quoque de libris philosophorum
infidelium adunare, dummodo sint propria philosophiae, vel
communia ei et theologiae, et quae communiter habent fideles
et infideles reperire. Et nisi hoc fiat, non perficietur, sed
multum ei derogabitur. Et non solum debet hoc fieri propter
complementum philosophiae, sed propter conscientiam Chris-
tianam, quae habet omnem veritatem ducere ad divinam, ut
ei subjiciatur et famuletur. Atque propter hoc, philosophia
infidelium est penitus nociva, et nihil valet secundum se con-
siderata, nam philosophia secundum se ducit ad caecitatem
infernalem et ideo oportet quod secundum se sit tenebrae et
caligo.
CAPITULUM XVIII.

His consideratis !, patet intentum principale; et manifestum
est quod omnes philosophi infideles et Poetae et Sibyllae et

! From this point tothe end of Part II is omitted here in O. andis transposed
to Part III. Vide note on p. 54.

= ————— —— — -— w—— — - -— oe ~- -- —

PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 65

quicunque sapientiae sunt dediti, inventi sunt post philosophos
veros et fideles, qui fucrunt filii Seth et Noe cum filiis suis,
quibus Deus dedit vivere sexcentos annos propter studium
sapientiae complendum, ut dicit Josephus primo Antiquitatum,
asserens quod in minore tempore non potuerant complere philo-
sophiam praecipue propter astronomiam in qua est major diffi-
cultas, eo quod a caelestibus homines mortales multum distant ;
sed Deus eis revelavit omnia, et dedit eis vitae longitudinem,
ut philosophiam per experientias complerent. Sed propter
malitiam hominum qui abusi sunt viis sapientiae, ut Nimroth,
et Zoroaster, et Atlas, et Prometheus, et Mercurius aut Tris-
megistus, et Aesculapius, et Apollo, et alii qui colebantur
sicut Dii propter sapientiam, Deus obscuravit cor multitudinis,
et recidit paulatim usus philosophiae usquequo iterum Salomon
eam revocavit et perfecit omnino, sicut Josephus docet octavo
Antiquitatum. Et iterum propter peccata hominum evanuit
studium sapientiae, donec Thales Milesius resumpsit eam, et
ejus successores dilataverunt, usquequo Aristoteles consum-
mavit, quantum fuit possibile juxta idem tempus. Sed isti
ab Hebraeis didicerunt omnia, sicut Aristoteles dicit in libro
secretorum, quoniam philosophi infideles, ut Nimroth et alii,
fuerunt post Seth, Noe, Sem, et Abraham ; et post Salomonem,
qui secundo perfecit eam, fuerunt reliqui philosophi infideles
ut Thales et Pythagoras, Socrates et Plato, et Aristoteles.
Ideo manifestum est, quod philosophiae perfectio fuit primo
data sanctis, Patriarchis et Prophetis, quibus lex Dei similiter
fuit ab uno et eodem Deo revelata ; quod non fuisset factum,
nisi philosophia omnino esset sanctis Dei et legi sacrae con-
formis et utilis ac necessaria propter intellectum legis et
excusationem et defensionem ; insuper ut fiat ejus persuasio,
et probetur et communicetur et dilatetur ; nam omnibus his
modis necessaria est, sicut discurrendo per partes singulas
philosophiae apparebit. Et ideo philosophia non est nisi
sapientiae divinae explicatio per doctrinam et opus, et propter
hoc una est sapientia perfecta, quae sacris literis continetur.

VOL. I. F

Know-
ledge

implies
study

of the
languages
in whic
knowledge
is recorded.

PARS TERTIA

HUJUS PERSUASIONIS.

DE UTILITATE GRAMMATICAE !.

Declarato igitur, quod una est sapientia perfecta, quae sacris
literis continetur per jus canonicum et philosophiam, qua

mundus habet regi, nec alia requiritur scientia pro utilitate
generis humani, nunc volo descendere ad ea hujus sapientiae
magnifica, quae maxime valent exponi. Et sunt quinque,
sine quibus nec divina nec humana sciri possunt, quorum certa
cognitio reddit nos faciles ad omnia cognoscenda. Et primum
est Grammatica in linguis alienis exposita, ex quibus emanavit
sapientia Latinorum. Impossibile enim est, quod Latini
perveniant ad ea quae necessaria sunt in divinis et humanis,
nisi notitiam habeant aliarum linguarum, nec perficietur eis
sapientia absolute, nec relate ad ecclesiam Dei et reliqua tria
praenominata. Quod volo nunc declarare, et primo respectu
scientiae absolutae. Nam totus textus sacer a Graeco et
Hebraeo transfusus est, et philosophia ab his et Arabico
deducta est; sed impossibile est quod proprietas unius linguae
servetur in alia. Nam et idiomata ejusdem linguae variantur
apud diversos, sicut patet de lingua Gallicana, quae apud
Gallicos et Picardos et Normannos et Burgundos multiplici
variatur idiomate. Et quod proprie dicitur in idiomate
Picardorum horrescit apud Burgundos, immo apud Gallicos
viciniores: quanto igitur magis accidet hoc apud linguas
diversas? Quapropter, quod bene factum est in una lingua,

! [ have kept this title, which is given in all the MSS. But it must always
be remembered that it is not grammar in the ordinary acceptation of the word,
but knowledge of certain foreign languages, of which Bacon is urging the im-
portance.

LINGUARUM COGNITIO. 67

non est possibile ut transferatur in aliam secundum ejus
proprietatem quam habuerit in priori.

Unde Hieronymus, in epistola de optimo genere inter-
pretandi, sic dicit, *Si ad verbum interpretor, absurdum
resonat' Quod si cuiquam videatur linguae gratiam inter-
pretatione non mutari, Homerum exprimat in Latinum ad
verbum. Si quis autem eundem in sua lingua per se inter-
pretetur, videbit ordinem ridiculosum, et poetam eloquentis-
simum vix loquentem. Quicunque enim aliquam scientiam
ut logicam vel aliam quamcunque bene sciat, eam, etsi
nitatur in linguam convertere maternam, videbit non solum
in sententiis sed in verbis deficere. Et ideo nullus Latinus
sapientiam sacrae scripturae et philosophiae poterit ut oportet
intelligere, nisi intelligat linguas a quibus sunt translatae.

Et secundo considerandum est quod interpretes non
habuerunt vocabula in Latino pro scientiis transferendis, quia
non fuerunt primo compositae in lingua Latina. Et propter
hoc posuerunt infinita de linguis alienis, quae sicut nec intelli-
guntur ab eis qui linguas ignorant, sic nec recte proferuntur
nec scribuntur ut decet; atque, quod vile est, propter
ignorantiam linguae Latinae posuerunt Hispanicam, et alias
linguas maternas, quasi infinities pro Latino. Nam pro mille
millibus exemplis unum ponatur de libro vegetabilium
Aristotelis, ubi dicit, ‘Belenum in Perside pernitiosissimum,
sed transplantatum Jerusalem fit comestibile.’ Hoc vocabulum
non est scientiale laico Hispanicorum. Nam jusquiamus vel
semen cassilaginis est nomen ejus in Latino. Quae sicut
multa alia prius ab Hispanis scholaribus derisus cum non
intelligebam quod legebam, ipsis vocabula linguae maternae
scientibus, tandem didici ab eisdem.

Tertio, oportet quod interpres optime sciat scientiam quam
vult transferre, et duas linguas a quibus et in quas transferat.
Solus Boethius primus interpres novit plenarie potestatem
linguarum. Et solus dominus Robertus, dictus Grossum
Caput, novit scientias!. Alii quidem mendici translatores

! Of this bold reformer of ecclesiastical abuses, and champion of civil liberties,
Bacon is never tired of speaking. He held the see of Lincoln from 1235 till
his death in 1253. ‘ Quietis nescius, multis adversans, quam plurimisque ei

F 2

Many
words have
no Latin
equivalent.

A trans-
lator
should
know (1)
his subject,
(2) the two
languages
he is hand-

ling.

68 OFERIS MAJORIS PARS TERTIA.

defecerunt multum tam in scientiis quam in linguis; quod
ostendit ipsorum translatio. Nam tanta est perversitas et
horribilis difficultas, maxime in libris Aristotelis translatis !,

adversantibus,’ is Matthew Paris’ description of him. Visiting Pope Innocent
IV in 1250 to protest against the abuses of the Hospitallers and Templars, and
finding that his opponents had deafened the papal ear with bribes, ‘O gold, gold,’
he cried, ‘how great is thy power, especially in the Court of Rome!’ In the
last year of his life, he wrote to the Pope, plainly telling him that his vow of
obedience to the Church forbade compliance with his extortionate demands for
money. ‘ Filialiter et obedienter non obedio, contradico et rebello.' The Pope
could not contain himself for anger. ‘Who is this mad old man,’ he cried, ‘who
dares to sit in judgement on our actions?' But Cardinal Aegidius and others re-
strained his wrath. ‘If we are to tell the truth,’ they said, ‘the things he writes
are true. He is a Catholic man of most holy life, more religious and more
excellent than we. He is held for a great philosopher, deeply learned in Latin
and Greek literature, zealous for justice, a teacher in theological schools,
a preacter to the people, a lover of chastity, an uprooter of simony.’ (Matthew
Paris, ad ann. 1253.)

It would seem probable that his scientific works were written before his
elevation to the bishopric. Among them are, Libellus de physicis lineis angulis
et Águris per quas omnes actiones naturales complentur; a treatise De natura
locorum ; and a treatise De artibus liberalibus. These were printed in Venice,
1514. Among the Harleian MSS. are two, as yet unedited: 7402, a treatise
on the Calendar; and 4350, on the Celestial Sphere. Of Greek, according
to Bacon, his knowledge was but slight; but he introduced several Greek
scholars into England, one of whom, Nicolas, translated the apocryphal
Testaments of the twelve patriarchs, brought from Athens by John of Basing-
stoke. (Cf Matthew Paris, ad ann. 1252). It seems probable that Bacon in
the early part of his career profited much from Grosstéte’s teaching. The
language of the Libellus de physicis lineis, as to the propagation of force, and
as to the laws of reflection and refraction, bears a remarkable resemblance to
that of Bacon.

1 Cantor, in his History of Mathematics, speaking of the school of translation
set up at Toledo in the twelfth century under the direction of Raymund, the
archbishop of that city, by Dominic Gundisalvi and John of Seville, remarks :
* Their labours were conducted in a circuitous fashion which had its conse-
quences. The Arabic was first translated into Castilian, and from this the
Latin version was made. Bearing in mind that the Arabic text was taken from
the Greek by men whose powers of translation were not wholly beyond
suspicion, we may imagine what sort of Aristotelian philosophy reached the
mediaeval student after three repetitions of bungling.’ Cantor, vol. i. p. 684.
Jourdain, in his work Recherches critiques sur l'áge et l'origine des traductions
latines d’ Aristote (Nouvelle édition, 1843), has supplied specimens of these
translations which enable us to form some judgement of their value; since he
distinguishes those made directly from the Greek text from those made from
Arabic versions, The latter are not so inferior to the former as might have
been expected ; probably because the Arab scholars of the tenth and eleventh
centuries knew more Greek than the European scholars of the twelfth and

LINGUARUM COGNITIO. 69

quod nullus potest eos intelligere. Sed quilibet alii contra-
dicit, et multiplex reperitur falsitas, ut patet ex collatione
diversorum interpretum et textuum diversarum linguarum.
Et similiter in textu sacro inveniuntur falsa, et male translata
quamplurima. Nam Hieronymus probat translationem LXX
interpretum et Theodotionis et Aquilae multas habuisse
falsitates, quae fuerunt vulgatae per totam Ecclesiam. Et
omnes stabant maxime pro translatione LX X, sicut pro vita,
et reputabatur Hieronymus falsarius et corruptor scripturarum,
donec paulatim claruit veritas Hebraica per solum Hiero-
nymum in Latinum conversa. Ne tamen nimia novitae
deterreret Latinos, ideo, ut ipse scribit, aliquando coaptavit
se LXX interpretibus et aliquando Theodotioni, aliquando
Aquilae, et ideo multa dimisit, et propter hoc remanserunt
plura falsa. Nam ut Augustinus probat de doctrina Christi
libro secundo male translatum est quod habetur in libro Sapien-
tiae, ‘Spuria vitulamina non dabunt radices altas. Nam debent
esse spuriae plantationes, ut Augustinus probat per Graecum.
Et tamen Hieronymus dimisit hoc, sicut alia, propter pacem
Ecclesiae et doctorum. Atque scitur manifeste, quod Hiero-
nymus humanum aliquid passus aliquando in translatione
sua oberravit, sicut ipsemet pluries confitetur. Nam quod
decimum nonum male transtulerat Isaiae, resumit in saginali
quinto dicens, ‘in eo quo transtulimus zucurvantem et lasct-
vientem nos autem verbum Hebraicum acmon dum celeriter
scripto vertimus, ambiguitate decepti refracnantem diximus.
Et aliud quod in eodem capitulo male transtulerat revolvit
dicens, * Melius reor proprium errorem reprehendere, quam
dum erubesco imperitiam confiteri, in errore persistere. In eo
veroquotranstuli, * eterit terra Juda Aegypto in festivitatem," in
Hebraico legitur agga, quod interpretari potest etiam festivitas,
unde aggus in festivum vertitur, et “or, quod significantius
Aquila transtulit gerostn, cum aliquis pavidus et timens
circumfert oculos, et adveniens formidat initium ; ergo, si
voluerimus in bonam partem accipere quod recordatio Judaeae
Aegypto sit gaudii recte festivitas dicitur; sin autem, ut

thirteenth ; although sometimes the Arabic translation was made from an inter-
mediate Syriac version.

Parts of
Scripture
and of the
Fathers
still un-
translated.

So too of
Avicenna
and of

Aristotle.

20 OPERIS MAJORIS PARS TERTIA.

arbitror, in timore pro festivitate vertitur in formidinem vel
pavorem.'

Quarta causa est et ratio hujus rei, quod quamplurima -
adhuc desunt Latinis tam philosophica quam theologica.
Nam vidi duos libros Machabaeorum in Graeco, viz. tertium,
et quartum, et Scriptura facit mentionem de libris Samuel et
Nathan et Gad videntis et aliorum, quos non habemus. Atque
cum tota certificatio historiae sacrae sit a Josepho in Antiqui-
tatum libris, et omnes sancti expositionum suarum radices ac-
cipiant a libris illis, necesse est Latinis ut habeant illum librum
incorruptum ; sed probatum est quod codices Latini omnino
sunt corrupti in omnibus locis, in quibus vis historiae consistit ;
ita ut textus ille sibi contradicat ubique, quod non est vitium
tanti auctoris; igitur ex translatione mala hoc accidit et
corruptione ejus per Latinos. Nec est remedium nisi de novo
transferantur vel ad singulas radices corrigantur. Similiter
libri doctorum magnorum, ut beatorum Dionysii, Basilii,
Johannis Damasceni, et aliorum multorum deficiunt ; quorum
tamen aliquos dominus Robertus praefatus episcopus vertit in
Latinum, et alii quosdam alios ante eum; cujus opus est
valde gratum theologis. Et si libri istorum translati essent,
non solum augmentaretur sapientia Latinorum, sed haberet
Ecclesia fortia adjutoria contra Graecorum haereses et
schismata, quoniam per sanctorum eorum sententias, quibus
non possunt contradicere, convincerentur.

Similiter fere omnia secreta philosophiae adhuc jacent in
linguis alienis. Nam solum quaedam communia et vilia ut in
pluribus translata sunt ; et de hujusmodi etiam multa desunt.
Nam libri integri omittuntur in mathematicis et in naturalibus
et in logicalibus et aliis, praeter magna secreta scientiarum, et
artium, et naturae arcana quae nondum sunt translata ; ut est
secunda philosophia Avicennae, quam vocant orientalem, quae
traditur secundum puritatem philosophiae in se, nec timet
ictus contradicentium lancearum ; et tertia quae fuit conter-
mina! vitae suae, in qua experientias secretas congregavit,
sicut ipse in prologo primae philosophiae suae annotavit. Et
similiter cum Aristoteles complevit octo partes naturalis

* Sk, Jul. O. has conscientia.

LINGUARUM COGNITIO. 71

philosophiae principales, quae multas sub se continet scientias,

de prima parte non habemus omnia, de aliis vero quasi nihil.

Et eodem modo de metaphysica, quae sunt novem, cum ipse
compleverit eas, nihil habemus quod de metaphysica ulla
dignitate vocari potest propter defectus multiplices et prae-
grandes. De mathematicis vero, cum sint quinque scientiae
magnae, non habemus nisi primam, et parum de secunda.

Etiam de logica! deficit liber melior inter omnes alios, et alius The
post eum in bonitate secundus male translatus est, nec potest Pert of his
sciri, nec adhuc in usu vulgi est, quia nuper venit ad Latinos, Llc, viz
et cum defectu translationis et squalore. Nec est mirum si dico and s Foetic
istos libros logicae meliores ; nam oportet esse quatuor argu- tore, issu
menta veridica ; duo enim movent intellectum speculativum seu
rationem, scilicet dialecticum per debilem habitum et initialem,

qui est opinio, ut disponamur ad scientiam, quae est habitus
completus et finalis, in quo quiescet mens speculando veritatem.

Et hic habitus non adquiritur per demonstrationem. Sed cum
voluntas seu intellectus practicus sit nobilior quam specula-

tivus, et virtus cum felicitate excellit in infinitum scientiam
nudam, et nobis est magis necessaria sine comparatione, necesse

est ut habeamus argumenta ad exercitandum per intellectum
practicum, praecipue cum magis simus infirmi in hac parte

quam in speculatione. Libenter enim gustamus de ligno
scientiae boni et mali; sed difficiles sumus ad lignum vitae, ut
virtutem dignitatem amplectamur propter futuram felicitatem.
Quapropter oportet quod habeat intellectus practicus sua
adjutoria ut excitetur per propria argumenta, sicut speculativus

per sua, et ideo necesse fuit ut traderetur de his argumentis

quibus moralis philosophia et theologia utuntur abundanter.

Nam sicut speculativae scientiae gaudent argumentis specu-

lativis opinionis et scientiae nudae, sic practicae scientiae,

ut theologia, et moralis philosophia practica, considerant
argumenta, quibus ad praxim, i.e. ad opus bonum excitemur,

et flectamur ad amorem felicitatis aeternae. Et hic sunt

duo modi flectendi nos; unus est qui promovet animam ad
credendum et consentiendum et commiserandum, et ad com-

! The inclusion of Rhetoric and Poetic in Logic is restated in Part iv. ch. 2,
and also in Of. Tertium, cap. 75.

72 OPERIS MAJORIS PARS TERTIA.

placendum, et eorum actus, et ad contraria cum necessitate.
Et hoc argumentum vocatur rhetoricum, et est respectu
intellectus practici, sicut argumentum dialecticum ad intel-
lectum speculativum. Et hic habitus qui flectit nos ad
amorem boni operis habetur per argumentum poeticum ; quia
poetae, ut Horatius et alii Graeci et Latini, vitia prosequuntur,
et virtutes magnificant, ut alliciantur homines ad honorem et
odium peccati. Nam, ut ille dicit,
* Aut prodesse volunt, aut delectare poetae.
Omne tulit punctum qui miscuit utile dulci.'

Non enim parum prodest civibus, qui delectat in moribus;
oportet enim non solum docere, sed delectare et promovere.
Unde tam poeta quam orator debet haec tria facere, ut
docendo reddat auditores dociles, per delectationem faciat
attentos, et promovendo seu flectendo cogat in opus. Et
haec argumenta in salutiferis rebus sunt fortissima, in puris
speculativis impotentia, sicut demonstratio efficacissima est in
speculationibus nudis, sed impotens est omnino in practicis,
et in his quae pertinent ad salutem, secundum quod Aris-
toteles dicit, primo moralis philosophiae, quod perprimum est
mathematicum uti argumento rhetorico, et rhetorem demon-
strationem experiri, quoniam, ut dicit secundo, haec scientia
non est contemplationis gratia, sed ut boni fiamus. Aris-
toteles igitur fecit libros de his argumentis, et Alpharabius
in libro de scientiis affirmat duas partes logicae debere
constitui de his duobus argumentis, quia sola logica deberet
docere cujusmodi sunt argumenta, et qualiter componantur
propter usum omnium aliarum scientiarum. Et tunc logica
speculativis scientiis per argumenta, videlicet duo, quae sunt
dialecticum et demonstrativum, moralibus autem ministrat
practica argumenta. Et quia theologia et jus canonicum
mores et leges et jura determinant, ideo haec duo argumenta
sunt eis necessaria. Etiam quamvis Latini nondum habent
scientiam horum argumentorum secundum artis logicae tra-
ditionem, tamen necessaria sunt multis modis. Qualiter autem
componantur haec argumenta, non est ad praesens dicendum.
Sed in hoc opere, quod Vestra Beatitudo postulavit dicitur
explicari. Nihil tamen de scientiis speculativis utilius est

LINGUARUM COGNITIO. 73

propter fidem probandam infidelibus ut flectantur ad creden-
dum et amorem fidei Christianae. Et similiter ut artificialiter
praedicemus omnibus quibus praedicatio necessaria est, et sic
de aliis utilibus persuasionibus ad salutem. Magnum autem
adjutorium habemus per Augustinum in tertio et quarto de
doctrina Christi, et per libros Tullianos, et per libros Senecae
et epistolas, quae possunt colligi in lingua Latina de his argu-
mentis, quamvis ipsa textura Aristotelis nobis deficiat.

Quinta ratio est ad hoc, quoniam ex sensu sunt compositae The fathers

et expositae, et ideo cum scientiae fuerunt traditae Latinis

vocabula Graeca et Hebraea et Chaldaea et Arabica, praeter
ea quae in textibus continentur. Et nos sumus filii et suc-
cessores sanctorum et sapientum usque ad haec ultima
tempora. Nam vidimus aliquos de antiquis qui multum labora-
verunt, sicut fuit dominus Robertus praefatus translator,
Episcopus Lincolniensis, et dominus Thomas venerabilis
antistes sancti David nuper defunctus, et frater Adam de
Marisco, et magister Hermannus translator! et quidam alii
sapientes. Sed quoniam eos non imitamur, ideo ultra illud
quod credi potest deficimus a potestate scientiarum, quia
expositiones authenticas non possumus intelligere, et per eas
nec intellectum scientiarum possumus obtinere. Et pro
infinitis pono duo exempla. Hieronymus dicit in prologo
Daniel, quod Daniel et Esdras scribuntur libris Hebraicis, sed
Chaldaeo sermone, et una pericope Jeremiae. Hanc autem
pericopen Jeremiae omnes theologi dicunt esse Threnos
Jeremiae: quia pericope idem est quod pars parva seu par-
ticula; sed omnes Hebraei sciunt quod scribimus Z7»eri literis
Hebraicis et Hebraeo sermone. Deinde possumus hanc
pericopen sumere decimo capitulo Jeremiae, ubi dicitur sic,
‘Ergo dicetis eis, Dii qui coelum et terram non fecerunt
pereant de terra, de his quae sub coelo sunt.’ Nam hoc
tantum in Jeremia habet sermonem Chaldaeum, sicut omnes
Hebraei sciunt literati. Et certum est quod Hebraei et
Chaldaei eandem habent linguam, sed diversum idioma, sicut

1 Omitted in O.

make much
useof words

a linguis alienis, omnes sancti et philosophi Latini, qui ex- of foreign
. . . . . e 4 . Origin,
ponunt scientias, usi sunt caeteris copiose, et multiplicant nobis

The
Hebrew
alphabet.

74. OPERIS MAJORIS PARS TERTIA.

Gallicus et Picardus. Idioma enim est proprietas linguae
apud aliquam nationem determinatam, unde Hebraeus dicit
Eloim pro Deo vel Diis ; Chaldaeus dicit 7/oa, pro coelo vel
coelis. Pro on, Hebraeus dicit /o, Chaldaeus dicit /a, et sic
in aliis.

Tamen quod haec pericope scribatur sermone hic Hebraeo
et Chaldeo, ponetur alphabetum ! Hebraeum, ut facilius valeat
intelligi quaestio proposita, et primo scribuntur figurae
Hebraicae; secundo in linea superiori ponuntur nomina; et
supremo assignantur litterae quae literis Hebraicis corre-
spondent; ut literarum Hebraicarum sciamus virtutes et
potestatem sonorum, secundum quod quaedam sunt vocales
et quaedam consonantes.

’ b n 1 | n * ’ 3 x
iot eth heth zain vaf he dalet gimel beth aleph
i t h Z v e d g b a

"n b y D ) D b 5
pe pe ain samech nun mem lamet chaf chaf
P P S n m l ch ch

n v " P Y
taf shin ish koph .tsadik
t sh r k ts

Sunt autem sex vocales, viz. aleph, ain, he, heth, iot, vau ;
reliquae sunt consonantes: he et heth aspirantur, ut he in
principio, heth non solum in primo sed in fine, et generatur
in gutture, he in ore; aleph similiter in ore; ain in gutture ;
sed considerandum quod solum iot habet unum sonum sicut
i nostrum, et sit consonans et vocalis sicut apud nos j. Vau
vero, ut dicit Hieronymus in Hebraicis quaestionibus, habet
duplicem sonum, viz. v nostrum et o: reliqua vero quatuor
habent sonum quinque vocalium nostrarum, viz. a, e, i, o, et u;
sicut patet per Hieronymum in libro interpretationum. Et

! Neither this Hebrew alphabet nor the Greek alphabet which follows will
be found in Jebb's edition, which has moreover many other omissions, supplied
here from Jul This is the more strange as Jebb undoubtedly had this MS.
before him, and made use of it in the first part. He had the advantage of using

it a year or two before it was so damaged by fire as to render much of it
illegible.

LINGUARUM COGNITIO. 75

hanc diversitatem sonorum signant per puncta et tractus.
Nam si sub aleph trahatur linea sine puncto sic, €, vel cum
puncto, € sonatur a. Si vero duo puncta fiant jacentia sub
aleph e transverso 8, vel duo stantia M, vel tria in modum
trianguli €, vel quinque puncta hoc modo ¥, sonatur e. Si vero
tria puncta iaceant sub aleph ex obliquo descendentia sic ¥
sonatur u. Si vero unus punctus ponatur sub litera € sonatur
i. Si vero unus punctus fiat supra sonatur o, sic, &. Et ita
est de ain, et he, et heth, quae habent hos quinque sonos per
istorum signorum diversitatem. Et cum vaf sonatur v potest
esse signum trium punctorum ut dictum est sic ?, vel potest
poni unus punctus sic 3

Ideo oportet quod ad consonantes ponantur haec signa, ut
sciatur sonus vocalis syllabicandus cum consonante: ut si volo
designare ba, be, bi, bo, bu, scribam sic: 2 2 3 3 3. Et
habent alia signa per quae designant sonos consonantium
aliquando fortificari aliquando remitti. Unde quando tractus
ponitur super literam tunc remittitur: quando punctus in
ventre ponitur tunc fortificatur. Ut quando super Dalet
ponitur tractus sic 5 tunc debilem sonum reddit ut nostri z,
ut cum dico, adamas. Quando punctus in ventre ejus col-
locatur, sic, 3, tunc fortiter sonat, ut cum dico, dado....

Manifestus ergo et vilis est error omnium in hac parte
propter ignorantiam harum linguarum.

Aliud exemplum accipiam de Graeco et multa exempla The Greek
Graeca addentur in sequentibus. Sed volo hic ponere alpha- alphabet.
betum Graecum cum diphthongis quibus scribunt; multo
enim evidentius per hoc patebit quae dicenda sunt.

a b g d e Z i th i
alpha vita gemma delta e pente — zita ita — thita iota
a p y 3 € ¢ oH 0 t
k l m n x Oo P r S t
kappa labda mi ni xi omicron pi ro sima taf
K A ph oN é 0 T p c T

y ph ch ps
ypsilo phi chi psi omega
v ¢ x v w

76 QPERIS MAJORIS PARS TERTIA.

Sunt autem septem vocales quantum ad figuras diversas,
quum habent triplex i et duplex o; sed quatuor tantum
habent quantum ad sonum principalem, videlicet, a, e, i, o.
Diphthongus apud Graecos est conjunctio duarum vocalium.
Sonus unius vocalis habetur ut vocalis cum consonante. Et
finales literae in diphthongis sunt iota et ipsilo. Potest
igitur ipsilo consequi alpha sic, av, et tunc sonat quantum
a cum v consonante, quia sonus aliquantulum similis est sono
ipsius a cum f, et ideo vulgariter exemplificamus quod sonat
af. Et potest consequi e, sic ev, et tunc sonat quantum
e vocalis cum v consonante, quasi ef, ut dictum de alpha et
ipsilo. Vel potest consequi iota, sic w, et sonat quasi if, ut
dictum de aliis. Vel ipsilo potest consequi o micron, sic ov,
et tunc sonat u vocalem. Et sic solum habent Graeci sonum
hujus vocalis u. Quum autem iota consequitur alpha sic, at,
tunc sonat e, quasi e. Quum e, sic «, tunc sonat i per iota:
Si o, SiC ot, tunc sonat y per ypsilo. Et hi octo diphthongi
vocantur proprii. Et alii tres dicuntur improprii ; et fiunt
per subscriptionem hujus literae iota ad alpha, ita, et o mega,
sic, a, 7, *. Aliquando ponitur iota in linea, sicut in aliis
diphthongis sic as, mt, ev. Sed remanet sonus literae princi-
palis, scilicet ejus cui subscribitur iota. Nam cum subscri-
bitur a, quae est alpha, sonat a: quum vero 1, quae est ita,
sonat ita: si vero w, quae est o mega, sonat solum o mega. Et
his tribus diphthongis utuntur Graeci semper in dativo casu
primae declinationis.

... Et! licet exemplificare in praesenti loco de Jacob qui
cum obviaret Esau fratri suo veniens de Mesopotamia et
distaret dicit, Vidi faciem tuam quasi faciem Dei vidissem.
Quaerit Augustinus, qualiter poterat homo sanctus hominem
reprobatum comparare Deo? et solvit quod multipliciter Deus
in scriptura accipitur pro vero Deo, aliquando aliter. Et hoc
multis modis: sed ut LXX interpretes designaverunt quod
non loquebatur de vero Deo ideo apposuerunt articulum
Graecum ad nomen dei. Nam hoc est de proprietate articuli
ut veritatem rei designet. Sed hoc non apparet in Latino,

! There is evidently a hiatus here. The subject considered is now the use of
the article in Greek.

LINGUARUM COGNITIO. 77

quia Latini non habent articulum. Nam satis innotescit in
Gallico. Unde cum dicitur Parisius Li vets vent, iste arti-
culus li designat proprium et verum regem talis loci, quasi
regis Franciae. Et non sufficeret hoc ut denotaret adventum
regis Angliae. Nullus enim diceret de rege Angliae veniente
Parisius, Lz reis vent, sed adjungeret aliud dicens, Li rezs de
Engletere vent. Et ideo articulus solus sufficit ad veritatem
et proprietatem rei de qua est sermo designandam. Propter
quod Augustinus dicit quod Graecum hoc sit mpdcwmov cod,
quod in Graeco sonat prosopon theu ; cum articulo enim non
sic, prosopon tu theu, zpóewzorv ro) be08. Prosopon hic signi-
ficat vultum vel faciem. Theu est genitivus casus hujus
nominis theos quod est Deus, et tu est articulus genitivi.
Magna ergo necessitas est ut Latini sciant linguas propter
dicta sanctorum et caeterorum sapientum.

Sexta ratio est propter errorum falsitatum infinitarum The text
correctionem in textu tam theologiae quam philosophiae, non oa nas
solum in litera, sed in sensu. Quod autem correctio sit become

: os "TIT extremely
necessaria, probo per corruptionis magnitudinem. Et quo- conupt.
niam violentius et periculosius erratur in textu Dei quam
textu philosophiae, ideo convertam linguarum potestatem
ad corruptionem textus sacri, ut pateat necessitas earum,
propter! corruptionem infinitam exemplaris vulgati quod est
Parisiense. Et Deus novit quod nihil tam valida indigens
correptione potest Apostolicae Sedi praesentari sicut haec
corruptio infinita. Nam litera ubique in exemplari vulgato
falsa est, et si litera sit falsa vel dubia, tunc sensus literalis
et spiritualis falsitatem et dubitationem ineffabilem continebit,
quod volo nunc ostendere sine contradictione possibili. Nam
Augustinus contra Faustum dicit, ‘Si discordia in Latinis
codicibus est, recurrendum est ad antiquos et plures. Nam
antiqui praeponendi sunt novis, et plures paucioribus prae-

! From here to the end of the following sentence, supplied from Jul. The
corruption of the Biblical text is fully discussed in the Opus Minus, under the
head of the fifth sin of Theology (Brewer, pp. 330-349). See also the valuable
Memoir of Abbé Martin, La Vulgate Latine au xit siecle d'aprzs Roger Bacon.
Paris: Maisonneuve, 1888. The exemplar Parisiemse appears to have been
a text very carelessly compiled about 1230, and probably very carelessly copied,
to meet the demands of the multitude of students who were flocking to Paris.

Especially
the Paris
text.

Illustra-
tions.

48 OPERIS MAJORIS PARS TERTIA.

feruntur, Sed omnes antiquae Bibliae quae jacent in mona-
steriis, quae non sunt adhuc glossatae nec tactae, habent
veritatem translationis, quam sacrosancta a principio recepit
Romana Ecclesia, et jussit per omnes Ecclesias divulgari.

Sed hae in infinitum contradicunt exemplari Parisiensi:
igitur hoc exemplar magna indiget correctione per antiqua.
Caeterum Augustinus ibidem dicit, * Quod si dubitatio adhuc
remaneat in antiquis bibliis, recurrendum est ad linguas, scilicet
Hebraicam et Graecam' ; et hoc dicit secundo de doctrina
Christiana, et ostendit in exemplis. Et Hieronymus hoc
dicit ad Frecellam sororem et super Zachariam, et omnes
sancti concordant; sed antiquis bibliis concordant linguae
Graecorum et Hebraeorum contra exemplar Parisiense; igitur
oportet quod corrigatur. Caeterum Hieronymus dicit ad
Damascenum in hoc casu, * Ubi est diversitas, non est veritas
nota. Sed illi qui nituntur cum omni veritate quantum pos-
sint corrigere textum sunt duo ordines Praedicatorum et
Minorum. Jam de correctione formaverunt varias scripturas,
et plus quam una biblia contineat; contendunt ad invicem,
et contradicunt infinities, et non solum ordines ad invicem,
sed utriusque ordinis fratres sibi invicem contrariantes plus
quam ordines totales; nam omnis dominus alii contradicit,
et in eadem correctores sibi invicem succedentes mutuas
eradunt positiones cum infinito scandalo et confusione. Unde
cum ad viginti annos praedicatores redegerunt correctionem
in scripturis, jam venerunt alii, et novam ordinaverunt correc-
tionem, quae continet plus medietate unius bibliae; quantum
vix ponatur in tanta scriptura quantum Novum continet Testa-
mentum. Et quia vident se errasse in antiqua correctione,
jam fecerunt statuta quod nullus ei adhaereat; et tamen
secunda correctio propter horribilem sui quantitatem simul
cum veritatibus multis habet sine comparatione plures falsi-
tates quam prima correctio.

Quod autem dixi in universali, potest patere in exemplis ;
nam infinities accidit corruptio additione, subtractione, con-
junctione, divisione orationis, dictionis, syllabae, literae, diph-
thongi, aspirationis notae: et non solum litera, sed sensus
literalis et spiritualis mutantur; et non solum cadunt haec

LINGUARUM COGNITIO. 79

vitia circa unam orationem, sed circa multas, immo penes
folia quamplurima; et de singulis unum ponam exemplum
vel duo. Nam multi prologi superflui ponuntur in textu, cum
non sint prologi textus in quibus redditur ratio translationis
librorum quibus praeponuntur, sed sunt epistolae familiaribus
missae, ut epistola Hieronymi ad Paulinum, quae in capite
bibliae reputatur prologus et vocatur a vulgo, quae tamen in
libro epistolarum Jeronymi continetur ; vel respectu prologi in
commentarios et in originalia non in textum, sicut idem quod
praemittitur ante librum Ecclesiastis. Nam patet quod pro-
logus est ibi originalis, et patet ex sententia. Et sic est de
multis aliis, quae non sunt in bibliis antiquitatis. De una
oratione superflua est exemplum Deuteronomii 27. ‘ Male-
dictus qui dormit cum uxore proximi sui, et dicet omnis
populus Amen ;’ quoniam nec antiqui codices, nec Hebraeus,
nec Graecus habent versum hunc. De superfluitate dictionis
horribile est ac nefandum octavo Genesis, cum dicitur quod
* Corvus ad arcam non est reversus, et Hebraei et Hieronymus
in originali habent affrmativam. Et accepta est negatio a
paucis temporibus de alia translatione, scilicet LXX inter-
pretum, cujus falsitatem Hieronymus ostendit locis infinitis,
et jam a tempore Isidori et antea evacuata est. Nam ipse
dicit in libro de officiis quod generaliter omnes ecclesiae Latinae
utuntur translatione Hieronymi, pro eo quod veracior sit in
sententiis et clarior in verbis; excepto quod propter nimium
usum psallendi in ecclesia solius psalterii translatio scilicet
LXX interpretum remansit. Sed antiquitus Romana Ecclesia
jussit translationem hanc ubicunque haberi. Augustinus et
alii et ipsemet Hieronymus tempore suo usi sunt sicut Ecclesia
translationeantiqua. Et ideo Augustinum quum recitat textum
hunc decimo sexto de Civitate Dei et exponit oportuit quod
uteretur translatione quae fuit vulgata et recepta apud Latinos,
nec potuit aliud facere. Omnis vero glossator quiinfixit glossas
super textum accepit auctoritatem Augustini de Civitate Dei
et eam posuit infra textum, sed non mutavit eam nec intulit
negationem . . . inter caeteros hoc fecit. Et sic vulgatus est
error horribilis cum contradictorium pro contradictione pona-
tur Nam videtur in philosophia quod ejusdem libri est

80 OPERIS MAJORIS PARS TERTIA.

aliquando duplex et triplex translatio; et una habet diversum
vel aliquando contrarium alteri. Sed nullus est qui ausus est
translationem unam miscere cum alia.

Quod autem ecclesiastici habent in legendo negationem hoc
est de corruptione exemplaris apud studentes ad ecclesiasticos
derivatum, et de syllabae mutatione, et per consequens totius
dictionis. Et exemplum mirabile est de Joseph, qui dicitur
in exemplari vulgato venditus fuisse triginta argenteis propter
exemplum Domini, sed secundum antiquos codices et He-
braeum, et Graecum, et Arabicum, et Hieronymum in origi-
nali, et Josephum in antiquitatum libro, debent esse viginti
nontriginta, Et similiter in Psalterio ad syllabae mutationem
mutatur tota dictio cum infinito errore, cum dicitur, ‘ Sitivit
anima mea ad Deum fontem vivum. Nam cum ecclesia in
solo Psalterio utatur translatione LXX interpretum, Hierony-
mus correxit hanc translationem bis, et posuit forfem ubi
ponimus fozfem per errorem propter similitudinem dictionis,
et propter hoc quod in praecedenti versu fit mentio de fonte ;
sed ut dixi Hieronymus correxit fortem, et ita est in Hebraeis
bibliis et in psalteriis antiquis monasticis. Nam hoc diligenter
inspexi; et omnino certum est quod non est hic error vilissimus
propter similitudines praedictas.

. De literae mutatione est exemplum notabile primo Judicum,
cum dicitur in monte Ares, quod interpretatur testaceo, ut
penultima litera sit e non i, sed communiter habetur testacio
per i, ut sit nominativus casus, et idem quod testificatio a Zes/e ;
sed si deberet esse ablativus, derivatur a festa. Nam in omni-
bus antiquis bibliis est /fesfaceo per e, et in Graeco, et in
Hebraeo, ubi habetur hares, Hieronymus transtulit /esfass,
vel aliquid derivatum a “esta; nam Aares in Hebraeo festam
vel aliquid praedictorum significat in Latino. Unde Hiero-
nymus in sexto libro super Isaiam exponens idem verbum
decimo sexto capite, * His qui laetantur super muros cocti
lateris, dicit hares testam sive coctum laterem significat. Et
in decimo octavo libro super idem vicesimo quarto Isaiae,
* Erubescet luna, dicit quod hares testam sive coctum vel
ariditatem sonat. Quod vero tricesimo primo et tricesimo
secundo Jeremiae confunduntur haec nomina Ananeel et

LINGUARUM COGNITIO. 8r

Anameel per errorem, ut in litera indifferenter ponitur m in
penultima, est error magnus in mutatione unius literae. Nam
Hieronymus dicit in originali, quod Ananeel per n scriptum est
turris, per m est filius patruelis Jeremiae, et sic invenitur in
Hebraeo. De aspirationis nota exemplum primo ad Thessa-
lonicenses, cum dicitur, ad cujus ore, ut sit ablativus casus
hujus nominis os, orts, et non genitivus hujus nominis hora,
horae ; Scribitur enim in ablativo casu, et glossatur non a sancto,
sed a magistro sententiarum, qui glossavit epistolas ; sed sicut
defecit multipliciter in expositione propter ignorantiam Graeci,
ita fecit hic. Quum procul! dubio in Graeco, a quo sumptus
est genitivus hujus nominis Zoera, invenitur oras, et aspiratur
tam apud Graecum quam apud Latinum. Scilicet Os, orzs, non
aspiratur. Hoc enim verbum, Zora, est Graecum, licet Latino
nomine declinatur, sicut Domina: sed Graecus declinat sic,
hora, horas, hora, horam, hora. Unde nominativus et dativus,
et vocativus, similes sunt: accusativus in am, genitivus in as;
ablativum non habent Graeci. Et hoc in Graeco est horas,
sicut ego legi diligenter et omnibus possim probare qui sciunt
Graecum, et in Graeco invenitur aspiratio. Haec exempla
volui assumere ut quae probant quod necesse est linguas sciri
propter textus Latini corruptionem tam in theologia quam in
philosophia. Quomodo vere de corruptione plene probo et
in speciali per omnes corruptiones bibliae, in aliud tempus
differtur propter rei magnitudinem quae potest Vestrae Sancti-
tati praesentari, sed non nunc ut sufficiat, sed magis per alium
in sequentibus explicabo.

Septima ratio est, quia necesse est ut Latini sciant linguas
specialiter propter sensus falsitatem, etsi litera esset verissima.
Nam tam in theologia quam in philosophia necessariae sunt
interpretationes et praecipue in textu sacro, et in textu
medicinae et scientiarum secretarum ; quae nimis occultantur
propter ignorantiam interpretationum. Nam medici confusi
sunt propter malas interpretationes, quas vocant synonyma ;
non est autem eis possibile uti medicinis authenticis propter
errorum istorum synonymorum ignorantiam ; et ideo accidit

1 The following passage, down to the end of the paragraph, is omitted in
O. and D., and has been supplied from Jul.

VOL. I. G

Even when
the text is
correct it is
wrongly
interpreted.

82 OPERIS MAJORIS PARS TERTIA.

in manibus eorum infinitum periculum. Eodem modo est in
textu sacro; nam summa difficultas, quae est apud ipsum
sciendum est propter varietatem et obscuritatem infinitarum
interpretationum, et in exemplo familiari pro infinitis aliis
apparet. Vulgus enim hoc nomen Israel pro patriarcha inter-
pretatur virum videntem Deum. Et praevaluit hoc in usu
usque ad tempus Hieronymi, et etiam usque quo sua translatio
et sua expositio jussae sunt per omnes ecclesias divulgari.
Sed ipse dicit in originali quantae grandis auctoritatis sunt, et
eorum verbis nos opprimit qui Israel virum videntem Deum
interpretati sunt. Nos tamen magis consentimus Domino vel
Angelo qui illi hoc nomen imposuit quam auctoritati alicujus
saecularis eloquentiae. Et ideo probat egregie quod affirmat.
Nam illi qui sic interpretati sunt crediderunt quod hoc voca-
bulum significet idem conjunctum vel divisum, sicut respub-
lica apud nos. Sed hoc non est generaliter verum, immo in
pluribus habet instantiam in omni lingua. Nam apud Hebraeos
Is est vir, Ra videns, E/ Deus; et ideo crediderunt multi
quod hoc nomen patriarchae habet resolutionem in illa tria.
Sed Hieronymus reprobat per multa argumenta ; quatuor
enim possunt sumi e dictis suis a parte vocis, et quatuor vel
quinque a parterei. Nam in illis tribus nominibus aliae literae
sunt et plures quam in nomine patriarchae, et aliter ordine et
syllabicatae reperiuntur. Ex hoc ergo triplici argumento
sumto penes literas concluditur per Hieronymum quod id
significari non potest hinc inde; cum potentia significationis
ejusdem sumitur propter vocis identitatem, sed vocem et
literas nimis variari, quum in nomine patriarchae sunt hae
quinque literae per ordinem: Iod, Sin, Resh, Aleph, Lamet,
sicut ipsum Hebraeum hic positum declarat owl, Israel.
Sed in hoc triplici vocabulo hae octo literae habent hunc
ordinem, scilicet, Aleph, Iod, Sin, Resh, Aleph, He, Aleph,
Lamet, ut hic Hebraeum ostendit, 0NniDp^w, Et quarto argui
potest explicatione. Nam sicut puncta ostendunt nomen
proprium non retinet apud Hebraeum sonum praecisum
illorum vocabulorum. Nam secundum majorem quasi Iserael
sonatur in quatuor syllabis, tamen ibi vocabulorum sonus in
solis tribus syllabis coarctatur, quoniam punctum sub litera

LINGUARUM COGNITIO. 83

sonat i, et duo puncta sonant e, et linea cum puncto sub ea
sonat a. Sed argumenta fortiora trahuntur ex sensu vocis
secundum Hieronymum. Et hoc ostendit ipsum Hebraeum
hic scriptum hoc modo: ‘

DANDY DYToKToY notre npr oN *» op “HY “NY apy ND ipm
:5am

Et textus Graecus habet sic : ‘ quia invaluisti cum Domino [et
cum hominibus valebis !].'

Nam secundum Hieronymum et per textum Hebraeum, et
Graecum, et Latinum, et per Josephum patet quod Israel non
debet dici vir videns Deum, sed principalis vel princeps cum
Deo, quoniam in Hebraeo ad literam est sic: * Et dixit Deus
non vocabitur nomen tuum a modo Jacob, sed Israel ; quoniam
principalis vel princeps fuisti cum Deo, et cum hominibus
poteris principari, Et ideo dicit Hieronymus quod sensus
est, * Non vocabitur nomen tuum supplantator, hoc est Jacob,
sed vocabitur nomen tuum princeps cum Deo, hoc est Israel.
Quoniam ego princeps sum, sic tu, qui mecum luctari potuisti,
princeps vocaberis. Si autem mecum pugnare invaluisti,
quanto magis cum hominibus; hoc est, cum Esau, quem
formidare non debes??' Et quoque Latinum habet : * Quoniam
si contra Dominum fuisti, quanto magis contra homines
praevalebis?' Et Josephus primo antiquitatum libro, Israel
ideo appellatum dicit, quia contra Angelum steterit. Omnia
igitur haec, scilicet principari cum Deo, et invalescere, et
fortem esse, et stare cum Deo ut patet reducuntur ad
eundem sensum, sed diversis vocabulis interpretationum,
quorum nullum de virtute significationis suae potest elicere
visionem Dei. Et ideo vera interpretatio est Princeps cum
Deo. Et adhuc confirmat hoc Hieronymus per argumentum
derivationis; nam Sarith et ab Israel nomine derivatur, et
principem sonat. Unde Sara uxor Abrahae princeps dicitur,

! The words in brackets are omitted in the MSS.

2 See Jerome’s Liber Hebraicarum Quaestionum in Genesim. Jerome adds:
‘Quamvis igitur grandis auctoritatis sint, et eloquentiae ipsorum umbra nos
opprimat qui Israel virumt sive mentem videntem deum transtulerunt, nos magis

Scripturae et Angeli qui ipsum Israel vocavit auctoritate ducimur quam cujus-
libet eloquentiae saecularis."

G2

84 OPERIS MAJORIS PARS TERTIA.

ut dicit Hieronymus super septimum decimum capitulum
Geneseos ; quapropter si vulgus vel aliqui antiqui, ut Eusebius
Caesariensis in libro nominum Hebraeorum quem Hieronymus
in Latinum vertit, et alii, famosa abutentes interpretatione
dicunt Zsraz/ interpretari per virum videntem Deum, dicamus
cum Hieronymo!. Illud vero quod in libro Nominum inter-
pretatur Israel Vir videns Deum omnium pene sermone de-
cretum non tam vero quam violenter interpretatum videtur.
Et igitur per Eusebium in libro Nominum quem Hieronymus
transtulit in Latinum et per Ambrosium et alios forsitan
sanctos allegare si quis concedat quod recta hujus vocabuli,
Israel, expositio sit Vir videns Deum, dicendum est quod locuti
sunt secundam vulgatam expositionem, antequam veritas fuerit
patefacta quam postea beatus Hieronymus vera et perfecta
interpretatione Latinis revelavit, sicut in ejus libris continetur
et in glosa etiam habetur.

Et si forsan dicitur quod consuetudo vulgi theologorum
modernorum hanc interpretationem frequentet, patet responsio
per supradicta secundum Augustinum, et Cyprianum, et
Isidorum, et alios et per varias declarationes?. Nam secundum
eos manifestatae veritati cedat consuetudo, et relicto errore
vulgi sequamur veritatem. Et quod ex mera ignorantia venit
non debet allegari, sicut accidit in proposito, et praecipue
contra auctorem et doctorem sacrum non licet contraire, nisi _
pro se rationes sufficientes et auctoritates allegat. Et ad om-
nem affirmationem poterit quilibet Hebraicae peritos consulere,
et inveniet sententiam Hieronymi ratam et inconcussam *.
Summa vero necessitas remediorum falsitatis requiritur in his
interpretationibus propter formam Hebraei sermonis ; nam in
interpretationibus vulgatis quae in fine bibliae ponuntur, sunt
infinitae occasiones errorum : propter hoc erramus quod unum
vocabulum aestimatur simplex secundum normam Latinorum,
quod est multiplex apud Hebraeos: et abundantius erratur
quod tali vocabulo dantur variae interpretationes tanquam

! The remainder of the paragraph is omitted in O. and is supplied from
Jul.

! et... declarationes om. in O.

3 This sentence omitted in O.

LINGUARUM COGNITIO. 85

ejusdem sint vocabuli Hebraei, cum tamen quaelibet sit diversi,
eo quod vocabulum Hebraeum apud nos male consideratum in
scriptura una habet diversas literas apud Hebraeos, penes quos
recepit diversas interpretationes, secundum quod Hieronymus
ponit exemplum in epistola de mansionibus. Nam oportet si
ar scribatur per aleph, significat lumen ; si per atv, inimicum, si
per keth, foramen; per he, montem; dicit igitur quod vicesimo
Numerorum quidam interpretati sunt his modis quatuor ; sed
opiniones tres destruit, quia in Hebraeo scribitur hic per Ze,
et ideo solum montem in hoc loco designat. Sed in prae-
dicando et legendo theologi recurrunt ad omnes quatuor
expositiones in hoc vocabulo, et sic alias, igitur multipliciter
errant.

Est ultima ratio scientialis de necessitate linguarum, quod Latin
Grammatica in lingua Latinorum tracta est a Graeco et Byer’
Hebraeo. Nam litteras accepimus a Graecis, ut docet Pris- formed on

. 1 . . TP the model
cianus, et! totam rationem tractandi partes omnes Priscianus o£ Greek
accepit a Graecis et miscet Graecum in multa abundantia per M orew
omnes libros suos. Et ipsa vocabula linguae Latinae, et tam
theologica quam philosophica, ab alienis linguis pro parte
maxima sunt transfusa, quorum aliqua suspicantur Latini esse
alterius linguae; et de aliquibus non considerant quod ab
aliena lingua descendunt. Multa vero aestimantur quod sint
penitus Latina, cum tamen sint Graeca, vel Hebraea, vel
Chaldaea, seu Arabica, in quibus tam in pronunciatione quam
in scriptura et sensu accidit multiplex error Latinorum ; nec
est modicum errare in vocabulis, quia per consequens errabitur
in orationibus, deinde in argumentis, tandem in his quae
aestimantur concludi*. Nam Aristoteles dicit quod ‘qui
nominum ignari sunt, saepe paralogizantur.’ Et primum et
principale fundamentum doctrinae ponit Boethius in certa et
integra cognitione terminorum, sicut docet in libro de disci-
plina scholarium, atque nos experimur hoc in singulis scientiis.

Nam principalis difficultas? et utilitas est, quod homo sciat
intelligere vocabula quae dicuntur in scientia et prudenter

! The following six lines supplied by Jul., om. in O.
3 The last six words om. in O.
* difficultas et om. in O.

86 OPERIS MAJORIS PARS TERTIA.

sine errore proferre; quando veraciter scit hoc, potest per
scriptum perficere sine ulteriori doctrina si sit diligens in
studio. Nam textus scientiarum sunt ei plani, quando noverit
proprie ac certe intelligere et interpretari ; et sine difficultate
potest quemlibet sapientem intelligere, et cum quolibet suf-
ficienter conferre, et a quolibet si necesse est edoceri. Et
Aristoteles dicit in primo coeli et mundi, quod parvus error in
principio est magnus in principiatis ; qui enim in fundamentis
errat, necesse est ei in errore totum aedificium cumulare.
Aestimamus igitur linguam nostram Latinis dictionibus esse
compositam, et pauca esse vocabula aliarum linguarum, cum
tamen quae communiter utuntur sunt de linguis alienis, ut
domus, scyphus, clericus, laicus, diabolus, Satanas, ego, pater,
mater, ambo, leo, ago, malum !, et sic de infinitis, quae vix in
magno volumine possunt congregari; praecipue si scrutemur
vocabula singularum scientiarum, et maxime theologiae et
medicinae; quo volumine nihil esset utilius, si vocabulorum
omnium recta scriptura ac pronunciatio debita cum fideli
derivatione et recta interpretatione probarentur?. Sed nunc in
his quatuor erratur in magnum totius detrimentum sapientiae,
qucd paucis exemplis potest intelligi. Nos enim non con-
sideramus ordinem linguarum, nec quod prior lingua non
recepit interpretationem posterioris, nec quod diversae linguae
in eo quo diversae sunt non se mutuo exponunt: sed quod
dicit Hieronymus, et maxime prior ex posteriori non potest
originem habere, ut certum est omni homini rationem habenti ;
unde Graecum non oritur ex Latino, nec Hebraeum ex Graeco,
et non debet Hebraeum capere etymologiam ex Graeco, nec
Graecum ex Latino: unde Hieronymus dicit contra quosdam
in dicto loco memorato, quod Sara non Graecam sed Hebrai-
cam debet habere rationem, Hebraea enim est. Et saepius
dicit quod Lenaeus a Aj, id est, /acus, dicitur, non a /erio,
quia Graecum non potest Latinam etymologiam recipere; sed
quod hcc facimus graviter et indifferenter. Et nos contra;
nam dicimus quod amen, licet sit Hebraeum, dicitur ab a,
quod est szze, et mene Graeco, quod est defectus. Et cum

1 The last nine examples om. in O.
2 J.'s reading, praeliarentur, is unintelligible. Jul. has probarentur.

LINGUARUM COGNITIO. 87

parasceue sit Graecum, dicimus quod derivatur a faro, paras,
et coena, coenae, quae sunt Latina. Et! dicunt quod dogma
dicitur a doceo, et sic de infinitis quae omnia falsa sunt. Et non
solum vulgus Latinorum sed auctores in his oberrant,et Hugo
et ejus sectatores qui aestimant judtleum a jubilo derivari,
cum tamen judileum debet esse Ilebraeum. JFudilo est
Latinum; sed non debet dici Fudsleum ut litera 7 sit in
secunda syllaba sicut in Fubslo. Debet 7 esse e litera ut
dicatur jubcleus, sicut vult Isidorus et Papias, et omnes libri
antiqui sic habent. Nam dicitur a jobel quod est Hebraeum.
Ita aestimamus quod multa vocabula quae sunt in usu
Latinorum debent exponi per alias linguas.

Assueti autem in hoc credimus quod longe plura, quam Man
veritas sit, capiunt etymologiam aliunde. Nam sola illa voca- [arin of
bula, quae oriuntur et derivantur ex Graeco et Hebraeo, origin
debent habere interpretationes per linguas illas. Ea enim, thought to
quae pure Latina sunt, non possunt habere expositionem nisi ¢ foreign.
per vocabula Latina. Nam purum Latinum est omnino
diversum ab omni lingua, et ideo non potest habere inter-
pretationem aliunde: sed Latini non hoc considerant: imo
indifferenter pura Latina per alias linguas interpretantur.
Unde multis modis hoc verbum coe/um quod est pure
Latinum Graece interpretantur dicentes quod coe/um dicitur
quasi casa helzos, i.e. domus solis, nam sol dicitur helios;
sed incongrue dicunt et falso. Debent enim dicere, Casa
heliu, cum helios sit nominativi casus, heliu genitivi. Deinde
falso dicitur. Nam sicut Varro peritissimus Latinorum et
Plinius in prologo plene confirmat, coelum dicitur a coelo,
coelas, quod est scu/fo, zs, quia stellis sculptum est et orna-
tum. Quod etiam est lege scripturae vocabulorum. Nam
coelo, coelas, pro sculpo, sculpis, scribitur per diphthongum ae
in omnibus libris antiquis. Et sic hoc verbum coelum apud
omnes codices antiquos scribitur per diphthongum eandem.

Et ideo derivatur a coelo quod est sculpo. Etex hoc sequitur
quod non derivatur a celo, celas quod est occulto, occultas,
sicut illi qui huic nomini dant etymologiam absurdam dicentes
sic dici quod occultatur et elongatur a nobis, vili errore sicut

! The following passage, to the end of the paragraph, supplied from Jul.

Greek
diphthongs
misunder-
stood.

88 OPERIS MAJORIS PARS TERTIA.

priores decepti. Similiter hoc nomen ave, quod est pure
Latinum, Graece exponunt, dicentes quod dicitur ab a, quod
est sine, et ve, quasi size ve: sed hoc fieri non debet, quia hoc
vocabulum non sumitur a Graeco vocabulo cognatae signi-
ficationis. Nam chacre in Graeco signat ave in Latino, sed
haec duo non concordant. Hic ergo est unus modus quo in
infinitis Graecis vocabulis errat Latinus.

Alius modus est, quod in Graecis vocabulis non intelligimus
eorum scripturam, quam habent multipliciter variatam ; quia
vocabula consimilia in sono distinguunt in significato: unde
habent triplex et duplex o, et duplex t, ac p et c; et habent
undecim diphthongos, et multa alia, ut sic varietatem suorum
vocabulorum in significando designent. Nam cezos quod est
inanis, a quo cenodoxia, i.e. inanis gloria, de quo Deutero-
nomi septimo, per e breve scribitur. Et cezos quod est novus,
a quo encenia, i. e. innovationes, ut nova festa et dedicationes,
de quo Johannes decimo, et scribitur per ae diphthongum, sic
caenos. Cenos vero quod communis, a quo cenobium et ept-
cenium, scribitur per oi diphthongum, quam Latinus proferat
e, sed deberet proferri i, ut diceret czzos, unde ab hoc dicitur
cinomia, quod est secundum Hieronymum in correctione
Psalterii, communis vel omnimoda musca. Unde Papias dicit
quod scribitur per diphthongum in prima syllaba, sic coznomza.
Et hoc manifestum est in Graeco Psalterio. Et cynos, canis, qui
scribitur per y Graecum, unde cysoria, i.e. musca canina, de qua
Exodi octavo, et xezos per x, quod est peregrinus, a quo xenza,
quae sunt munera seu dona, de quibus liber Machabaeorum,
et secundus Ecclesiastici. Et schenos per sche est funis, a quo
schenobates, qui graditur in fune et super funem. Scena est
umbra, vel tabernaculum, a quo scenopegia, i.e. fixio tabernaculi,
et scenofactoria ars est in qua Paulus Apostolus laborabat.
Cum igitur derivativa istorum vocabulorum et composita
sic variantur in significatis, licet sint similia in sermone
et sono, manifestum est quod non est possibile evadere in
sensu literali sine errore, qui non advertit scripturam hujus-
modi. Unde magni viri et famosi expositores aliquando
decepti sunt, sicut Rabanus, qui dicit quod scenofactorta ars
docet facere funes, quia aestimabat quod schenos, quod est

LINGUARUM COGNITIO. 89

funis, esset idem a quo nomen derivatur. Sed Beda docet
contrarium volens quod a scena derivatur, et hoc manifestum
est per scripturam vocabuli. Scilicet! ignoratione Actuum in
Graeco textu scribitur vocabulum penultima syllaba sine
aspiratione et per vocalem quae vocatur z/a, quod est i longum,
et sic scribitur sceza pro /abersaculo; sed schenos pro fune
scribitur per oe. diphthongum et per aspirationem. Et sic
contentio est inter doctores de cinomia et de caeteris prae-
dictis. Unde de xenits credit vulgus quod nihil sit, et corri-
gunt in textu Latino dicentes exenia. Sed in Bibliis antiquis
non est sic, nec in Graeco; nec potest sic dici secundum
Graecam grammaticam quia oporteret quod ex praepositio
Graeca poneretur primo quod non est possibile, quia vocabu-
lum incipit per consonantem sicut patet per grammaticam
Graecam. Per hunc modum accidit error quasi in infinitis
vocabulis.

Tertius modus est, quod licet Latini multum communicant Differences
cum Graecis, tamen in aliquibus differant, quod non obser- of gender
vatur ut oportet. Nam cum dicat Priscianus et omnes Latini mination
sciunt, quod nomen arboris apud Latinos est foeminini generis no Latin,
et terminatur in us, et nomen fructus est neutrius, et terminatur
in um ; ut fomus, pomum ; pyrus, byrum ; et sic de aliis, aesti-
matur quod hoc sit intelligendum de omnibus vocabulis, quae
sunt in usu Latinorum, ut de malo et de amygdalo et aliis.

Nam regula Latinorum est solum intelligenda de Latinis
dictionibus, non de Graecis nec aliis. Et quod hoc sit verum
patet primo quod Latinus dat regulas de Latinis, et non
pertinet ad eum ordinare regulas de linguis alienis. Deinde
Priscianus dicit quod omne Graecum cadens in usum Lati-
norum retinet genus suum quod habuit apud Graecos. Et
ideo cum malum pro arbore sit Graecum et neutrius generis, est
sic apud usum Latinorum. Et ideo tam pro fructu quam pro
arbore est ejusdem generis et ejusdem terminationis. Et hoc
probatur per Virgilium qui dicit in Georgicis mala tnsifa arbores
quae inservantur in fructus. Et super hoc Servius commentator
qui fuit major quam Priscianus, cujus auctoritate saepius utitur,
dicit, quod hoc, omme nomen arboris est foeminint generis,

! This sentence, and the three following, have been corrected from Jul.

9o OPERIS MAJORIS PARS TERTIA.

intelligendum est de Latinis, non de Graecis. Et certum est
quod malum est Graecum, licet secundum morem Latinorum
aliquantulum sit aliter prolatum. Nulla dictio apud Graecos
terminatur in m literam, sed in n; et Latini omnes consue-
verunt terminare dictiones suas in m, ut scamnum, lignum,
pomum, et hujusmodi. Idem multoties Latinus mutat ali-
quam vocalem in vocabulo Graeco, ut ubi dicit Graecus
grammaticos, Latinus dicit grammaticus, et sic multipliciter ;
et sic est hic. Nam Graecus dicit melon pro arbore et fructu,
Latinus mutat e in a, sicut n in m,et dicit malum. Sed ista
mutatio non mutat vocabulum secundum substantiam et
secundum radicem, quia acceptum est a Graeco, licet aliter
prolatum, et hoc omnes auctores testantur. Caeterum per
textum Latinorum in antiquis libris, tam de theologia, quam
de philosophia, invenitur semper ma/um pro arbore. Nam in
primo Joel invenitur communiter apud omnes Biblias malum
pro arbore, etiam usque correctores dimiserunt illud in novis
Bibliis: et quarto Canticorum ubi dicitur, ‘szcut malum inter
ligna sylvarum' ; sic exponit Beda in originali, et duodecimo.
Ecclesiastis est amygdalum et malogranatum in singulari et
malogranata in plurali, quod non fieret, si malum non esset
neutrius generis. Mutantur igitur hujusmodi vocabula se-
cundum formam Latinorum. Et praecipue mirum est quod
in aliquo correctores dimittunt antiquam literam et in alio
abradunt, quod est omnino contra rationem.
Mistakesin Similiter in pronunciatione literarum Graecarum multum
prosody erratur, propter hoc, quod Latini volunt formam suam servare
neglect in Graecis dictionibus; et in hoc peccatur maxime, cum
differences, Omnes Poetae et omnes antiqui Latini proferebant secundum
primam institutionem. Sed nos moderni violavimus hoc
multis modis contra usum omnium antiquorum ; verbi gratia,
cum Priscianus dicit, quod nomina possessiva desinentia in
nus longantur et acuuntur in penultima, ut Bovinus, Latinus,
equinus, intelligenda est regula de Latinis dictionibus, non de
Graecis, propter aliquas rationes tactas prius. Et ideo cum
Adamantinum, Byssinum, Chrystallinum, Hyacinthinum,
Bombycinum, Onychinum, Amethystinum, Smaragdinum,
et hujus modi sunt Graeca, debent breviari in penultima,

LINGUARUM COGNITIO. 91

sicut Graeci faciunt. Praeterea nec ista sunt possessiva. Nam
duae tantum sunt terminationes possessivorum apud Graecos,
scilicet in cos, ut Grammaticos; et in nios, ut Uranios,
i.e. coelestis. Caeterum omnes Poetae Latini breviant penul-
timam, et ideo non est poetica licentia quia communiter fit
ab omnibus et ubicunque: quod enim raro fit et ex causa,
licentiae poeticae ascribendum est, sed non quod fit semper et
communiter. Unde Juvenalis, ‘amethystina convenit ilh.
Et idem dicit, ‘Grandia tolluntur crystallina’; penultimam
corripiendo, sicut omnes faciunt, et nullus facit contrarium:
igitur non est poetica licentia sed ex lege naturali. Et cum
secundo Regum septimo decimo capitulo habeatur, ' siccaret
ptisanas, expositio famosa vocabulorum Bibliae, cui omnes
adhaerent, nititur probare quod media sit producta ; et auctor
illius expositionis defendit se per versum Horatii,

‘Tu cessas, agedum sume hoc ptisanarium orizae.'
Sed error est, nam sicut per omnes auctores probatur, nun-
quam abscinditur in metro, nisi una syllaba in fine dictionis ;
et ideo sic debet scandi, ‘ Ptisanari’ orizae, ut haec syllaba sa
brevietur, et haec syllaba za longetur. Et hoc patet aliter,
quia in omnibus derivativus a ante 7zw» longatur; ut con-
trarium, armarium et hujusmodi infinita quae observantur in
hac scansione, sed non modo vulgato cum dicitur ptisanar’
orizae ut duae syllabae auferantur, quia ibi breviatur haec
syllaba za, ut patet. Ergo oportet quod media hujus dic-
tionis pisana sit brevis. Praeterea erratur in scriptura, nam
in novis Bibliis habetur “fsanas quod nihil est, et debet
P anteponi, sicut in hoc nomine Ptolemaeus. Etin hoc modo
erratur infinities in aliis vocabulis, et tam violenter mutamus
veras accidentium causas et regulas, quod non est remedium
per magistros. Quoniam consuetudo cogit omnes male pro-
ferre, ut in uno patet exemplo pro mille millibus. Butyrum
habet penultimam correptam apud auctores ; unde Statius,

*Lac tenerum cum melle bibit, butyrumque comedit.'

Et Macer in libro herbarum :

‘Cum butyro modicoque oleo decocta tumorem."
Et Graecus sic breviat. Atque componentia ipsum requirunt
hoc. Nam componitur de Zyros et bos, et tyros est breve in

Importance
to the
Church of
linguistic
studies,

(1) for ex-
planation
of liturgy,

92 OPERIS MAJORIS PARS TERTIA.

prima syllaba et est lacticinium, quod a bove venit. Sed
longe sunt majores errores apud multos, et ignorantia veritatis
apud omnes circa accentus. Sed major disputatio requiritur
quam praesens scriptura concedit !.

? Cum jam manifestavi quomodo cognitio linguarum sit
necessaria Latinis propter studium sapientiae absolutum nunc
volo declarare quomodo oportet eum haberi propter sapientiam
comparatam ad Dei Ecclesiam et rem publicam fidelium et
confusionem infidelium et eorum reprobationem qui converti
non possunt. Nam quadrupliciter in eis necessaria est eccle-
siae, primo videlicet propter officium divinum, eo quod Graecis
et Hebraeis et Chaldaeis utuntur in officio sicut in Scriptura.
Et plura accipimus quorum Scriptura non facit usum, ut
agios, atheos, athanatos, iskiros, ymas, eleison, et hujusmodi.
Cum ergo ignoramus scripturam et pronuntiationem rectam et
sensum multum deficimus a veritate et devotione psallendi.
Nam loquimur sicut pica et psittacus et talia bruta animalia
quae voces emittunt humanas, sed nec recte proferuntur nec
intelliguntur quae dicuntur. Quum enim dicimus aéleluta
infinities in anno, deceret multum et expediret ut omnes per
totam ecclesiam psallentes scirent quid sint duo vocabula,
scilicet allelu et ia. Nam allelu significat idem quod Laudate,
et za denotat Dominum, quum est unum de decem nominibus
Dei, sicut Hieronymus scribit ad Marcellum ; et praecipue
significat znvistbilem, et Deus est maxime invisibilis. Verum
non quodcunque invisibile, sed Deum designat. Et cum in
omni Missa dicimus Osanna, haec dictio est composita ex
corrupto et integro. Nam ut Hieronymus dicit ad Damasum
Papam, Os est idem quod Salvifica, et az est indicatio depre-
cantis, secundum quod per aleph scribitur syllaba prima; unde
significat idem quod, sa/va deprecor. Nam aliter scribitur
prima syllaba per e literam, et tunc significat conjunctionem
quod Latinus sermo non habet. Et cum gloriosam Virginem

! The subject of accentuation is treated with some fullness in the Greek
grammar by Bacon preserved in Corpus Christi College, Oxford ; and also in
Compendium Studi, cap. xi (Brewer, pp. 508-514).

* All that follows, to the end of Part III, is omitted in Jebb's edition, and
has been restored here from Jul.

LINGUARUM COGNITIO. 93

salutamus, dicentes, Ave Maria gratia plena Dominus tecum,
multum esset necessarium ad intellectum veracem et intellec-
tum ut quilibet litteratus sciret sensum vocabuli; et praecipue
cum multi aestimantes scire in hoc oberrent. Mirum quidem
vocabulum est Maron, et significat dominum a quo venit
Maria, et idem est quod dominatrix, ut dicit Hieronymus in
interpretationibus. Et hoc valde competit beatissimae Virgini,
quae dominatur supra omnem immunditiam peccati expellen-
dam a nobis et diabolicae fraudis et nequitiae, quia ipsa est
terribilis peccato et de moribus sicut castrorum acies ordinata.
Haec vero interpretatio est peritissima et sine calumnia.
Dicit autem Hieronymus quod multi aestimaverunt interpretari
.. .. quod ipse non recipit et dicit quod debet dici Stella
Maris, vel amarum mare secundum Hebraicam interpreta-
tionem. Et vere dicitur Stella Maris ut nos dirigat ad
portum salutis, et Amarum Mare quia in omni paupertate et
amaritudine temporali vixit in hoc mundo, et ipsius animam
pertransivit gladio in morte Filii, ut sit nobis exemplum omnis
patientiae et consolatrix in omnibus adversitatibus hujus
mundi. Necesse est ergo nobis in omnibus psalmodiis et
obsecrationibus nostris ut sciamus recte proponere et intelli-
gere quaecunque et juxta verborum proprietatem devote
nostras petitiones sonare, ut quod recte et devote petimus,
Dei et sanctorum pietatem et merita ecclesiae consequamur.
Sed hoc non possumus facere sine notitia vocabulorum alterius
linguae. Et ideo multum expedit et necessarium est ut hoc
sciamus.

Secunda causa est quod Ecclesiae necessaria est cognitio (2) for ex-
linguarum propter sacramenta et consecrationes. Nam Planation
intentio necessaria est sacramento, ut theologi sciunt. Et ments and
intentionem praecedit intellectus et notitia rei faciendae. ion,
Et ideo per omnem modum expediret Ecclesiae ut sacerdotes
et praelati omnia vocabula sacrificiorum et sacramentorum et
consecrationum scirent recte proferre et intelligere, sicut
a principio sacri et summi pontifices et omnes sancti
patres et institutores ordinum ecclesiasticorum constituerunt
et sciverunt qualiter in verbis et sensibus mysteria Dei con-
sisterent. Unde incipiendo a primis ut ab exorcismis et

94. OPERIS MAJORIS PARS TERTIA.

catharizationibus, et sic per baptismum et omnia sacramenta
discurrendo, non solum decens sed expediens et necessaria est
ut ab eis qui ministrant sacramenta sciretur recta pronuntiatio
et debitus intellectus, quatenus in nullo derogaretur sacramento.
Sed modo per universam Ecclesiam innumerabiles proferunt
verba instituta ab Ecclesia et nesciunt quod dicunt, nec ver-
borum servant rectam pronuntiationem, quod esse non potest
sine injuria sacramenti. Utinam fiat cum plena efficacia
effectus sacramentalis! Et cum Ecclesia statuit hoc ex certa
notitia, et omnes patres antiqui sciverunt rectam pronuntia-
tionem et sensum vocabulorum secundum quod competebat
sacramentis, nos nullam habemus excusationem ; sed turpis et
vilis ignorantia est nulla tergiversatione excusanda. Et quum
in consecrationibus ecclesiarum cuspide baculi pastoralis
fuerint factae literae alterius linguae secundum ordinem
alphabeti, certum est quod paucissimi faciunt figuras debitas
secundum quod a sanctis patribus et Ecclesia fuerint institutae,
propter ignorantiam characterarum alterius linguae. Et
praecipue in hoc erratur quod tres figurae sunt quae nullo
modo scribi deberent in Graeco alphabeto. Nam procul
dubio figurae quae vocantur episemon, koppa, sanpi non sunt
de alphabeto Graecorum, nec Graecis inservierunt in ordine
literarum ; sed sunt figurae et notae numerorum. Modo
vero Latini non considerant quod Graeci numerant per literas
alphabeti, et quod ad complendam computationem interserunt
tres figuras prius nominatas, scilicet has s, 5, ?. Sed hoc
faciunt quum numerant, non quasi nominetur figura pro
literis et scriptis. Unde in scribendo nunquam utuntur his
tribus figuris nec ponunt eas in ordine alphabeti. Sed
Ecclesia instituit quod literae solae alphabeti scriberentur in
consecratione ecclesiae, et deceret uti literis non notis nume-
rorum. Quapropter valde indignum est quod per universam
Ecclesiam fiat hujus erronea scriptura.

Et vile est quod haec nomina IHC, XPC, scribuntur per
literas Graecas et aestimatur quod sunt Latinae, aut nescitur
cujus modi sunt Graecae. Nam procul dubio in hoc nomine
IHC prima est iota quae valet i nostrum; secunda est ita,
quae valet elongum. Tertia est sima quae valet s nostrum.

LINGUARUM COGNITIO. 95

Et in hoc nomine XPC, prima est chi quae valet ch aspiratum.
Secunda est ro quae valet r nostrum. Tertia est sima.

Tertia vero causa est de notitia linguarum Ecclesiae Dei (3) for due
necessaria, Nam multi Graeci et Chaldaei et Armeni et el forem
Syrii et Arabes et aliarum linguarum nationes subjiciuntur Churches,
Ecclesiae Latinorum, cum quibus multa habet ordinare et
ilis varia mandare. Sed non possunt haec recte pertractari
nec ut oportet utiliter nisi Latini sciant linguas earum. Cujus
signum est quod omnes dictae nationes vacillant fide et
moribus, et ordines ecclesiae salutares per sincerum non
recipiunt in lingua materna. Unde accidit quod apud
tales nationes sunt mali Christiani et ecclesia non regitur ut
oportet.

Quarta causa est propter totius Ecclesiae doctrinam a (4) for
principio usque in finem dierum. Nam dicit Dominus, Iota doutine,
unum aut unum apex non peribit a lege donec omnia fiant.

Et ideo docetur publice in libro de senibus Scripturarum quod
singulae literae alphabeti Graeci figurabant super populum
antiquum, et oportet numerum centenariorum annorum quibus
decurrebat status illius gentis juxta singulas aetates et saecula
[computare] secundum spirituales vires et potestates literarum.
Et deinde . . . . ecclesiae Latinae per necessitates literarum
Latinarum. Et consimilis est consideratio super ecclesia
Graeca per literas sui alphabeti. Et in hujus consideratione
mirabili tempora ponuntur secundum omnes status Ecclesiae
usque in finem, et per quot centenarios annos durabit quae-
libet immutatio quae accidet Ecclesiae in decursu suo, cui si
prophetias et testimonia digna necteremus possemus per Dei
gratiam praesentire utiliter ea quae Ecclesia recipiet tam in
prosperis quam in adversis. Et ideo nil utilius esset hujus veri-
tatis literarum consideratione et aliis considerationibus simi-
libus. Nam ad certificationem harum rerum multae materiae
requiruntur, quarum saltem una non ignobilis est per literas
linguarum diversarum. Et nequeo satis admirari cum videatur
inexpertis habere debile fundamentum, scilicet literas alpha-
beti quae sunt prima puerorum rudimenta, sed secundum
documentum apostoli munera sunt magis necessaria et majori
honore circumdanda. Et sicut Deus elegit infirma ut fortia

(5) for

commerce

96 OPERIS MAJORIS PARS TERTIA.

quaecumque confundat, ita in rebus quas reputamus minimas
posuit majestas majora quam possit intelligere mens humana.
Et sic est in his literis triplicis alphabeti. Unde non sine
maxima causa in epitaphio Domini scriptum est Hebraice
Graece Latine, ut doceremur quod Ecclesia cruce Domini
redempta habeat considerare veritates literarum triplicis,
alphabeti; praecipue cum Ecclesia incepit in Hebraeis et
profecit in Graecis et consummata est in Latinis.

Quinto multum est necessaria reipublicae Latinorum diri-

with foreign £endae cognitio linguarum propter tria. Unum est com-

nations.

meatio utilitatum necessariarum et mercatis et negotiis sine
quibus Latini esse non possunt, quia medicina et omnia pre-
tiosa recipiuntur ab aliis nationibus. Et inde oritur magnum
malum Latinis et fraus eis infertur infinita quia linguas
ignorant alienas, licet per interpretationes eloquantur. Nam
hae raro sufficiunt.

Ex his ergo quae circa linguas dicta sunt patens est quod
Latini magnum habent sapientiae detrimentum propter lin-
guarum ignorantiam. Unde ex hac parte gloriari non possunt
de sapientia; immo multum inglorii et cum vario sapientiae
damno languent.

PARS QUARTA

HUJUS PERSUASIONIS.

In qua ostenditur potestas mathematicae in scientiis, et
rebus, et occupationibus hujus mundi.

DISTINCTIO PRIMA,

HABENS CAPITULA TRIA.

CAPITULUM I.

Manifestato quod multae praeclarae radices sapientiae The key
dependent ex potestate linguarum, per quas est introitus in greater
sapientiam Latinorum, nunc volo revolvere fundamenta ejus- sciences is
dem sapientiae penes scientias magnas, in quibus est specialis mathe-
potestas respectu caeterarum scientiarum et rerum hujus
mundi. Et sunt quatuor scientiae magnae, sine quibus caeterae
scientiae sciri non possunt, nec rerum notitia haberi: quibus
scitis, potest quilibet gloriose proficere in sapientiae potestate
sine difficultate et labore, non solum in scientiis humanis,
sed divina. Et cujuslibet istarum tangetur virtus non solum
propter sapientiam absolute, sed respectu caeterorum prae-
dictorum. Et harum scientiarum porta et clavis est mathe-
matica, quam sancti a principio mundi invenerunt, ut ostendam,
et quae semper fuit in usu omnium sanctorum et sapientum
prae omnibus aliis scientiis. Cujus negligentia jam per triginta
vel quadraginta annos destruxit totum studium Latinorum.
Quoniam qui ignorat eam non potest scire caeteras scientias
nec res hujus mundi, ut probabo. Et, quod pejus est, homines
eam ignorantes non percipiunt suam ignorantiam, et ideo
remedium non quaerunt. Ac per contrarium hujus scientiae
notitia praeparat animum et elevat ad omnium certificatam
VOL. I. H

Authorities
for this
view.

Boethius.

98 OPERIS MAJORIS PARS QUARTA.

'
cognitionem, ut si radices sapientiae datas circa illam cognoscat,
et eas radices recte applicet ad caeterarum scientiarum et rerum
cognitiones, tunc omnia sequentia poterit scire sine errore et
sine dubitatione, ac de facili et potenter. Sine his enim nec
praecedentia nec consequentia sciri possunt ; unde perficiunt
priora et regulant, sicut finis ea quae sunt ad finem, et dis-
ponunt et aperiunt viam ad sequentia. Ad quod nunc intendo
innuere per auctoritatem et rationem ; et primo in scientiis
humanis et rebus istius mundi, deinde in divina, et ultimo
prout ad Ecclesiam et caetera tria comparantur.

CAPITULUM II.

In cuo probatur per auctoritatem, quod omnis scientia
requirit mathematicam.

Per auctoritatem quidem sic procedo. Dicit Boetius! in
secundo prologo Arithmeticae, quod * mathematicae quatuor
partibus si careat inquisitor, verum minime invenire possit.'
Et iterum ‘Sine hac quidem speculatione veritatis nulli recte
sapiendum est. Et adhuc dicit ‘ Qui spernit has semitas sapien-
tiae, ei denuncio non recte philosophandum. Et iterum,
* Constat quisquis haec praetermiserit, omnis sapientiae perdi-
disse doctrinam. Quod etiam omnium virorum authenticorum
sententia confirmat dicens, *Inter omnes priscae auctoritatis
viros, qui Pythagora duce puriore mentis ratione viguerunt,
constare manifestum est, haud quemquam in philosophiae disci-
plinis ad cumulum perfectionis evadere, nisi cui talis prudentiae
nobilitas quodam quasiquadrivio investigatur.’ Etin particulari
ostenditur per Ptolemaeum et ipsum Boetium ?. Cum enim

! Boethius, as appears from a letter addressed to him by Theodoric which
is quoted by Cassiodorus, made Latin translations of many of the Greek mathe-
maticians ; Euclid, Nicomachus, Archimedes, Ptolemy, &c. These, however,
have disappeared ; the two books De Institutione Arithmetica, and the five
books De Musica, with a few doubtful fragments of his Geometry, alone remain.
The expression quadrivium, as applied to the four sciences of arithmetic,
music, geometry, and astronomy, seems to have originated with Boethius.

* In the introduction to the Almagest Ptolemy remarks that mathematic holds
an intermediate place between the invisible and incomprehensible object of

MATHEMATICAE IN PHYSICIS UTILITAS. 99

sint modi tres philosophiae essentiales, ut dicit Aristoteles

in sexto Metaphysicae, mathematicus, naturalis, et divinus, non
parum valet mathematicus ad reliquorum duorum modorum
scientiae comprehensionem, ut docet Ptolemaeus in capitulo Ptolemy.
primo Almagesti quod et ipse ibidem ostendit. Et cum divinus

sit dupliciter, ut patet ex primo Metaphysicae, scilicet Philoso-
phia prima, quae Deum esse ostendit, cujus proprietates excelsas
investigat, et civilis scientia quae cultum divinum statuit,
multaque de eo secundum possibilitatem hominis exponit, ad
utramque istarum multum valere mathematicam idem Ptole-
meus asserit et declarat. Unde Boetius in fine arithmeticae
mathematicas medietates asserit in rebus civilibus inveniri.
Dicit enim quod ' arithmetica medietas reipublicae comparatur
quae a paucis regitur, idcirco quod in minoribus ejus terminis
major proportio fit, musicam vero medietatem optimatum
dicit esse rempublicam. eo quod in majoribus terminis major
proportionalitas invenitur. Geometrica medietas popularis
quodammodo exaequatae civitatis est : namque vel in minoribus

vel in majoribus aequali omnium proportionalitate componun-

tur. Est enim inter omnes paritas quaedam medietatis aequum

jus in proportionibus conservantis.’ Et quod sine hisrespublica

regi non potest, Aristoteles et ejus expositores in moralibus in
pluribus locis docent. De his vero medietatibus exponetur,
quando ad divinas veritates applicabuntur. Cum vero omnes
modi Philosophiae essentiales, qui sunt plures quam quadra-
ginta scientiae ad invicem distinctae, reducantur ad hos tres,
sufficit nunc per auctoritates dictas persuasum esse valorem
mathematicae respectu modorum philosophiae essentialium.

Modi autem philosophiae accidentales sunt grammatica et Alphar-

logica. Et quod sine mathematica non possunt sciri scientiae *P'"*

proves

istae patet per Alpharabium in libro de scientiis. Nam etsi dependence
. . ee e . Lo) Inmar
grammatica pueris ministrat ea quae vocis sunt et proprietates and of logic

on mathe-

Theology, and the shifting phenomena of nature. Ta piv dAAa bdo yérn roo MAUC.
Oewpnrixot paddov dy tis elxaciay wardAnpw eczoc 7d yey Ocodoyucdy bd 7d

wayreAós dpaves abrot xal dvewiinwroy, 70 Bi puoudy Ba 7d Tis Ans dataror xal

EbnAov* ds Bia Tovro pnBlwore Ay Uca: wepi abrüv Ópovofjaas rods duAocoQdoUrras:

póvov 82 7d pabnparixdy, el ris Uferagrinws abrQ wpoclpxovro BeBaíay wai áperá-

McTroy Tois peraxepopdvas Tiw el5naw wapdoxo. He indicates also the value

of mathematical study in elevating and consolidating character.

H 2

IOO OPERIS MAJORIS PARS QUARTA.

ejus in prosa, et metro, et rhythmo, nihilominus tamen hoc facit
pueriliter, et per viam narrationis, non per causas, nec per
rationes. Nam alterius scientiae est dare causas horum,
scilicet illius, quae vocum naturam plenarie habet considerare,
et haec sola est musica, cujus species et partes multae sunt.
.Nam una est prosaica, et altera est metrica et tertia est
rhythmica, et quarta est melica in cantu. Et praeter has
habet plures. Et prosaica docet causas omnium elevationum
vocum in prosa, secundum accentuum differentias et secundum
cola et commata et periodos et hujusmodi!. Et metrica docet
omnes rationes et causas pedum et metrorum. Et rhythmica
de omni modulatione et proportione suavi rhythmorum docet,
-quia omnia ista sunt quaedam genera cantus, licet non sic ut
in cantu usuali. Nam accentus dicitur quasi accantus, de
accino, accinis. Unde ad musicam pertinent sicut docet
Cassiodorus in musica, et Censorinus in libris de accentu, et
sic de aliis. Hoc autem testantur auctores musicae, et libri
de illa scientia. Et his concordat Alpharabius in libro de
divisione scientiarum. Ergo grammatica dependet causaliter
ex musica.

Eodem modo logica. Nam finis logicae est compositio
argumentorum quae movent intellectum practicum ad fidem
et amorem virtutis et felicitatis futurae, ut prius ostensum
est, quae argumenta traduntur in libris Aristotelis de his argu-
mentis, ut declaratum est. Sed haec argumenta debent esse
in fine pulchritudinis, ut rapiatur animus hominis ad salutiferas
veritates subito et sine praevisione, ut docetur in illis libris.
Et Alpharabius? hoc docet maxime de poetico, cujus sermones

! For a fuller discussion of punctuation, metre, and rhythm, see Opus
Tertium, ch. 62 and 63.

? Abu Nasr Muhammed ibn Muhammed ben Tarchán ben Auzelag el Farabi,
known in the Western world as Alpharabius, was born A. p. 870 in the town
of Farab (afterwards called Otrar) in Turkestan, and is one of many instances
proving that Mahommedan learning in the Middle Ages was not limited to the
Arab race. He was ignorant of Arabic till he came to Bagdad for the purposes
of study. Having acquired it he became one of the most zealous students of
Aristotle, devoting himself specially to the PAysics and the De Anima. The
latter part of his life was spent in Damascus, where he died in 950 a.p. Of
his original works the most important was Liber de scientiis earumque numero
partibus et praestantia, This work was translated by Dominicus Gundisalvi, at

MATHEMATICAE IN PHYSICIS UTILITAS. tor

debent esse sublimes et decori, et ideo cum ornatu prosaico,
et metrico, et rhythmico insigniti, secundum quod competit
loco et tempori et personis et materiae de qua sit persuasio.
Et sic docuit Aristoteles in libro suo de poetico argumento,
quem non ausus fuit interpres Hermannus transferre in Latinum
propter metrorum difficultatem, quam non intellexit, ut ipse
dicit in prologo commentarii Averrois super illum librum. Et
ideo finis logicae pendet ex musica. Sed finis est nobilissimum
in re, et imponit necessitatem eis quae sunt ad finem, ut Ari-
stoteles dicit in secundo Physicae; nec habent utilitatem suam
ea quae naturaliter ordinantur ad finem, nisi quando ad finem
suum comparantur, ut patet in singulis. Et ideo tota utilitas
logicae nascitur ex comparatione logicalium omnium ad hujus-
modi argumenta, et ideo cum dependeant ex musicalibus
necesse est logicam mendicare potestatem musicae. Et haec

Toledo, in the twelfth century. In the following century Hermannus Ale-
mannus translated Aristotle's Rhetoric from the Arabic, and with it certain
commentaries of Alpharabius. * Omnia enim,' he says, 'in glosa super hunc
librum exquisite Alfarabius pertractavit' Hermann observes, however, that
* Alfarabius multa exempla Graeca propter ipsorum obscuritatem pertransiens
derelinquit.’ The Arabic version of Aristotle's Poetics seems to have been
made not by Alfarabius but by Averroes. Hermann remarks on the extreme
difficulty of rendering this version into Latin, * propter disconvenientiam modi
metrificandi in Graeco cum modo metrificandi in Arabico, et propter vocabulorum
obscuritatem, et plures alias causas."

Alpharabius is one of the authors (Aristotle, Avicenna, and Algazel being the
others) from whom David the Jew compiled the work De Cassis, of which
Albertus Magnus gives a long description, and which is cited both by Bacon
and by Thomas Aquinas. See Jourdain, pp. 112, 138-145, 184-5; also
Wuestenfeld, Geschichte der Arabischen Aerste und Naturforscher (Gottingen,
1840).

The short treatise, De Scientis, is interesting for its comprehensive and
encyclopaedic survey of Science. It consists of five chapters. 1. De Scientia
Linguae et partibus ejus. 2. De Scientia Logicae et partibus ejus. 3. De
Scientiis doctrinalibus, quae sunt Geometria, Arithmetica, Scientia de Aspec-
tibus, Scientia stellarum doctrinalis, Scientia Musicae, Scientia de Ponderibus,
Scientia de Ingeniis. 4. De Scientia naturali et partibus ejus; et Scientia
divina et partibus ejus. 5. De Scientia civili et partibus ejus, et de Scientia
judicandi, et de Scientia eloquendi.

Like Bacon, Alfarabi includes rhetoric and poetic as parts of Logic. ‘ Rhe-
torica movet animum auditoris et inclinat ad illud quod voluerit, ut credatur id
quod dicit et generet in eo cognitionem proximam certitudini. Proprium est
autem Poeticae sermonibus sensum facere imaginari pulcrum aliquid et dubium
quod non est, ita ut auditor credat et aliquid abhorreat vel appetat . . . quoniam
Imaginatio plus operatur in homine quam scientia vel cognitio.'

Without
mathe-
matic the
Categories
are un-
intelligible.

102 OPERIS MAJORIS PARS QUARTA.

omnia sunt secundum sententiam Alpharabii in libro de
scientiis, et patent similiter per Aristotelem et Averroem in
libris suis, licet Latini horum usum non habeant. Sed non
solum dependet cognitio logicae a mathematica propter suum
finem, sed propter medium et cor ejus, quod est liber pos-
teriorum, nam ille liber docet artem demonstrandi. Sed nec
principia demonstrationis; nec conclusiones, nec ipsa tota
potest cognosci, nec manifestari nisi in mathematicis rebus,
quia ibi solum est demonstratio vera et potens, ut omnes sciunt
et exponetur post. Quapropter necesse est logicam a mathe-
maticis dependere.

Item propter suum principium, non solum propter medium
et finem. Nam liber praedicamentorum est primus liber
logicae secundum Aristotelem. Sed constat praedicamentum
quantitatis cognosci non posse sine mathematica. Nam sola
mathematica constituitur de quantitate cognoscenda Quan-
titati vero annexa sunt praedicamenta de quando et ubi. Nam
quando attinet tempori, et ubi oritur ex loco. Praedicamentum
habitus non potest cognosci sine praedicamento ubi, ut docet
Averroes in quinto Metaphysicae. Major vero pars praedica-
menti qualitatis continet passiones et proprietates quantitatum,
quia omnia quae sunt in quarto genere qualitatis vocantur quali-
tates inquantitatibus Et omnes passiones earum quae absolute
debentur eis sunt qualitates, de quibus magna pars geometriae
et arithmeticae constituuntur, sicut sunt rectum et curvum, et
caetera quae lineae debentur, et triangulatio et omnis reliqua
figuratio, quae superficiei et corpori assignantur; et primum
incompositum in numeris, ut docet Aristoteles quinto Meta-
physicae et caeterae passiones numerorum absolutae. Quicquid
autem dignum est consideratione in praedicamento relationis
est proprietas quantitatis, ut sunt proportiones et proportion-
alitates, et medietates geometricae, et arithmeticac, et musicae,
et species majoris inaequalitatis et minoris. Substantiae vero
spirituales non cognoscuntur per philosophiam nisi per cor-
porales, et maxime supercoelestes, secundum quod Aristoteles
docet undecimo Metaphysicae. Nec inferiora cognoscuntur
nisi per superiora, quia coelestia sunt causae inferiorum. Sed
coelestia non cognoscuntur nisi per quantitatem, sicut patet

MATHEMATICAE IN PHYSICIS UTILITAS. — 103

ex astronomia. Et ideo omnia praedicamenta dependent ex
cognitione quantitatis, de qua est mathematica, et ideo virtus
tota logicae dependet ex mathematica.

CAPITULUM III.

In quo probatur per rationem quod omnis scientia requirit Mathe-

mathematicam. matical
examples

used to

Quod vero per auctoritatem de tota mathematica ostensum strate
est, potest nunc per rationem similiter ostendi. Et primo, sciences.
quia aliae scientiae utuntur exemplis mathematicis, sed
exempla ponuntur propter evidentiam rerum de quibus
scientiae constituuntur; quare ignoratis exemplis, ignorantur
ea propter quorum intelligentiam adducuntur. Cum enim
alteratio in naturalibus non inveniatur sine augmento et
diminutione quibuscunque nec haec sine alteratione: non
potuit Aristoteles ad purum manifestare differentiam inter
augmentum et alterationem per aliquod exemplum naturale,
quia semper concomitantur se aliquo modo; propter quod
posuit exemplum mathematicum in quadrangulo quod addito
gnomone crevit, et non alteratur. Quod exemplum ante
vigesimam secundam propositionem sexti libri elementorum
non potest intelligi. In illa enim sexti probatur, quod
quadrangulus minor est omnino similis majori. Et ideo non
alteratur minor, cum fiat major de minore per gnomonis
additionem.

Secundo, quia mathematicarum rerum cognitio est quasi Com- |
nobis innata. Socrati enim interroganti geometrica a puero Pr henslon
pusione, ut recitat Tullius primo Tusculanarum quaestionum matical
ita respondebat, quasi geometriam didicisset. Et hoc saepe truth
expertum est in multis ; quod non accidit in aliis scientiis, ut
ex sequentibus magis erit manifestum. ^ Quapropter cum sit
quasi innata, et tanquam praecedens inventionem et doctrinam,
seu saltem minus indigens eis quam aliae scientiae, prima erit
inter scientias et praecedens alias, disponens nos ad eas;
quoniam quae innata sunt vel prope disponunt ad acquisita.

Tertio, quia haec scientia prius est inter omnes partes

Earliest
discovered.

Easiest of
apprehen-
sion.

Accessible
to tbe
dullest.

The first
step in
teaching.

104 OPERIS MAJORIS PARS QUARTA.

philosophiae inventa. A principio enim humani generis haec
primo inventa est. Quoniam ante diluvium et post, per filios
Adae, et per Noe et filios ejus, sicut ex prologo compositionis
astrolabii secundum Ptolemaeum, et ex Albumazar in majori
introductorio astronomiae, et ex primo antiquitatum libro
manifestum est, et hoc quantum ad omnes ejus partes,
scilicet geometriam, arithmeticam, musicam, astronomiam.
Ilud autem non contigisset, nisi quia haec scientia est prior
aliis, et naturaliter eas praecedens. Quare manifestum est,
quod haec debet primo sciri, ut per eam promoveamur ad
omnes scientias posteriores.

Quarto, quia nobis est nata via a facilibus ad difficilia.
Sed haec scientia est facillima. Quod manifestum est in eo,
quod non refugit intellectum alicujus. Laici enim et omnino
illiterati figurare et computare sciunt, et cantare, et haec sunt
opera mathematicae. Sed primo incipiendum est ab his quae
sint communia laicis et literatis ; et non solum damnosum est
clericis, sed omnino turpe et vile; quod ipsi ignorant quod laici
utiliter et pulchre sciunt. Quinto videmus quod clerici licet
rudissimi mathematicalia possunt scire, quamvis ad alias
scientias non valeant attingere. Insuper semel et bis
audiendo plus homo de ea potest cognoscere certo et veraciter
sine errore, quam decies de aliis partibus philosophiae, ut
patet experienti. Sexto, quoniam nata est nobis via ab his
quae conveniunt statui et ingenio puerili, quia pueri a nobis
notioribus et primo addiscendis incipiunt Sed hujusmodi est
mathematica, quoniam primo docentur canere, et eodem modo
possunt capere modum figurandi et numerandi, et longe
facilius et necesse esset eis scire de numeris ante cantum ; quia
in proportionibus numerorum tota ratio numeri exemplariter
explicatur, sicut auctores musicae docent, tam in ecclesiastica
musica, quam in philosophica. Sed ratio numerorum a figuris
dependet, quia numeri lineares, et superficiales, et corporales,
et quadrati, et cubici, et pentagoni et hexagoni, et caeteri,
a lineis et figuris et angulis cognoscuntur. Expertum enim
est, quod pueri melius et citius addiscunt mathematicalia, ut
manifestum est in cantu, et etiam per experientiam scimus,
quod pueri melius addiscunt et capiunt mathematicalia, quam

MATHEMATICAE IN PHYSICIS UTILITAS. — 105

alias partes philosophiae. Nam Aristoteles dicit in sexto
Ethicorum quod juvenes possunt cito scire mathematicalia, non
sic naturalia, nec metaphysicalia, nec moralia. Quare dis-
ponendus est animus prius per haec quam per alia.

Septimo, ubi non sunt eadem nobis nota et naturae, nata It leads
est nobis via a notioribus nobis ad notiora naturae. Sive jrom things
simpliciter et facilius scimus ea, quae nobis notiora sunt, et usto things
cum magna difficultate devenimus in ea, quae sunt notiora nature. to
naturae. Et nota naturae sunt male et imperfecte nobis
cognita, quia intellectus noster se habet ad ea, quae sunt sic
manifesta naturae, sicut oculus vespertilionis ad lucem solis, ut
vult Aristoteles secundo Metaphysicae ; sicut sunt maxime Deus
et angeli, et vita futura et coelestia, et aliae creaturae nobili-
ores aliis. quia quanto sunt nobiliores, tanto sunt nobis minus
notae. Et haec vocantur nota naturae. et simpliciter. Ergo
per oppositum ubi eadem sunt nota nobis et naturae, multum
proficimus circa nota naturae, et omnia quae ibi sunt, et ad ea
possumus attingere ut sciamus ea perfecte. Sed in mathe-
matica tantum, ut dicit Averroes! primo physicae et septimo
metaphysico et super tertio coeli et mundi, sunt eadem nobis
nota et naturae sive simpliciter. Ergo sicut in mathematica
ad ea quae sunt nobis nota complete attingimus, sic ad ea
quae sunt nota naturae et simpliciter. Quare ad intima illius
scientiae possumus simpliciter attingere. Cum ergo hoc non
valeamus in aliis, manifestum est quod haec est magis nota.
Quapropter ab ea sumenda est origo nostrae cognitionis.

Item octavo, quia omne dubium fit notum per certum, et It is the
omnis error evacuatur per solidam veritatem. Sed in mathe- Sd cem
matica possumus devenire ad plenam veritatem sine errore, et
ad omnium certitudinem sine dubitatione: quoniam in ea
convenit haberi demonstrationem per causam propriam et
necessariam. Et demonstratio facit cognosci veritatem. Et
similiter in ea contingit haberi ad omnia exemplum sensibile,
et experientiam sensibilem figurando et numerando, ut omnia

1 In his commentary on the first book of De Natur. Auscult., Averroes says,

* Illa quae sunt cognita apud nos in rebus naturalibus non sunt illa quae sunt
cognita simpliciter, id est, naturaliter. Quod est contrarium in mathematicis :

illa enim quae sunt cognita in illis simpliciter, et sunt causae priores in esse,
sunt cognita apud nos.’

106 OPERIS MAJORIS PARS QUARTA.

ad sensum manifestentur: propter quod non potest esse
dubitatio in ea. Sed in aliis scientiis excluso mathematicae
beneficio, tot sunt dubitationes, tot opiniones, tot errores
a parte hominis, ut non possint explicari, ut manifestum est,
quoniam demonstratio per causam propriam et necessariam
non est in eis ex propria potestate, eo quod in naturalibus
propter generationem et corruptionem propriarum causarum,
sicut effectuum, non est necessitas. In metaphysicis non potest
fieri demonstratio nisi per effectum. Quoniam inveniuntur
spiritualia per corporales effectus et creator per creaturam,
sicut patet in illa scientia. In moralibus non possunt esse
ex propriis demonstrationes, ut Aristoteles docet. Et similiter
nec in logicalibus nec grammaticalibus, ut planum est, possunt
esse demonstrationes potissimae propter debilitatem materiae
de qua sunt illae scientiae. Et ideo in sola mathematica sunt
demonstrationes potissimae per causam necessariam. Et ideo
solum ibi potest homo ex potestate illius scientiae devenire ad
veritatem. Similiter in aliis scientiis sunt dubitationes, et
opiniones, et contrarietates a parte nostra, ut vix concordetur
in una vilissima quaestione, nec in uno sophismate ; non enim
sunt in eis ex sua proprietate experientiae figurationum et
numerationum, per quas omnia certificari debent. Et ideo in
sola mathematica est certitudo sine dubitatione.

Quare patet quod si in aliis scientiis debemus venire in
certitudinem sine dubitatione et ad veritatem sine errore,
oportet ut fundamenta cognitionis in mathematica ponamus ;
quatenus per eam dispositi possumus pertingere ad certitu-
dinem aliarum scientiarum, et ad veritatem per exclusionem
erroris. Et haec ratio potest per simile magis manifestari, et
principale etiam propositum nonum Euclidis. Sicut enim
cognitio conclusionis se habet ad cognitionem praemissarum,
ut si sit in eis error et dubitatio, non possit veritas haberi per
eas de conclusione, nec certitudo, quia dubium non certificatur
per dubium, nec verum per falsum probatur, licet possit
syllogizari ex falsis, syllogismo inferente non probante; sic
est de scientiis totalibus, quod illae in quibus sunt dubitationes
vehementes et multiplices, atque opiniones et errores, dico
saltem a parte nostra, oportet quod hujusmodi dubitationes et

MATHEMATICAE IN PHYSICIS UTILITAS. |. 107

falsitates evacuentur per aliquam scientiam nobis certam, et in
qua nec dubitamus nec erramus. Cum enim conclusiones et
principia propria eis sint partes totalium scientiarum, sicut
pars se habet ad partem, ut conclusio ad praemissas, sic
scientia ad scientiam, ut scilicet scientia, quae est plena
dubitationibus et opinionibus respersa atque obscuritatibus,
non valeat certificari, nec manifestari, nec verificari, nisi per
aliam scientiam notam et verificatam, et nobis certam et
planam, sicut est de conclusione per praemissas. Sed sola
mathematica, ut prius habitum est, manet nobis certa et
verificata in fine certitudinis et verificationis. Quapropter
per hanc oportet omnes alias scientias sciri et certificari.

Et quoniam jam per proprietatem istius scientiae ostensum Considera-

. . ee . oe: . tion of the

est, quod mathematica est prior aliis, et eis utilis et necessaria, subject.
nunc ostenditur hoc per rationes sumptas a parte sui subjecti. matter of
Et primo sic, quia nobis est via nata a sensu ad intellectum, matics
quoniam deficiente sensu deficit scientia quae est secundum leads us to
illum sensum', ut dicitur primo Posteriorum, quoniam secundum conclusion,
quod proficit sensus, proficit humanus intellectus. Sed quan-
titas est maxime sensibilis, quia est sensibile commune, et ab
aliis sensibus sentitur, et nihil potest sentiri sine quantitate
quapropter maxime potest intellectus proficere circa quanti-
tatem. — Secundo, quia ipse actus intelligendi secundum se
ipsum non perficitur sine quantitate continua, quia dicit
Aristoteles in libro de Memoria? et Reminiscentia quod omnis
intellectus noster est cum continuo et tempore. Unde quanta
et corpora intelligimus intuitu intellectus, quia species eorum
apud intellectum sunt. Incorporeorum autem species non sic
recipiuntur intellectu nostro; aut si fiant in eo, secundum
quod Avicenna dicit tertio Metaphysicorum, non tamen hoc
percipimus propter occupationem fortiorem intellectus nostri
circa corpora et quanta. Et ideo per viam argumentationis
et admirationis corporalium et quantorum investigamus
rerum incorporalium notitiam, sicut Aristoteles facit in libro

! éayepór 82 al Sri ef Tis aloOnois txdddorwey dvd-yan xal tmorhpny Tid éxAeXoc-
wéiva, Analyt. Post. i. 18.

2 Ob« lybéxera voety obbiv árev ToU avrexous, o05. árev xpórov rd pij) ty xpéry
Gera. De Memoria, cap. 1.

in which
wise men
of all ages
concur.

1o8 OPERIS MAJORIS PARS QUARTA.

undecimo Metaphysicorum. Quapropter proficiet maxime
intellectus circa ipsam quantitatem, eo quod quanta et corpora
in quantum hujusmodi appropriantur intellectui humano
secundum statum communem intelligendi. Unumquodque
est propter quod et illud magis.

Ad omnem autem confirmationem potest ratio ultima sumi
ex experientia sapientum ; nam omnes sapientes antiqui
laborarunt in mathematica, ut omnia scirent, sicut nos vidimus
de aliquibus nostri temporis, et audivimus de aliis, qui per
mathematicam, quam bene sciverunt, omnem scientiam cog-
noverunt. Inventi enim sunt viri famosissimi, ut Episcopus
Robertus Lincolniensis, et Frater Adam de Marisco, et multi
alii, qui per potestatem mathematicae sciverunt causas omnium
explicare, et tam humana quam divina sufficienter exponere.
Hujus autem rei certitudo patet in scriptis illorum virorum,
ut de impressionibus, sicut de iride et de cometis, et de
generatione caloris, et locorum mundi investigatione, et de
coelestibus et aliis, quibus tam theologia quam philosophia
utitur. Quapropter manifestum est quod mathematica est
omnino necessaria et utilis aliis scientiis.

Hae rationes sunt universales, sed in particulari contingit
hoc ostendi descendendo ad omnes partes philosophiae, quo-
modo per applicationem mathematicae sciuntur omnia. Et
hoc nihil aliud est, quam ostendere scientias alias non debere
sciri per argumenta dialectica et sophistica quae introducuntur
communiter, sed per demonstrationes mathematicas descen-
dentes in veritates et opera aliarum scientiarum et regulantes
eas, sine quibus nec possunt intelligi, nec manifestari, nec
doceri, nec disci. Si quis vero in particulari descenderet
applicando mathematicae potestatem ad singulas scientias,
viderit quod nihil in eis posset sciri magnificum sine mathe-
matica. Sed hoc nihil aliud esset, nisi constituere tractatus
certos de omnibus scientiis, et per vias mathematicae verificare
omnia quae scientiis caeteris sunt necessaria. Sed hoc non
est praesentis speculationis.

MATHEMATICAE IN PHYSICIS UTILITAS. |. 109

DISTINCTIO SECUNDA.

In qua ostenditur, quod res hujus mundi requirunt mathe-
maticam, habens capitula tria.

CAPITULUM I.

In primo docetur in universali quod coelestia et inferiora
requirunt mathematicam.

Quod de scientiis jam ostensum est, potest de rebus mani- In the
festari. Nam impossibile est res hujus mundi sciri, nisi sciatur science of
‘mathematica. De coelestibus enim certum est omnibus, quia the need

duae scientiae magnae mathematicae sunt de eis, scilicet of mate”
astrologia speculativa, et astrologia practica. Prima specu- obvious.
latur quantitates omnium quae sunt in coelestibus, et omnia
quae ad quantitatem reducuntur, tam discretam quam con-
tinuam quantitatem. Nam numerum coelorum et stellarum,
quarum quantitas potest per instrumenta comprehendi, certi-
ficat, et figuras omnium, et magnitudines et altitudines a
terra ac spissitudines et numerum ac magnitudinem ac parvi- :
tatem, ortum et occasum signorum stellarum, et motum tam
coelorum quam stellarum, et quantitates et varietates eclip-
sium. Item descendit ad quantitatem et figuram habitabilis,
et omnium partium ejus magnarum,.quae vocantur climata,
et ostendit diversitatem horizontium et dierum ac noctium
secundum singula climata. Haec ergo determinantur hic, et
multa eis annexa. Practica vero descendit ad hoc, ut ad
omnem horam sciamus loca planetarum et stellarum, et
aspectus et compositiones earum et omnia quae in coelestibus
renovantur, atque descendit ad ea quae fiunt in aere, cujus-
modi sunt cometae, et irides, et caetera ibi renovata, ut
sciamus loca eorum, et altitudines, et magnitudines, et figuras,
et multa quae oportet considerare in his. Et haec omnia
fiunt per instrumenta ad haec idonea, et per tabulas, et per
canones, id est, regulas ad haec certificanda inventas, quatenus

Terrestrial
things are
governed
by celestial.

The laws
of force in
both re-
vealed by
mathe-
matic.

IIO OPERIS MAJORIS PARS QUARTA.

via paretur ad judicia, quae fieri possunt secundum potes-
tatem philosophiae, non solum in naturalibus, sed in his quae
sumunt inclinationem ex natura, et gratis sequuntur coelestem
dispositionem ; et non solum ad judicia praesentium praete-
ritorum et futurorum, sed ad opera miranda, ut omnia pros-
pera hujus mundi promoveantur, et adversa reprimantur,
utiliter ac magnifice. Nec sunt haec dubia. Nam patriarchae
et prophetae a principio mundi certificaverunt haec, sicut
caetera. Et Aristoteles renovavit certificationem antiquorum,
et produxit in lucem. Et omnes sapientes in rebus magnis
in hoc concordant, et experientia docet. Sed de his expositio
fiet suo loco.

Planum ergo est, quod coelestia sciuntur per mathematicam,
et quod praeparatur per eam via ad haec inferiora. Quod
autem haec inferiora non possunt cognosci sine mathematica,
patet primo per hoc, quod non scimus res nisi per causas,
si proprie accipiatur scientia, sicut Aristoteles dicit Sed
coelestia sunt causae inferiorum. Ergo non scientur haec
inferiora, nisi sciantur coelestia, et illa sine mathematica sciri
non possunt. Ergo horum inferiorum scientia dependet ex
eadem. Secundo possumus videre ex propriis, quod nihil
horum inferiorum nec superiorum sciri potest sine mathe-
maticae potestate. Nam omnis res naturalis producitur in
esse per efficiens et materiam in quam operatur, nam haec
duo concurrunt primo. Agens enim per suam virtutem movet
et transmutat materiam, ut fiat res. Sed virtus efficientis et
materiae sciri non potest sine magna mathematicae potestate,
sicut nec ipsi effectus producti. Sunt ergo haec tria, efficiens,
materia et effectus. Et in coelestibus fit mutua influentia
virtutum, ut lucis et aliarum, et est in eis alteratio, licet non
ad corruptionem. Et sic potest ostendi, quod nihil in rebus
sciri potest sine geometriae potestate. Habemus ex hoc
argumento, quod similiter aliae partes mathematicae sunt
necessariae: qua ratione enim illa, et aliae: et proculdubio
longe magis, quia nobiliores sunt. Si ergo propositum osten-
datur in geometricis, non est necesse in hac persuasione de
aliis fieri sermonem.

Primo ergo ostendo propositum geometricae a parte

MATHEMATICAE IN PHYSICIS UTILITAS. 111

efficientis. ; Omne enim efficiens agit per suam virtutem quam What is
facit in materiam subjectam, ut lux solis facit suam virtutem species.”
in aere, quae est lumen diffusum per totum mundum a luce
solari. Et haec virtus vocatur similitudo, et imago, et species !
et. multis nominibus, et hanc facit tam substantia quam
accidens, et tam spiritualis quam corporalis. Et substantia
plus quam accidens, et spiritualis plus quam corporalis. , Et
haec species facit omnem operationem hujus mundi ; nam
operatur in sensum, in intellectum, et in totam mundi mate-
ram per rerum generationepf, quia unum et idem fit ab
agente naturali in quodcunque operetur, quia non habet
deliberationem ; et ideo quicquid ei occurrat facit idem. Sed
si in sensum et intellectum agat, fit species, ut omnes sciunt.
Ergo in contrarium, et in materiam fit species. Et in his
quae habent rationem et intellectum, licet multa faciant
secundum deliberationem et electionem voluntatis, tamen
haec operatio, quae est generatio speciei, est naturalis in eis
sicut in alis. Unde substantia animae multiplicat suam
virtutem in corpore et extra corpus, et quodlibet corpus
extra se facit suam virtutem, et angeli movent mundum per
hujusmodi virtutes. Sed Deus facit virtutes de nihilo, quas
multiplicat in rebus; agentia creata non sic, sed alio modo de
quo non est ad praesens curandum. Hujusmodi ergo virtutes
agentium in hoc mundo faciunt omnem operationem. Sed
duo sunt modo attendenda circa ista: unum est ipsa multi-
plicatio speciei et virtutis a loco suae generationis; et aliud
est operatio varia in hoc mundo propter rerum generationem
et corruptionem. | Secundum sciri non potest sine primo. Et
ideo oportet primo ipsam multiplicationem describi.

CAPITULUM II.

In quo canones multiplicationis virtutum agentium se-
cundum lineas et angulos explicantur.

! All that is said in this fourth part of the Opus Majus on the subject of
speces must be studied in connexion with the much fuller treatment of the
subject in the treatise De Muliiplicatione Specierum.

Force in
& homo-
geneous
inedium

propagated

112 OPERIS MAJORIS PARS QUARTA.

Omnis autem multiplicatio vel est secundum lineas, vel
angulos, vel figuras. Dum vero species in medio raritatis
unius incedit, ut in toto coelo, et in toto igne, et in toto aere,

in straight Vel in tota aqua, semper tenet vias rectas, quia Aristoteles

lines.

The law of

refraction.

dicit quinto Metaphysicae quod natura operatur breviori modo
quo potest, et linea recta est omnium brevissima. Quod etiam
patet per vicesimum primi elementorum Euclidis dicentis,
in omni triangulo duo latera sunt tertio longiora.

Sed cum corpus secundum est alterius raritatis et densitatis,
ita ut non sit omnino densum, sed permutat aliquo modo
transitum speciei, sicut aqua, quae est quodam modo rara, et
quodam modo densa, et crystallus similiter et vitrum, et hujus-
modi per quorum media possumus videre, tunc species aut
venit perpendiculariter super corpus secundum, et adhuc
incedit per lineam rectam sicut prius; aut si non cadat per-
pendiculariter, tunc de necessitate mutat incessum rectum, et
facit angulum in introitu corporis secundi. Et hujus de-
clinatio ab incessu recto vocatur fractio radii et speciei'. Et
haec causa est, quia perpendicularis fortior est et brevior, et
ideo natura operatur meliori modo super eam, sicut docent
geometricae demonstrationes, de quibus postea fiet mentio
magis suo loco. Sed haec fractio est duplex, quoniam si
corpus secundum est densius, prout accidit descendendo a
coelo in haec inferiora, tunc omnes virtutes stellarum quae
non cadunt perpendiculariter super globum elementorum,
franguntur inter incessum rectum et perpendicularem du-
cendam a loco fractionis. Et si corpus secundum est sub-
tilius sicut est ascendendo ab aqua superius, tunc inter
fractionem et perpendicularem ducendam a loco fractionis

! Refraction is described for the first time in the optical work of Ptolemy,
the Greek text of which is lost, but of which an Arabic version was translated
into Latin in the twelfth century by the admiral Eugenio, who served under
Roger, king of Sicily. This translation has been recently edited (1885) by
Gilberto Govi of Turin. The account of refraction will be found in the .fifth
section of the work (p. 142 et seq. Ptolemy did more than state the fact of
refraction. He measured the amount of deviation of the refracted ray for
different angles of incidence, in the three media of air, water, and glass. Ashe
shows himself to be aware of the error caused by refraction in astronomical
observations (p. 151), it is strange that no mention of it should have been made
in the Almagest.

MATHEMATICAE IN PHYSICIS UTILITAS. |. 113

cadit incessus rectus. Et haec est admiranda varietas in
operatione naturae, sed nec mirum, cum infinita mirabilia
fiunt per naturam secundum leges istarum fractionum; et
per artificium juvans naturam possunt fieri ea quae mundus
capere non potest, ut in scientia perspectiva explicabo. Sed
cogetur per haec temporibus Antichristi ad ea quae ipse volet
pro magna parte.

Quod autem haec sint vera auctores docent, et omnes periti Artificial
sciunt, atque instrumenta possunt ad haec fieri, ut sensibiliter gence of
hujusmodi incessus videamus ; sed usquequo habeamus instru- r25s-
menta, possumus pér effectum naturalem hoc probare sine
contradictione, ut docet haec figura. Accipiatur ergo dimidia
sphaera crystalli vel vas vitreum, cujus inferius sit rotundum,
plenum aqua. Cum ergo a centro solis veniunt radii per
aerem ad corpus crystalli, vel vitri,
quod est densius aere, illi qui non sunt
perpendiculares super corpus tale (et hi
sunt qui non vadunt in centrum ejus,
ut ex geometricis planum est), fran-
guntur inter incessum rectum et per-
pendicularem ducendam a loco frac-
tionis, ut est radius ac, qui cum
transiverit per totum corpus vasis,
venit ad aerem subtiliorem et non
perpendiculariter. Ergo oportet ut sic
vadat, ut incessus rectus sit inter ipsum
et perpendicularem ducendam a loco
fractionis, et ideo non ibit in c, sed de-
clinat ad /, super principalem perpendi-
cularem, quae venit a sole, ut est Of
radius. Et eodem modo est ex alia
parte, quod per duplicem fractionem
A f concurret in eodem puncto f, in quo
radius O f. Sed infiniti radii exeunt
a sole super hoc corpus; ergo infiniti congregabuntur in eodem
puncto per duplicem fractionem. Sed congregatio luminum
est causa caloris. Ergo ibi fiet calor comburens. Et hoc est
verum, ut patet ad sensum ; nam si apponatur combustibile,

VOL. I. I

Fic. 1.

Law of
reflection.

II4 OPERIS MAJORIS PARS QUARTA.

ut lana, vel bombyx, vel pannus, comburetur. Cum ergo hic
sit combustio, et hoc fieri non potest nisi per congregationem
radiorum, et radii non possunt congregari nisi per duplicem
fractionem, quia una non sufficeret, nec tertia requiritur, ergo
oportet ponere hanc varietatem fractionem, quod est mirabile
in oculis sapientum. Nam unde est, quod natura sic operatur?
Certe nihil est jucundum naturae, vel voluntati, nisi quod
reficit varietas ; sed causae occultae sunt. Nec oportet causas
modo investigare, cum per experientiam certissimam istud
miraculum sciamus, et in sequentibus aliae experientiae sub-
jungentur.

Quando vero secundum corpus est ita densum, quod nullo
modo permittet transitum speciei, dico de sensibili transitu,
quantum ad judicium visus humani, tunc dicimus speciem
reflect. Secundum tamen Aristotelem et Boetium visus
lyncis penetrat parietes. Ergo species transit secundum
veritatem !, et hoc est verum: sed visus hominis non judicat
de hoc, sed de reflexione, quae necessario fit. Nam propter

difficultatem transitus per den-

¢ d sum, cum in aere a quo venit

inveniat viam facilem, multiplicat

se copiosius in partem a qua

venit. Et potest esse primo in

generali duobus modis ; nam aut

b C j cadit perpendiculariter super

FiG. a. densum, et tunc redit in se

omnino per eandem viam a qua

venit, et geminatur radius in eodem loco, ut a radius cadit
perpendiculariter, et hoc est in planis ad angulos rectos, ut
docetur in undecimo geometriae, sicut in sphaericis, quando
cadit in centrum. Et causa hujus est ; quia anguli incidentiae
et reflexionis semper sunt aequales, ut multiplex demonstratio
docet, et auctores omnes supponunt, et instrumenta ad hoc facta
edocent ad oculum. Sed non sunt nisi duo anguli recti ex

! Recent discoveries give much interest to this expression. Here, as in the
case afterwards to be noticed of the time occupied in the passage of light, Bacon
conceived that processes might take place of which human sense was not keen
enough to take cognizance. See De Mull. Specierum, Pars II, cap. 5.

MATHEMATICAE IN PHYSICIS UTILITAS. |. 115

casu a ó ad densum. Ergo per eosdem redibit radius reflexus,
et ideo in ecdem loco. Sed linea a c quae cadit ad obliquos
angulos, et non perpendiculariter, non redit in se ipsam, sed
usque ad 4d, propter aequalitatem angulorum incidentiae et
reflexionis. Quandocunque vero cadit radius ad angulos obli-
quos, tunc angulus acutus vocatur angulus incidentiae; et ab
ilo obtuso angulo separatur perlineam reflexam angulus
aequalis angulo incidentiae, qui angulus continetur inter lineam
reflexam et densum, ut est angulus Z c g, et hic vocatur angulus
reflexionis, quem oportet necessario aequari angulo acuto a
parte altera, et hoc ad visum probamus in speculis. Nam
non possumus videre res, nisi oculus sit in termino reflexionis,
ut si oculus sit in Z, videbit; et si non, non videbit per illum
radium reflexum. Et haec riota sunt, atque experientiae satis
dabuntur de hoc in sequentibus.

Possunt autem congregari radii infiniti per reflexionem. Artificial
sicut per multiplicationem, ut fiant combustiones validae. cence of
Sed a plana superficie non possunt radii congregari in unum. reflected
quia unus vadit ad unum locum, et alius ad alium. Nec mye
a convexo speculo ; sed a concavo sphaerico, ‘columnari, et
pyramidali, 'annulari, et ovali, et sic de aliis. Si ergo specu-
lum concavum sphaericum ad solem ponatur, concurrunt radii
infiniti in punctum unum per reflexionem. Et ideo oportet,

. ut speculo concavo ad solem posito ignis accendatur, sicut
dicitur ultimo proposito libride speculis, et ibidem demonstratur.
Sed instrumentum ad hoc factum esset pulchrum valde, et
tunc videretur ad oculum, sicut prius dictum est de fractione.
Unde si fieret speculum de chalybe bono, vel de argento,
facilius accideret combustio; sed una combustio non fit per
omnes radios cadentes in speculo, sed per solos illos qui
cadunt in circumferentiam unius circuli circa axem speculi,
quia omnes, qui cadunt in una circumferentia, cadunt ad
angulos aequales, et ideo reflectuntur ad punctum unum in
axe, quia anguli reflexionum sunt aequales, et qui cadunt in
alia circulatione, redeunt ad aliud punctum, et qui in tertia ad
tertium, et sic de infinitis circulis imaginandis circa axem
speculi: oportet enim quod ad puncta diversa vadant radii
cadentes in diversis circumferentiis, propter hoc quod non
I 2

116 JA OPERIS MAJORIS PARS QUARTA.

cadunt ad angulos aequales. Et illi qui cadunt in minori
circulo altius reflectuntur, et qui in maximo ad punctum
infimum, scilicet ad polum sphaerae, seu ad extremitatem axis,
reflectuntur. Sed nec natura nec ars contentae sunt hujus-
modi combustione, imo volunt sic figurare corpora, ut omnes
radii cadentes in totam superficiem speculi concurrant in
punctum unum. Et sic adhuc ut in omni distantia quam
volumus; et hoc est ultimum quod geometriae valet facere
potestas. Nam hoc speculum potenter combureret omne quod
posset objici. Et credendum est quod Antichristus his utetur,
ut civitates et castra et exercitus comburat. Quoniam si
modica congregatio radiorum per fractionem vel speculum
concavum comburit sensibiliter, quanto ergo magis in infini-
tum, quando radii infinities infiniti congregabuntur per hoc
speculum? Aestimant sapientes hoc esse necessarium. Et
auctor in libro de speculis comburentibus docet hoc instru-
mentum fieri, sed gratis in illo libro occultavit multum de
artificio, et dicit quod in alio libro posuit residuum, quod non
est translatum apud Latinos. Sed sunt Latini qui, mala
gratia illius auctoris occultantis perfectionem suae sapientiae,
devenerunt ad hoc magnificum naturae secretum, quia ille
auctor multum excitat peritos in sapientia ut residuum per-
ficiant, et docet quod debet esse quasi annularis figurae, vel
ovalis, ut, si amputarentur coni unius ovi, fieret annularis
figura, si vero unus conus remanet, fit ovalis. Tali vero figura
artificialiter facta secundum quod competit, oportet quod
omnes radii cadentes in totam superficiem speculi cadant ad
angulos aequales, et ideo reflectantur ad consimiles, et propter
hoc in punctum unum. Elaboratur autem circa hoc speculum
faciendum a peritissimo Latinorum !, et Vestrae Magnificentiae
gloria poterit praecipere, ut compleatur, cum vobis fuerit
annotatus. Haec autem triplex multiplicatio secundum lineas

1 This was Peter Peregrinus of Maricourt. See Opus Tertium, cap. 13.
Reference to De Mult. Specierus (Pars II, cap. 7) will show that Bacon
was aware of the properties of a surface produced by the rotation on its axis
of a conic section. Vitello, Bacon's contemporary; in the ninth book of his
Opies, after proving geometrically that parallel rays falling on a parabolic
mirror are reflected to the same point, explains how such mirrors are constructed
(lib. ix. prop. 44).

MATHEMATICAE IN PHYSICIS UTILITAS. | 117

dicitur esse principalis propter hoc, quod ab ipso agente
venit.

Sed quarta est magis mundo necessaria, quamvis vocetur Diffused
accidentalis multiplicatio. Nam lumen accidentale vocatur @*
respectu lucis principalis venientis a re, quoniam hoc non
venit ab agente, sed a multiplicationibus principalibus, ut in
domo cadit per fenestram multiplicatio principalis a sole, sed
in angulo domus venit a radio fenestrae lux accidentalis. Non
possent autem corpora mortalium semper exponi speciebus
principalibus sine sui corruptione, et ideo temperavit Deus
omnia per hujusmodi species accidentales.

Quinta vero est aliena ab istis, nam non tenet leges com- Propaga-

munes naturae, sed sibi vindicat privilegium speciale. Et haec through
multiplicatio non fit nisi in medio animato, ut in nervis sen- nerves.
suum: nam species sequitur tortuositatem nervi, et non curat
de incessu recto, et hoc fit per virtutem animae regulantis in-
cessum speciei, secundum quod opera rei animatae requirunt.
De hac in perspectivis veritatibus aliquid dicetur. Quatuor
primae sunt communes rebus mundi inanimatis, secundum
quas natura delectatur operari; quinta ad sensum noscitur
pertinere.

CAPITULUM III.

In quo datur multiplicatio secundum figuras.

Deinde considerandum est, quo modo fiat multiplicatio From the
secundum figuras. Et oportet quod multiplicatio fiat sphaerice. PE eeede ia
Nam agens multiplicat se aequabiliter in omnem partem, et se- every.
cundum omnes diametros, et omnes differentias positionis, quae direction.
sunt sursum, deorsum, ante, retro, dextrorsum, sinistrorsum.

Ergo undique exeunt lineae in omnem partem ab agente
tanquam a centro; sed lineae undique exeuntes ab uno loco
non possunt terminari, nisi ad superficiem concavam sphaerae.
Et hoc patet, quia oculus non videt nisi per speciem venientem,
sed si infiniti oculi ponerentur undique, omnes viderent eandem
rem ; ergo per infinitas lineas exit species: sed infinitae non
terminantur nisi ad superficiem sphaericam. Si vero dicatur,

118 OPERIS MAJORIS PARS QUARTA.

quod lumen intrans per magnum foramen triangulare vel
alterius polygoniae figurae, non cadit sphaerice, sed quando
intrat per parvum foramen ; dicendum est, quod latera parvi
foraminis parum distant, et ideo lux in parva distantia potest
figuram suam recuperare, sed quando transit per figuram
magnam, non potest ita de facili, sed in aliqua distantia
sufficienti, si obstacula amoverentur. Quod patet per xiv et
xv primi elementorum Euclidis, ut ostendit figura.

Fic. 3.

Nam trahantur radii ab intersectione quantum est ab inter-
sectione ad solem, oportet per dictas propositiones ut bases
triangulorum sint aequales. Sed illae bases sunt diametri
luminum. Ergo oportet ad minus, ut diameter speciei sit
aequalis diametro solis in aliqua distantia, et per consequens
multiplicatio erit sphaerica aequalis, et potest variari secundum
diversitatem distantiae, sed semper sphaerice. Nec est
instantia de luce ignis, quae ascendit in figura pyramidali:
quia haec non est multiplicatio ex propria natura lucis, sed
est propter motum corporis ipsius ignis, cujus accidens est
lux, et accidens fertur secundum motum sui subjecti, sicut
lux solis in sole. Pyramidaliter vero ignem necesse est
ascendere, quoniam partes interiores semper elongantur a
frigido circumstanti, et ideo minus impediuntur et citius
expediunt se quam exteriores, et propter hoc altius ascendunt,
et caeterae quanto iis propinquiores, tanto citius sese expediunt,
et applicant se interioribus, aliquantulum deficientes ab
intimarum altitudine, et sic gradatim per ordinem remotiores
minus exaltantur, quia magis impediuntur a contrario circum-
stanti; et ideo oportet quod pyramis enascatur. Sed in
sphaera possunt omnes figurae regulares inscribi, ut patet ex
xiii libro elementorum Euclidis, inter quas una est pyramis.

Et licet jam secundum rationem inscriptionis geometricae

MATHEMATICAE IN PHYSICIS UTILITAS. |. 119

non possunt figurae irregulares inscribi, nec figurae rotundae ; Cones of
possunt tamen omnes figurae protrahi, et signari in sphaera. input
Et ideo non solum in sphaerica multiplicatione inveniemus each point
pyramides lateratas, quarum proprium est inscribi in sphaera, aes
sed pyramides rotundas !, quae signari possunt et figurari in acted on.
sphaerica multiplicatione. Et haec
est figura, quam specialiter elegit
natura in omni multiplicatione et
actione, et non quamcunque pyra-
midem, sed illam cujus basis est
superficies agentis, et cujus conus
cadit in aliquod punctum patientis,
quia sic potest a tota superficie
agentis species venire ad singula
puncta patientis per singulas pyra-
mides et infinitas, ut patet in figura.
Nam a quolibet puncto patientis fiunt
radii infiniti, et ideo possunt com-
binari infinities, ut fiant pyramides
rotundae infinitae, quarum omnium est una basis, scilicet,
superficies totius agentis; et ad quamlibet partem patientis
venit unus conus unius pyramidis, ut virtus veniat a toto
agente ad quodlibet punctum patientis, et non ab aliqua parte
determinata, quatenus virtus completa perveniat et tota,
non partialis et imperfecta, ut fiat actio completa, quia natura
facit secundum quod melius est.

PATIENS

AGENS

FIG. 4.

DISTINCTIO TERTIA.

In qua declaratur varietas actionis naturalis per geometriam,
habens tria capita.

CAPITULUM I.

His consideratis circa multiplicationem, sunt aliqua con- Idirect.
° . » . e action o
sideranda circa actionem ulteriorem. Nam lux per viam 4...

1 This is Bacon's expression for a cone. He uses the word conus to denote
the apex of the cone.

I20 OPERIS MAJORIS PARS QUARTA.

multiplicationis suae facit speciem luminosam, et haec actio
dicitur univoca, quia effectus est univocus, et unigenius, et
conformis agenti. Sed alia est multiplicatio aequivoca, ut
lux generat calorem, calor putrefactionem, putrefactio mortem,
et vinum inebriat, et sic de omni agente, quod multos effectus
facit praeter speciem suam et virtutem sibi univocam. Et sic
sol et stellae faciunt omnia hic inferius, et angeli movent
coelum et stellas, et anima corpus suum: virtus tamen agentis
facit omnia ista, et haec est completa actio agentis et suae
virtutis, ac a natura finaliter desiderata. De hac ergo actione
considerandi sunt aliqui canones seu regulae, et propter eam
principaliter, et tamen locum habent in actione univoca, et
veritatem habent ibi.
Force most Natura ergo, ut dictum est, fortius operatur super lineam
poent rectam quam super curvam, quia brevior est, et minus facit
vertically. patiens distare ab agente, et ideo plus capit de virtute
ipsius sicut prope ignem aliquis plus calefit quam remotior.
Caeterum melius est aequale quam inaequale, ut dicit Boetius
in practica geometriae. Sed in linea recta est aequalitas.
Item omnis virtus unita est fortioris operationis, sicut dicitur
in libro de causis. Sed uniformitas et unitas
major est in linea recta, sicut dicit Aristoteles
quinto Metaphysicae. Nam in curva est
angulus, qui facit dispersionem et difformi-
tatem, et repugnat unitati. Quapropter natura
operatur fortius super lineam rectam, quam
super fractam vel reflexam. Sed linea recta,
quae cadit ad angulos aequales, et perpen-
diculariter, sive in planis, sive in sphaericis,
€ à ila est super quam natura eligit operari tum
Fic. 5. propter aequalitatem et majorem uniformi-
tatem, tum propter brevitatem. Nam per xix
propositum primi elementorum Euclidis, in omni triangulo
majori angulo majus latus opponitur. Sed ex xvii primi
ejusdem libri, major angulus in triangulo est rectus, scilicet,
& c b. Ergo ei opponitur maximum latus scilicet, a 6.
Sed illa cadit non perpendiculariter. Ergo perpendicularis
b c est brevior: quare virtus veniens super eam operabitur

MATHEMATICAE IN PHYSICIS UTILITAS. |. 12%

fortius. Perpendicularis autem fortitudo non solum patet per
demonstrationem, sed per experientiam, unde lapis cadens
ab alto perpendiculariter fortius scindit ; et si homo cadit ab
alto magis laeditur: nam qui hominem cadentem ab alto
pelleret ab incessu perpendiculari, dummodo esset prope
terram, non laederetur; quod si non fieret, moritur ex casu
perpendiculari, et totus conquassatur.

Et considerandum, quod si a diversis punctis agentis

veniant ad eandem rem radii, unus perpendicularis super
agens, ét alius non perpendicularis super ipsum, semper erit
perpendicularis brevior. Ut posito, quod agens sit a c, tunc
a b est brevior quam c 2,
et ideo fortior quantum est
ex ratione hac. Et licet
€ 6 cadet super e d patiens
ad angulos rectos, et a 2
non, ut sic c & fortificetur f b
ex hujusmodi causa, nihilo-
minus non attinget ad forti-
tudinem a 0, quia brevior d
est, et quia 4 punctus e 7 Fic. 6.
similiter punctus est alterius lineae ut f 7, ad quam a 6 est
perpendicularis, et sic 4 habet rationem patientis princi-
paliter’. Et maxime super corpus sphaericum fit actio com-
pletissima, cum virtus non cadat ibi ad aliquem angulum,
sed transeat superficiem et corpus sphaericum, et nulla est
diversitas vel difformitas et plenitudo actionis ibi invenitur.
Nisi enim signentur circuli in sphaera non est ibi angulus;
sed cum signantur tunc anguli lineae perpendicularis erunt
aequales, sicut in planis, et complebitur actio. Sed tamen non
sunt recti sed obtusi ut patet geometrae.

Deinde sciendum est, quod natura operatur super lineas Refracted
fractas fortius, quam super reflexas, quia fractio est in partem s...
incessus recti, sed reflexio in contrarium vadit, et contra than re-
incessum naturalem quem appetit natura virtutis incedentis in ected
continuum et directum nisi impediatur, et ideo reflexio multum
debilitat speciem et virtutem, et magis quam fractio. Sed hoc

a C

1 This sentence and the first part of the following are omitted in J.

(X cote
t
ravs the
givcatet
number
elique

122 OPERIS MAJORIS PARS QUARTA.

intelligendum est de fractione et reflexione secundum pro-
prietatem incessus in eis. Si tamen consideremus, quod est
reflexio in eodem medio, et fractio in diversis, oportet quod
duplex medium magis impediat quam unum, et hoc saltem
quando reflexio fit in medio subtili, et fiat fractio in secundo
densiori, ut est in vase vitreo. Nam si congregentur radii
a speculo comburente, et post perspicuum comburens, oportet
quod major sit combustio, sicut inferius suis locis explicabitur.
Fractio vero quae est in corpore secundo densiori minus
debilitat, quam ea quae est in corpore secundo subtiliori. Nam
incessus perpendicularis est fortissimus, et ideo quae magis
accedit ad perpendicularem, magis est fortis. Sed fractio in
corpore secundo densiori declinat versus perpendicularem, quae
ab eodem puncto exit a quo fractio, ut patet superius in
figura, tam in planis, quam in sphaericis, et ideo nulla minus
debilitat. De reflexione vero quae est ad angulos rectos, licet
geminetur radius accidentaliter, et sic fit fortior actio, tamen
de natura illius reflexionis est, quod per se loquendo plus
debilitat speciem; nam omnino est in contrarium conatus
naturalis ipsius speciei, quoniam per eandem lineam redit
species super quam venit. Sed quando est ad angulos
obliquos, non est omnino in contrariam partem, sed a latere,
et ideo non tantum debilitat haec reflexio,sicut alia. Quantum
cst de natura reflexionis dico, sed propter geminationem
virtutis in eodem loco. et propter aequalitatem angulorum,
et conditiones perpendicularis, fortior est actio.

Et tamen considerandum hic, quod per casum radiorum ad
angulos obliquos possunt plures radii congregari per intersec-
tionem, quam per radios cadentes ad angulos rectos, non solum
cx proprietate speculorum. ut dictum est, sed propter radios
eccurrentes sibi infinites ex lege incidentiae et reflexionis ad
angulos obliquos, sicut accidit in aere, quando propter casum
hujusmodi et reflexionem | intersecant se radii in quolibet
puncto inünities, et fit calor, Nam paud sunt incdentes
perpenciculanter super aliquam rem, quia non nii ab uno
puncte agentis cadit unus perpendicularis ad unum punctum
patenus et ideo sunt pauci redlexi Sed infain non perpen-

*

ckuians exeunt a quoLbef puncto agents, et inhnid reflexi

MATHEMATICAE IN PHYSICIS UTILITAS. | 123

sunt eis respondentes. Deinde per casum perpendicularem
tantum duo conjunguntur in eodem loco aeris, scilicet, incidens
et reflexus ejus compar. Sed per casum ad angulos obliquos
incidentes infiniti se intersecant in quolibet puncto aeris. Et
similiter incidentes penetrant reflexos non sibi compares, et
reflexi reflexos infinities. Nam ad omne punctum terrae
incidunt radii infiniti, et ab eodem infiniti reflectuntur, et ideo
fortior operatio nascitur sic per accidens ex incidentibus et
reflexis ad angulos obliquos, quam ad rectos. Ars vero potest
juvare naturam in formatione actionis; nam potest sic figurare
specula, ut fiat congregatio virtutum magna per specula con-
cava, et maxime per ovalia, sicut dictum est. Sed virtus
principalis, scilicet recta fracta et reflexa, est fortior acciden-
tali, quia non venit accidentalis ab agente, sed a specie agentis,
et est species speciei, propter quod debilior est.

CAPITULUM II.

In quo consideratur fortitudo actionis secundum figuras.

Et cum pyramis, ut dictum est, requiratur ad actionem Short cones
naturae, considerandum est quod conus brevioris pyramidis muore potent
fortius operatur, tum quia minus distat ab than long.
agente, tum quia radii conterminales circa
conum pyramidis brevioris magis vicinantur, et
vicinia radiorum ac congregatio fortius opera-
tur; et hoc patet in figura. Nam per xvii
primi elementorum Euclidis, omnes anguli
circa punctum unum in superficie non valent
nisi quatuor rectos ; ergo quatuor anguli apud
conum pyramidis brevioris valent reliquos
quatuor apud conum longioris. Sed per xxi
ejusdem, angulus in cono pyramidis brevioris ll
est major quam angulus in cono pyramidis 7
longioris, scilicet a est major quam c; et per
xv ejusdem, anguli contrapositi sunt aequales,
scilicet a et 5, item c et 2; ergo c et d simul sumpti sunt
minores quam a et 6 simul conjuncti; ergo cum quatuor

Fic. 7.

Mutual
action of
large and
small
spheres.

124. OPERIS MAJORIS PARS QUARTA.

simul sumpti aequantur aliis quatuor simul sumptis per xiii,
tunc oportet quod Z4 et / sint majores quam f ete. Quapropter
radii qui continent e magis vicinantur quam radii continentes 4.
Et eodem modo radii continentes f propinquiores sunt quam
radii continentes /, et sic de infinitis radiis qui conterminales
sunt in pyramide breviori, oportet quod omnes magis vicinentur

quam radii qui simul terminantur in cono
a pyramidis longioris. Sed vicinia virtutum
est causa fortioris actionis. Sed tamen cum
incessus perpendicularium sit fortissimus, et
omnis accessus ad perpendiculares fortior est
recessu, tunc radii pyramidis longioris cum
magis accedant ad perpendiculares a c 6 d,
erunt fortiores. Item tot radii veniunt ad
conum pyramidis longioris, sicut ad conum
brevioris, quoniam infiniti utrobique. Sed
conus pyramidis longioris acutiorem habet
angulum per xxi. Ergo radii ejus magis uniuntur. Ergo
fortius comburent. Et dicendum est, quod hae rationes ad
utramque partem demonstrationes sunt, sed fortiores sunt ad
primam partem, et ideo praevalent. Unde quantum possunt
rationes ultimae, tantum concludunt, sed aliae potentiores sunt
et efficacius operantur.

Fic. 8.

CAPITULUM III.

Quantum alteretur de patiente, et quantum de agente
alterct, explanans.

Ad haec subjungendum est quod in corporibus sphaericis
aequalibus medietas cujuslibet recipit virtutem alterius, quia
radii extremi contingunt corpora illa, et ideo transeunt per
terminos diametri, et non attingit aliquis radius ad aliquam
partem alterius medietatis. Sed corpus minus recepit virtutem
majoris in majori sua portione, propter hoc quod radii extremi
corporis majoris non aequidistant semper, sed concurrunt, et
possunt amplecti plus medietate minoris. Nam diameter cor-
poris majoris est major diametro corporis minoris; et ideo

MATHEMATICAE IN PHYSICIS UTILITAS. | 125

possunt radii exeuntes a terminis diametri corporis majoris
transire ultra diametrum corporis minoris, ut majorem ejus
portionem comprehendant; et e contrario corporis majoris

OO Co

F1G. 9.

minor portio recipit virtutem a minori corpore, quia diameter
minoris corporis non aequatur diametro majoris, sed alicui
chordae minoris portionis corporis majoris. Et nullus punctus
sphaerici corporis potest facere virtutem a se, nisi ad spatium
quod separatur ab eo per lineam quae contingat illud corpus
in puncto illo a quo fit virtus; quoniam ab a puncto non
potest aliqua linea cadere inter lineam contingentem et corpus
sphaericum, ut demonstratur in

xv tertii elementorum Euclidis.

Et ideo spatium, quod est in

angulo contingentiae, et sic per

totam retro lineam contingentem

versus corpus, non recipiet vir-

tutem ab a puncto, sed totum

spatium ultra lineam contin- e

gentiae, in quo sunt puncta 2c de, d

recipiet virtutem. Et omnes b
radii qui exeunt a superficie cor-
poris sphaerici, quorum directio
cadit in centrum corporis illius, sunt perpendiculares super
ipsum et tales undique exeunt infiniti ut patet in figura.
Et tum ab eodem puncto superficiei corporis, a quo fit
radius perpendicularis, super idem corpus fiunt radii infiniti,
ut patet ad a punctum, et sic de omnibus; sed unus solus,
scilicet a ^, radius est perpendicularis super illud corpus,
quia ille solus, si protrahatur in continuum et directum, vadit
in centrum corporis, et ideo ille est fortissimus, et habet longe
plus de virtute.

FIG. 10.

126 OPERIS MAJORIS PARS QUARTA.

Convergent Et isti radii perpendiculares, eo quod concurrunt in centrum
rays from corporis, non sunt aequidistantes ; potest tamen oculus esse ita
objects — longe a corpore, quod non percipiat concursum, et judicabit
Parallel. radios tales esse aequidistantes, sicut accidit nobis de radiis
solis et stellarum, et ideo judicamus umbras rerum diversarum
aequidistantes, quando opponuntur soli, sed non secundum
veritatem. Multa enim videntur aequidistare, quia non per-
cipimus eorum concursum, ut parietes domus cujuslibet videntur
ad sensum aequidistantes, sed non sunt quia omne grave tendit
ad centrum naturaliter, et ideo rueret domus, si essent omnino
aequidistantes. Et circuli meridiani diversarum civitatum
videntur esse aequidistantes, et lineae meridiei, quia non per-
cipimus concursum, et tamen concurrunt in polo mundi.
Thecentral Est etiam sciendum, quod radii qui cadunt in centrum
ray of each corporis sphaerici a quo veniunt, sunt illi per quos judicamus
operative. stellas per foramina instrumentorum. Unde astronomus et
perspectivus, qui experiuntur hujusmodi, utuntur istis radiis
quia sensuales sunt et fortes. Quamvis enima portione aliqua
corporis sphaerici objecta rei patienti veniat una pyramis
habens radios infinitos, qui fiunt a singulis punctis illius
portionis, et omnes concurrunt in conum pyramidis cum radio
perpendiculari, tamen unus solus est perpendicularis in una
pyramide, et ille perpendicularis dominatur in fortitudine, et
est axis pyramidis et tota pyramis ab eo nominatur apud
experimentatores, et vocatur radius corporis agentis, ut patet

Fic. 11.

in figura. Nam sit a centrum, et Z c sit portio solis objecta
terrae, et ? conus pyramidis cadentis in terram, planum est
quod e 8 radius cadit in centrum solis, et nulli alii qui sunt
de corpore pyramidis, quamvis sint infiniti. Nam g d declinat
a centro solis, ut patet, et sic de omnibus aliis f ), c 6. Et ideo

MATHEMATICAE IN PHYSICIS UTILITAS. | 127

est perpendicularis super corpus solis, et axis pyramidis, et
ideo est fortior, et plus habet de virtute, quoniam virtus venit
secundum hunc radium a tota profunditate solis, quod non
accidit in aliis. Nam diameter A o est longior quam f g, et
quam omnes lineae cadentes in circulo a latere diametri, et
ideo plus capit de substantia solis, ideo plus habet de virtute.
Et £ 6 linea est brevior quam c 4, et omnes aliae quae a por-
tione solis descendunt in terram, quapropter plus habet de
virtute secundum praedicta. Et haec, quae nunc dicta sunt,
patent ex viii tertii elementorum Euclidis.

DISTINCTIO QUARTA.

CAPITULUM I.

In quo canones dicti applicantur ad lucem stellarum.

His principiis et hujusmodi datis per vias geometriae, Illustra-
potest homo verificare omnem actionem naturae, quia omnis °°"*
veritas circa operationem agentis in medium, vel in materiam
generabilem, vel in coelestia, et in totam mundi machinam,
sumit ortum mediate vel immediate ex jam dictis, et quibus-
dam similibus, quia non potui omnia in hac persuasione ponere,
quae opus majus requirit. Et quod dico manifestare volo per
aliqua exempla in diversis rebus mundi, et incipiam a supe-
rioribus. Aristoteles vero dicit in primo Meteorologicorum !
quod omnes stellae habent lucem a sole; et hoc patet per Lunar
eclipsin lunae : nam quando terra interponitur inter solem et °UP®*
lunam, ipsa eclipsatur, et quando non, tunc illuminatur; et
ideo similiter esset de aliis, si essent in tali situ in quo luna.

Sed non sunt, nam conus pyramidis umbrae non attingit nisi
usque ad orbem Mercurii, et ideo sola luna potest cadere in
umbra terrae. Et tamen stellae inferiores eclipsant superiores,
sicut Aristoteles vult secundo Coeli et Mundi, quando cadunt?

' Meteor. i. 8, $ 6. Aristotle explains that the earth's shadow reaches to
the moon, but not much beyond ; and that the distance of the stars from the
earth is many times as great as that of the sun; wherefore, dydyan wávra Tov
fpaor rà dorpa sepiopáv, xal unOevl riy yhw ávrippárrew abràv.

* In Meteor. i. 6, $ 11, Aristotle speaks of an occultation of one of the stars
in Gemini by Jupiter.

128 OPERIS MAJORIS PARS QUARTA.

inferiores inter solem et superiores, et hoc bene accidit, sed
non est ita notabile, sicut de luna. Sed quoniam, ut patet
ex praedictis, rara et perspicua permittunt transitum speciei,
ut aer et species oculi et stellarum transeunt per orbem ignis,
et per medium omnium orbium septem planetarum, necesse
est quod sint rara et perspicua, et quod non terminant visum.
Ergo non sunt densa. Ergo nec visibilia, quia solum est
visibile, ut docet Avicenna tertio de Anima, quod potest visum
terminare, et verum est hoc. Sed si non sunt visibilia, non
sunt lucida, quia lucidum est visibile. Et loquor de lucido
quod habet lucem fixam, et non transeuntem ac propriam
quae potest multiplicare a se radios, ut stella et ignis; non
loquor de lucido quod recipit lucem transeuntem sicut aer,
quem Aristoteles vocat lucidum ! in secundo de Anima: sed
hoc estaequivoce. Quapropter errant, qui aestimant sphaeram
ignis lucere naturaliter, sicut hic inferius, et praecipue cum
magis sit rarus quam aer, et ideo minus visibilis, et propter
hoc minus aptus luci, quia densitas est causa illuminationis, ut
dicit Averroes secundo Coeli et Mundi, et libro de Substantia
Orbis. Et similiter turpius erratur a vulgo, quando ponit
orbes stellarum lucere, praecipue cum dicant quoddam falsum,
et imponunt Averroi illud. Nam dicunt, quod stella non
differt ab orbe nisi per majorem aggregationem et minorem
lucis. Sed Averroes non dicit hoc, sed contrarium docet et
probat: bene enim dicit totum hunc sermonem praeter casum
genitivum ultimum, qui est /ucts, loco cujus dicit fersPicui
coelestis. Et quia fere omnia vocabula sermonis vulgati et
ipsius Averrois sunt eadem, et aestimant perspicuum et luci-
dum esse idem, propter verbum Aristotelis secundo de Anima,
ubi accipitur lucidum aequivoce, imponunt Averroi quod velit
orbem lucere propria luce et fixa, ut stella, licet minus. Sed
dicit contrarium, volens quod propter fortitudinem actionis
quam habet stella in hoc mundo, oportet quod multum
habeat de substantia coeli congregata in suo corpore, et
ideo perspicuum coeleste, quod dispergitur in partibus orbis,

! De Anima, ii. 7, $ 2 “Eos &j c &aqarés baoayts 32 Aé-qo 5 (ori uiv óparóv,

ov £00’ abrà 3° dpardy dAAd &' dAAST PLOY xppa* rowtror 3 lariv jp xal Ubwp . . .
pas 3 éarlv } rovrov lvépyea Tov kagavois j diapavés.

MATHEMATICAE IN PHYSICIS UTILITAS. 129

condensatur in corpore stellae, ut habeat fortem virtutem in
alteratione mundi. Et ideo docet ibi, et in libro de substantia
orbis, quod stella sola lucet, et nulla pars orbis. Et hic error
vulgatur apud philosophantes, et apud omnes Theologos,
quando loquuntur, et scribunt de stellis.

Quoniam vero in libro de proprietatibus elementorum Is the light
dicitur, quod sol est sicut candela, et stellae sicut specula, of themoon
aestimat totum vulgus studentium quod lumen quod venit reflected

JM . . from the

ad nos de luna et stellis sit lux solis reflexa a superficiebus ,44?
earum. Sed hoc est impossibile propter aequalitatem angu-

lorum incidentiae et reflexionis, ut patet in figura. Nam ut

prius visum est, si ita esset, tunc oportet angulum a incidentiae,

et angulum ? reflexionis aequari. Ergo ^ c radius non vadit

nisi in partem determinatam
terrae et non ubique, et sic de
toto lumine quod venit ad su-
perficiem lunae. Totum enim
est quasi unus radius, et cadit
ad angulos inaequales, et re-
flectitur in partem determina-
tam. Ergo si veniret ad terram,
non illuminaret luna nisi par-
tem Horizontis aliquam deter-
minatam ; sed nos videmus,
quod illuminat totum hemi-
sphaerium sicut sol Ergo
lux illa quae venit a luna et a
stellis non est reflexa. Et Averroes secundo coeli et mundi
hac demonstratione utitur, et sua confirmat auctoritate, quod
non est lumen solis reflexum a superficie stellarum, quod ad
nos descendit ab eis, sed proprium lumen et innatum, eductum
tamen de potentia materiae in corpore stellae per virtutem
solis venientis ad stellam, quae virtus alterat et transmutat
stellam, et facit lumen in ea; et quando habet lumen natu-
raliter genitum in ea, sicut sol habet lucem creatam, tunc
potest multiplicare lucem a se undique sicut sol. Et tunc
concedendum est quod lumen solis reflectitur a superficie
lunae, sed non venit ad terram, sed ad aliam partem mundi

VOL. I. K

«-

Fic, 12.

More than
half of the
earth illu-
minated

by the sun.

In space
are more
media than
one, as
tefraction
proves.

130 OPERIS MAJORIS PARS QUARTA.

declinat in coelestibus secundum aequalitatem angulorum
incidentiae et reflexionis.

Et per supradicta patet, quantum illuminatur de terra et
de stellis per solem. Nam majores earum portiones semper
illuminantur, quia minores sunt sole. Sol enim est centies
septuagies fere major tota terra, sicut ostendit Ptolemaeus in
quinto Almagesti !, et sic possunt omnia quae pertinent ad illu-
minationes et protractiones radiorum in coelestibus verificari,
ut in diversa figuratione lunae secundum aetates, et quare in
eclipsibus appareat rubea et pallida, et tota ratione eclipsis ;
nam hoc est propter lumen principale, quod a radiis princi-
palibus venit infra umbram, et quodammodo sic imperfecte
illuminatur per radios accidentales. Et non solum de his, sed
de aliis virtutibus factis a planetis et stellis in alias secundum
omnes diversitates conjunctionum et aspectuum, quibus astro-
nomi utuntur in suis considerationibus, in quibus multipli-
cantur non solum radii lucis, sed virtutes substantiales stellarum
ad invicem, secundum quod dicimus lunam in Ariete esse
calidam et siccam, in Geminis calidam et humidam, et in
Cancro frigidam et humidam: et quando conjungitur Saturno
fit frigida et sicca, et quando Iovi calida et humida, et sic de
omnibus talibus. Nam haec omnia certificantur per multi-
plicationes specierum et virtutum determinatas juxta principia
praetacta. Et non solum haec, quae pertinent ad qualitates
et naturas substantiales stellarum, sed ea quae pertinent ad
figuras, et magnitudines, et altitudines, et numerum coelorum
et stellarum, et ad hujusmodi consimilia.

CAPITULUM II.

In quo canones supradicti applicantur ad totum mundum.

Et non solum haec de coelestibus verificantur per dicta,
sed de elementis et toto mundo. Nam cum philosophi ante
Aristotelem posuerunt omnia esse unum corpus mundi, potest
destrui hoc per leges fractionis. Nam si quis per instrumenta
quibus experimur ea quae sunt in coelestibus, cujusmodi

1 Ptol, Sysetans, i. 16.

MATHEMATICAE IN PHYSICIS UTILITAS. I3I

vocantur armillae vel alia, accipiat locum alicujus stellae circa
aequinoctialem in ortu suo, et deinde accipiat locum ejusdem
quando venit ad lineam meridiei, distare sensibiliter inveniet
eam in loco meridiei plus a polo mundi septentrionali, quam
quando fuit in ortu. Ergo visus videt stellam diversis modis
in illis diversis temporibus: nam si videret eodem modo tunc
stellam in eodem loco inveniret semper. Sed quando stella
est in linea meridiei, tunc stella accedit ad zenith capitis
aspicientis, qui est punctus in coelo suprapositus capiti, qua-
propter cadunt radii in visum perpendiculariter, et in centrum
mundi, et ideo non franguntur, et propter hoc videt visus
stellam per rectas lineas in suo loco vero. Ergo quando visus
errat in ortu stellae non videbit per lineas perpendiculares,
quia multum distat stella a zenith capitis, et ideo radii cadunt
ad angulos obliquos, quapropter franguntur, et ideo visus tunc
videt per lineas fractas, et errat in loco stellae. Sic autem
Ptolemaeus! in libro quinto de opticis docet considerare, et
Alhazen in libro septimo et ego consideravi in instrumentis
hoc idem, et certum est. Quoniam ergo fractio radiorum cadit
in hoc mundo, planum est quod plura corpora sunt in mundo.
Et prima fractio invenitur secundum considerationem dictam Ray pass-
in superficie ignis immediate sub orbe coelesti, scilicet sub |» l9"
sphaera lunae: quapropter sphaera ignis est diversa a sphaera srhere to
coeli; cum tamen Platonici et Augustinus, et multi autores epee of
antiqui tangant Platonice quod ignis et coelum sunt unius "acted.
naturae. Sed hoc est impossibile propter demonstrationem
dictam, et propter alias demonstrationes naturales quas Ari-
stoteles in libro Coeli et Mundi affert, quibus nullus modernus
modo contradicit: nam trita est haec veritas in naturalibus.
Haec tamen demonstratio vulgo naturalium est ignota, nam
Aristoteles non tangit eam, nec ejus expositores. Quoniam
autem non est fractio in sphaera aeris, ut iidem autores
docent, et certitudo experientiae, ideo multum turbantur
sapientes, an sphaera aeris et ignis sint duae vel una. Videtur
enim per autores praedictos, et propter privationem fractionis,
quod una sit superficies aeris et ignis, et unum corpus. Sed
hoc est impossibile, quia Aristoteles dicit tertio Coeli et Mundi,

1 Ptol. Ofíscae, v. p. 15r, ed. Govi. Cf. Alhazen, vii. 15.
K 2

Laws of
climate.
Polar

132 OPERIS MAJORIS PARS QUARTA.

quod aer est gravis! in sphaera sua, et sequitur naturaliter
superficiem aquae non ignis; nam si ignis ascenderet in
sphaera sua, aer non sequeretur, ut dicit. quia cum aqua
descendit, aer sequitur ejus superficiem, ut videmus ad ocu-
lum. Quapropter non erunt unum corpus aer et ignis; et tota
dubitatio solvitur per legem fractionis. Nam tria requiruntur
ad hoc ut sit fractio, scilicet ut corpus secundum habeat
superficiem distinctam a primo, et quod sit alterius raritatis,
scilicet magis rarum vel minus, et quod radii cadant ad
angulos obliquos. Quod si aliquid istorum deficiat, non est
fractio possibilis. Propter primum enim non est fractio in
eodem corpore, licet habeat partem unam rariorem et aliam
minus raram, sicut aer est rarior superius quam inferius. Et
propter secundum non est fractio in orbibus coelestibus, quia
sunt ejusdem raritatis, quantum ad sensum nostrum. Et
propter hoc idem non est fractio in sphaera aeris, quia aer
gradatim subtiliatur usquequo in sua parte suprema aequetur
subtilitati ignis in parte inferiori, et ideo non est ibi fractio.
Quoniam autem fractio haec est inter incessum rectum et
perpendicularem ducendam a loco fractionis, ut docent hi
autores, et ipsa experientia, ideo sequitur quod corpus se-
cundum est densius priori et ideo corpus sub orbe coelesti
est densius quam orbis coeli. Quapropter oportet ponere
plenam diversitatem corporum mundi penes coelum et ele-
mentum. Et quando habuerimus haec, tunc per radios, et
pyramides luminosas stellarum venientium ad instrumenta
certificabimus omnia quae sunt in coelestibus, scilicet numerum
coelorum, et stellarum magnitudinem et spissitudinem, et
omnia quae sunt in coelis.

CAPITULUM III.

In quo per multiplicationes praedictas investigantur com-
plexiones locorum mundi circa polos ejus.

Posthaec descendemus ad sphaeras elementorum et investi-
gabimus omnes complexiones eorum secundum singulas partes

1 De Coelo, iv. 4, $ 5 àv rp abro? ydp xápa mávra Bápos Exec wAtw wupds, kal
ó anp.

-- -—m ———— M -— — —— —— —À — —— ——M— A Hu er T PREREE EPREEEE RE EN REPERI

MATHEMATICAE IN PHYSICIS UTILITAS. 133

habitationis, et inveniemus quod loca sub polis mundi sunt tempera-
naturaliter inhabitabilia propter frigus. Nec obstant nobis ture low,
rationes superius annotatae pro pyramidibus longioribus, nam standing
sicut ibi dictum est, demonstrationes pro pyramidibus brevi- PI of
oribus vincunt in hac parte, quamvis omnis homo qui nesciret summer.
hujusmodi radices multiplicationis lucis vinceretur per pyra-
mides longiores. Sed verum est, quod coni pyramidum
venientium ad loca sub polis nimis distant a sole, et ideo
debiles sunt, nec possunt nisi elevare vapores ab aqua et terra
in aerem, et non possunt eos consumere ; et ideo oportet quod
aer sit densus et caliginosus et congelatus per vapores ubique
et semper, ut ibi plantae et animalia non possint vivere, sicut
docet Ptolemaeus in libro de dispositione sphaerae. Sed si
cum pyramidibus longioribus addamus autoritatem Aristotelis
secundo de vegetabilibus dicentis, *quod apud eos! ubi prolon-
gantur dies, &c. et hoc est, ut docet commentator super illud
verbum, ubi est dimidius annus dies, et dimidius annus nox,
non sunt animalia nec plantae, quia calor combussit materiam
eorum; videbitur quod illa loca sub polis sint inhabitabilia
propter calorem, non propter frigus. Nam proculdubio ibi est
dimidius annus dies, et tunc videretur quod calor nimis abun-
daret, dum sol ingreditur primum gradum Arietis, usquequo
veniat ad primum gradum Librae, et hoc per dimidium annum.
Et adhuc additur quod diluculum matutinum incipit per
mensem et dimidium ante ortum solis super terram, et crepus-
culum vespertinum durat per mensem et dimidium ultra
occasum solis, ita ut lumen solis appareat super terram ante
ortum et occasum per totum tempus dictum, sicut nobis in
aestate post occasum et in aurora apparet lux solis; quare
per longitudinem crepusculi et aurorae multum augmentabitur
calor, quia non habent noctem profundam nisi per tres menses
anni, ut certum est per omnes autores et singulos sapientes.
Item sol nunquam recedit ab eis, nisi per maximam solis de-
clinationem, quae fere est 24? gradus, quia aequinoctialis est

! The reference apparently is to the apocryphal work, De Plants, lib. ii 7
"Edy ó fpuos paxpórgra Tj ")uépq spoodyy iv Tj zwíjoe aio wal xaraxvpievg Tis
bypérnros obx Exe: 1d qvróv Surdpes QAAXa wal kapmobs wpod-yeyr.

3 It may be noted, once for all, that in the oldest MSS. of the Opus Majus,

Tempera-
ture Piodi-
fied by
mountain
ranges.

134 OPERIS MAJORIS PARS QUARTA.

Horizon eorum. Sed a nobis recedit sol per duplicatam
declinationem, scilicet fere per 48 gradus. Ergo ex hujusmodi
appropinquatione augmentabitur calor. Quapropter con-
cluditur secundum veritatem, quod loca sunt ibi inhabitabilia
propter calorem. Sed cum Plinius in naturalibus et Martianus
in descriptione regionum mundi invenerunt per experientiam
certam, quod regiones sub polis sunt temperatissimae in hoc
mundo, sicut ipsi dicunt, et allegant experientiam hominum
qui ibi fuerunt, non possumus negare quin ibi sint regiones
temperatissimae ; et quis concordabit tantam contrarietatem ?
Certe nullus, nisi optime sciat principia multiplicationis et
actionis specierum. Persuasionem ergo do ad hoc, quod
naturaliter secundum dispositionem loci respectu coeli et solis
oportet quod locus sit inhabitabilis propter frigus; et sic
currunt auctoritates permultae.

Sed propter accidentalem dispositionem loci, simul cum
aliquibus causis naturalibus, potest ibi aliqua regio esse
combusta, et aliqua temperata. Nam propter rationes de
longioribus pyramidibus, et propter longitudinem diei, et
propter magnitudinem crepusculi et aurorae, et propter
hoc, quod sol non recedit ab eis nisi per maximam solis
declinationem, si adjungamus causam accidentalem cum
his, forsan inveniemus quod quaerimus. Nam proculdubio,
secundum quod Plinius et Martianus! et alii docent, montes
maximi sunt ad ubera aquilonis, ut montes Riphaei et Hyper-
borei et alii, quorum altitudo immensa est, propter quam
possunt prohibere frigus aquilonis, sicut accidit in montibus
Italiae apud loca quae sunt inter solem et montes. Et simul
cum hoc additur, quod montes inveniuntur lapidei, et alii
coagulati in crystallum et salem, sicut videmus in pluribus
locis mundi, qui montes habent superficies magis politas et
aequales, propter quod ab eis potest fieri major et melior
reflexio quam a montibus asperis. Nam a superficie polita

those which are contemporary with Bacon, Arabic numerals are generally used ;
invariably so where the numbers are large.

! For Pliny's account of the enviable life of the Hyperboreans see Hist.
Natural. iv. 12. Martianus Capella was a writer of the fifth century. His
work, much read in the Middle Ages, was a scientific encyclopaedia bearing the
fanciful title, De nuptiis philologiae et Mercurii de sepiem artibus liberalibus.

MATHEMATICAE IN PHYSICIS UTILITAS. 135

et aequali et leni fit sensibilis reflexio, ut patet in speculis:
et hoc est, quia partes concordant in unam actionem, et non
dissipatur species, sed integra redit sicut venit; sed propter
inaequalitatem superficiei corporis asperi nulla pars concordat
cum alia, sed elevatior primo reflectit, et depressior secun-
dario, et sic tota species dissipatur nec venit integra, propter
quod non videmus per corpora aspera sed polita. — Bonitas
ergo reflexionis, quae potest inveniri in locis aliquibus circa
polos propter polituram superficierum montium, valet co-
operari ad calorem generandum simul cum altitudine montium.
Et ulterius considerandum est, quod montes habent varias
figuras, nam aliquis potest habere figuram ad modum specu-
lorum comburentium, et alius ad modum speculorum sphaeri-
corum vel columnarium vel pyramidalium, et ubi figura speculi
comburentis invenietur cum caeteris causis caloris, necesse
est ibi esse combustionem validam, ita ut nihil ibi vivere
possit, et sic intelligendus est Aristoteles cum ejus commen-
tatore. Ubi autem temperantur causae caloris et frigoris, et
penes altitudinem montium, et penes lenitatem superficierum,
et penes figuram, necesse est quod sit locus temperatus, et
sic intelligendi sunt Plinius et Martianus et caeteri experi-
mentatores.

CAPITULUM IV.

In quo investigatur complexio locorum, qui sunt in medio
mundi.

Mundi vero loca in quibus sumus per totam habitationem Climate of
usque versus finem tertii climatis sunt tolerabilis caloris. znq^ —
Hierusalem quidem est in tertio climate, sed ultra sub Tropico tropical
Cancri incipit torrida zona, et locus malae habitationis. Et von
propter hoc, quod via solis est inter duos Tropicos, aestimat
vulgus quod totus ille locus est combustus et quod nihil ibi
sit temperatum; et ideo aestimant, quod locus sub aequi-
noctiali circulo sit maxime combustus, quia sol super capita
habitantium bis transit in anno, et non attingit ad Tropica
nisi semel, ut in solstitio aestivali venit ad Tropicum Cancri,

Effect of
solar ec-
centricity.

136 OPERIS MAJORIS PARS QUARTA.

et in solstitio hyemali accedit ad Tropicum Capricomi. Sed
eundo de uno ad aliud transit bis super aequinoctialem
circulum, scilicet in principio Arietis et Librae, et hoc est
in principio veris et autumni, propter quod aestimatur
a multis, quod locus sub aequinoctiali sit maxime com-
bustus, et ad hoc faciunt rationes secundum multiplica-
tiones praedictas. Nam ibi saltefn bis in anno sunt pyramides
breviores et radii cadentes ad angulos rectos ac perpendi-
culares, et per consequens non franguntur ; redeunt in se ut
geminentur radii, et ideo videtur prima facie quod tota forti-
tudo actionis naturalis ibi concurrit longe plus quam alibi.
Sed constat nobis quod sub Tropicis sunt Aethiopes comi-
busti. Ergo videtur quod locus sub aequinoctiali circulo:
sit combustissimus, sicut vulgus ponit. Sed proculdubio
Ptolemaeus vult libro praedicto, quod locus ille sit temperatus
respectu Tropicorum. Atque Avicenna docet primo de
Animalibus, et primo artis medicinae, quod locus ille est
temperatissimus. Et propter hoc theologi ponunt his diebus,
quod ibi sit paradisus, et ideo vulgus indoctum errat in hoc
loco. Et tenebimus sententiam Ptolemaei ad minus, quic-
quid sit de opinione Avicennae et theologorum, quamvis leges
multiplicationis specierum hic concludant quantum possunt.
Sed causae fortiores sunt in contrarium, quas Avicenna
egregie assignat, videlicet quod declinatio solis magna est ibi,
et aequidistantes sunt distinctae et distant multum. . Nam
cum tota declinatio solis sit fere 24 gradus de Coluro,
fere 12 debentur signis aequinoctialibus, scilicet Arieti et
Virgini, Librae et Piscibus, et octo fere debentur Tauro,
Leoni, Scorpioni, Aquario, et ut fere quatuor debentur
Geminis, Cancro, Sagittario, Capricorno. Et ideo quando
sol est in signis ubi declinatio est fere 4 graduum, fertur
propter confusionem aequidistantium super eandem regionem
per 40 dies, et comburit ut in Tropicis. Sed minus in aliis
ubi declinatio est octo graduum, minime vero ubi est 12,
et hoc est apud aequinoctialem.

Alia causa est propter aequinoctium, quia aer tantum tempe-
ratur de nocte, ut non possit esse calor superfluus de die, et
propter hoc ibi est aequalitas aeris, et nobiles complexionum

MATHEMATICAE IN PHYSICIS UTILITAS. . 137

dispositiones, ut docet Avicenna. Nec est dubium quin locus sit
temperatus, sed an sit temperatissimus, non percipio adhuc. Et
ideo non est certificatum an paradisus debeat ibi esse. Quoniam
si eccentricitas solis sit prout mathematici ponunt, impos-
sibile est pure temperatum esse sub aequinoctiali. Nam una
pars eccentrici, quae vocatur oppositum augis descendit ad
terram per quinque partes semidiametri eccentrici magis quam
reliqua quae dicitur aux!. Et ideo quando sol venit ad oppo-
situm augis comburit terram omnino, ut nihil ibi vivere possit,
tum propter appropinquationem, tum propter casum radiorum
ad angulos rectos, tum propter confusionem aequidistantium
in quibus moratur super eandem regionem ut comburat eam ;
et hoc est quando sol est in
Sagittario et Capricorno et
Scorpione. Nam oppositum
augis est in Sagittario, et in
locis propinquis ei comburit
similiter et distemperat. Et
ideo sol distemperabit Li-
bram et Arietem. Nam jam
transivit medietatem eccen-
trici, quando venit ad initium
Librae, et Libra satis appro-
pinquavit ad oppositum augis, ut intemperiem caloris possit
causare, sicut patet in figura. Sed constat, quod paradisus
habet plenum temperamentum. X Horum autem certificatio
non est praesentis persuasionis.

FIG. 13.

CAPITULUM V.

Et ideo? redeo ad propositum dicens quod complexiones Influence

- es os . of climate
locorum mundi inveniri non possunt, nisi homo sciat leges 5, .n-

* Aux is the Arabian form of the word afsis: used together with the related Perament.
expression oppositum augis to denote the two points of an orbit which are at the
greatest or least distance from the centre of motion. In modern astronomy
the aphelion or apogee of the earth's or the moon's orbit would be called
summa apsis, or aux; the perihelion or perigee would be sma apsss, or opposi-
tum augis. It need hardly be mentioned that in the Hipparchian or Ptolemaic
theory the sun's orbit was supposed to be eccentric to the circle of the heavens.
3 J follow O, in making this the beginning of a new chapter.

138 OPERIS MAJORIS PARS QUARTA.

multiplicationum praesignatas, quoniam nec falsum vitabit,
nec verum poterit confirmare. Sed locus est principium
generationis, quemadmodum et pater, ut dicit Porphyrius.
Et nos videmus, quod omnia variantur secundum loca mundi
diversa non solum in naturalibus, sed homines in moribus ;
quoniam alios mores habent Aethiopes, alios Hispani, alios
Romani, et alios Gallici. Nam et Picardi, qui sunt veris
Gallicis vicini,habent tantam diversitatem in moribus et in
lingua ut non sine admiratione possit esse unde sit tanta
diversitas locorum propinquorum.

Sed quoniam res hujus mundi in diversis locis consti-
tutae, quantumcunque propinquae sunt, recipiunt conos
diversarum pyramidum venientium a toto coelo objecto eis,
ideo accidit infinita diversitas. Nam ad singula puncta terrae
veniunt coni pyramidum singularum, et quilibet punctus est
centrum unius Horizontis novi. Et ideo videmus, quod
duae herbae simul nascuntur de terra sine medio, et ideo
duo gemelli in ventre matris sortiuntur diversitatem com-
plexionis, ut postea mores habeant diversos, et sequantur
artes diversas, et occupationes difformes per totam vitam.
Et ideo virtutes coelorum et stellarum producunt ubique
diversas res in proprietatibus et naturis, et in rebus gene-
ratis secundum propagationem. Et non solum multiplicatio
virtutis coelestis operatur, sed patris et matris, quoniam
descinduntur virtutes in seminibus, ut docent medici. Et
praecipue ab anima matris continuatur multiplicatio virtutis
et speciei super foetum usque in complementum generationis
et nativitatis. Et cum puer in nativitate exponitur aeri novo
tanquam alteri mundo, tunc recipit conos pyramidum coele-
stium secundum singulas partes, et sic recipit impressiones
novas, quas nunquam dimittit, quia quod nova testa capit,
inveterata sapit Et tunc confirmatur complexio radicalis,
quae semper manet usque ad finem vitae, licet complexio
currens mutetur tota die. Et ad hanc radicalem complexionem
sequuntur inclinationes ad mores et ad scientias et ad linguas,
et ad quaecunque artificia et negotia, et ad omnem diversi-
tatem quam videmus in omnibus. Et si coeli dispositio sit
mala in conceptione et nativitate pueri, tunc coni pyramidum

MATHEMATICAE IN PHYSICIS UTILITAS. 139

laedunt complexionem, et per consequens inclinatur homo ad
malos mores et artes perversas, secundum diversitatem coelestis
constellationis : et si constellatio bona est, tunc complexio est
bona, et sequitur inclinatio ad mores bonos et scientias utiles :
et si mediocritas accidat in coelesti constellatione, tunc homo
mediocris est in omnibus quantum est ex naturali dispositione,
licet poterit se mutare per libertatem arbitrii, et per gratiam
Dei, et per tentationem diaboli et per bonum aut malum
consilium, maxime a juventute. Et nunc quae dixi in univer-
sali, possunt confirmari si tempus esset per exempla in singulis
rebus. Sed jam de combustione facta per crystallum et
vitrum et specula concava et alia quae ad oculum patent,
ostenditur nobis sensibiliter, quod fractiones et reflexiones et
hujusmodi multiplicationes possunt effectus naturales produ-
cere. Atque vulgatum est quod irides et cometae et plures
aliae impressiones inflammatae in aere, et circuli circa solem
et lunam, fiunt per hujusmodi multiplicationes radiorum, cum
aliam causam non possunt habere. Et sic de omnibus aliis,
licet non sit in singulis evidens, quia non omnium agentium
species sunt visibiles.

CAPITULUM VI.

In quo datur causa fluxus et refluxus maris per radios.

Et nunc ponam unum exemplum omnibus occultum, et The tides.
pono ubi minus videtur quod multiplicatio secundum lineas
et angulos determinatos requiratur, ut in re quam difficillima,
quae tamen per multiplicationem redditur satis plana; et est
de fluxu et refluxu maris. Alpetragius vero in libro suo de
motibus coelestibus aestimat, omnia corpora mundi praeter
terram moveri motu coeli primi, et hoc verum est: sed
secundum quod magis elongantur tardius moventur, et cum
majori impedimento. Unde aqua tardius et irregularius
movetur in sphaera sua, quam alia corpora mundi. Addit
ergo iste, quod hic motus facit fluxum et refluxum; sed non
placet hic, quia fluxus et refluxus sunt determinati et certi, et

Flood tide
when moon
is ap-
proaching
meridian.

140 OPERIS MAJORIS PARS QUARTA.

currunt sicut luna variatur in partibus coeli. Sed motus aquae
a motu coeli est confusus, et inordinatus, et irregularis propter
hoc, quod virtus coeli primi nimis elongatur ab ejus origine,
quando est in aqua, et ideo praevalet virtus aquae propria,
scilicet sua gravitas, quia nititur quiescere in loco suo, propter
quod non potest hic motus esse ita regularis et distinctus
temporibus certis penes accessus et refluxus ut nos videmus
in mari. Et ideo Albumazar in majori introductorio astro-
nomiae determinat omnes differentias fluxus et refluxus, et
narrat quod accidunt omni die et nocte secundum quod luna
est in diversis partibus sui circuli et respectu solis. Sed non
dicit nobis causam, nisi quod luna est causa, et quod quando
luna est in uno loco tunc est fluxus, quando in alio tunc est
refluxus. Propter quod considerandum est, quod quando
luna ascendit super mare alicujus regionis, ejus radii cadunt
ad angulos obliquos, ut quilibet qui novit casum angulorum
potest hoc scire. Et quia cadunt ad angulos tales, oportet
quod sint debilis virtutis, ut prius ostensum est. Et ideo
solum possunt elevare vapores a fundo maris, et ampullas
tumentes, et ingurgitantes aquas maris, ut expellantur a canali-
bus suis, quos vapores non possunt radii ad aerem extrahere
nec consumere propter debilitatem suam ; et ideo oportet ut
aqua fluat a sedibus suis, donec durat hujusmodi ebullitio
vaporum. Sed cum luna accedit ad medium coeli, cadunt
magis et magis radii ejus ad angulos rectos, et fortificantur
super corpus maris, ac extrahunt vapores ad aerem et con-
sumunt, unde debilitatur fluxus paulatim, secundum quod luna
appropinquat lineae meridiei ; et quando venit ad illam lineam
sunt vapores castigati et consumpti, ita ut statim dum luna
descendit ad aliam quartam coeli incipiat refluxus, quia ces-
sante causa cessat effectus. Et pono exemplum sensibile ad
istud. Nam in pulmento posito super ignem, ignis in principio
resolvit vapores, et facit eos exire orificium vasis: quando
vero fortificatus est et continuatur consumit vapores, et liquor
residet in fundo vasis. Nam universaliter calor debilis resolvit
vapores et non consumit, calor enim solis fortis consumit,
unde in nocte, et in mane, et in vespere fit resolutio vaporum
major quam in meridie, et tunc consumuntur. Et similiter

MATHEMATICAE IN PHYSICIS UTILITAS. I4I

calor naturalis in principio post cibum et potum resolvit vapores
fortiter et facit somnum. Sed quando invaluit diu super
cibum consumit eos, et homo evigilat. Nam vapores resoluti
obstruunt vias spirituum et calorum venientium ad sensus
a corde et capite, et ideo oportet ut quiescant sensus, et hoc est
dormire. Et sic de omni virtute agente, cujus est proprium
resolvere et consumere. Primo resolvit dum debilis est, et
postea fortificata consumit.

Et dicit Albumazar et alii concordant, quod luna facit Explana-
effectum consimilem in quartis oppositis. Nam dum luna est don oí a c
in quarta inter oriens et meridiem fit fluxus in illa quarta et in when moon
quarta opposita, quae est inter occidens et angulum terrae, et opposite
dum resolvit quando est in quarta inter angulum medii coeli quarter.
et angulum occidentis. Similiter refluit tunc mare ab angulo
terrae usque ad angulum orientis. Sed non dant causam
hujus rei; solum dicentes quod luna effectum in quartis
oppositis habet consimilem. Sed quomodo operabitur luna
ubi non est? et constat, per medium terrae non transeunt
ejus radii. Ad hoc autem juvat nos multiplicatio reflexa.

Nam proculdubio coelum stellatum aut nonum est densum per
totum, nam visus noster stat ad alterum illorum, sed non
terminatur visus nisi per densum, ad quorum alterum multi-
plicati radii lunae existentes in quarta una reflectuntur ad
quartam oppositam, et sic virtus lunae est directa in quarta
una, et ejus reflexio in eodem tempore in quarta opposita.
Solis autem virtus est nimis potens, et ideo ad quoscunque
angulos cadat potest consumere vapores cito, quos resolvit.
Aliarum vero stellarum virtus est debilis propter earum elon-
gationem a terra, quamvis multo sint majores quam luna sit,
et propter debilitatem non faciunt hujusmodi operationem,
quamvis ad angulos diversos cadant earum radii ut lunae.
Nec tamen hic intelligo, quod sit ebullitio cum fervore caloris
ut in liquore super ignem, sed similitudo est quantum ad
resolutionem vaporum quam facit virtus lunae, aut per radios
lucis, aut per radios suae naturae substantialis, aut per
utrosque. Quando enim de nocte per radios stellarum, et in
mane et in vespere per solem fit resolutio vaporum de terra
et aqua, non propter hoc ebulliunt cum fervore, et tamen in

Influence
of stellar
rays on
health and
disease.

142 OPERIS MAJORIS PARS QUARTA.

maxima copia elevantur, et sunt nubes infinitae. Et ideo non
oportet ut aquae maris ferveant in fluxu.

CAPITULUM VII.

In quo multiplicatio virtutum comparatur ad sanitatem et
infirmitatem corporis humani.

Mira ergo potestas est hujus multiplicationis cum omnia
fiant secundum leges ejus et occulta et manifesta. Et horum
notitia non solum necessaria est in scientialibus, sed utilitates
magnas nobis praestat in corpore et in anima, si diligenter
investigemus, nam valde utile est scire has leges in conserva-
tione sanitatis. Quoniam cum non possumus vitare omnes
incidentias specierum et virtutum rerum malarum et nocivarum
sanitati, nec possumus semper aptare corpora nostra ad
pleniores casus virtutum venientium a rebus salutiferis, semper
tamen debemus esse solliciti ut rerum nocivarum virtutes non
capiamus principales, scilicet rectas fractas et reflexas, sed
accidentales si possumus, et si non possumus vitare omnes
principales, saltem vitemus rectas, et si non omnes rectas,
declinemus casum ad angulos rectos, et si non possumus saltem
caveamus pyramidis breviores. Et hae considerationes habent
locum, quando homo exponitur coelestibus impressionibus
nocivis, ut soli in aestate, et lunae de nocte, quae exhaurit
corpora. Unde multi mortui sunt non caventes sibi a radiis
lunae. Et praecipue quando homo exponitur radiis Saturni
et Martis, quoniam isti duo inducunt laesionem magnam et
corruptionem in rebus, ut experientia docet. Similiter quando
homo recipit species a locis corruptis et immundis, et quando
multiplicantur species leprosorum et infirmorum et maxime
illorum qui habent morbos contagiosos, nec non eorum qui
habent malas complexiones, et praecipue mulieris menstruatae ;
quoniam si ipsa aspiciat speculum novum, apparet nubes san-
guinea in speculo ex violentia menstrui inficientis, ut Aristoteles
dicit in libro de somnis et vigilia secundo!, et de serpentibus

1 De Insomniis, cap. a Eray trav karayyvíoy rais ^yoraitl. yvopdvew dpBAdbwouw
els 10 wáromrpor *yiveras Td tmwoARs ToU ivómrpov olov ve$éA5 alparwors.

MATHEMATICAE IN PHYSICIS UTILITAS. 143

et aliis rebus venenosis. Et maxime considerandum est
istud, quando homines et animalia nascuntur, et habent desi-
derium nocendi et animum malignandi. Nam ad hoc reducitur The evil
fascinatio, unde quod habet virtutis capit ex hac causa, ^
quoniam proculdubio tunc fit fortior impressio, eo quod
natura obedit cogitationibus animae et desiderio, et excitatur
ad fortiorem operationem, sicut Avicenna docet octavo de Ani-
malibus et quarto de Anima per exempla et experientias varias,
et certum est hoc. Unde Solinus narrat in libro de mirabili-
bus mundi !, quod in quadam regione aquilonari sunt mulieres
habentes geminas pupillas in oculis, quae cum irascuntur
interficiunt homines solo visu, de quibus dicit Ovidius, nocet
pupilla duplex. Et maxime cavendum est ne partes nobiliores,
sicut oculi et facies, exponantur hujusmodi speciebus: nam
vidi medicum excaecari dum intendebat curae habentis infir-
mitatem oculorum, propter multiplicationem speciei venientis
ab oculis patientis. Oportet enim in istis nocivis uti magnis
cautelis, et maxime quando malum est grave vel intolerabile..
Sicut Alexander doctrina Aristotelis ut historiae narrant,
basilisci speciem venenosam positi super murum civitatis ad
interficiendum exercitum per corpora magna polita retorsit in
eandem civitatem, ut per proprium destrueretur venenum.
Et per contrarium aptatio corporis ad species rerum salubrium
recipiendas, quanto efficacius potest homo, multum est utilis
per omnem modum tam sanis quam infirmis.

CAPITULUM VIII.

De infinitate Materiae ?.

Quoniam autem diutius tenui persuasionem ut ostenderem, Matter

quomodo in rebus mundi a parte suorum efficientium et is not oF

! Solinus probably lived in the third century a.p. His work, Collectanea
Rerum Memorabtilium, is in the main a recast of Pliny. It is from his work
rather than from that of Pliny, that such compilers as Isidore and Martianus
Capella derived their information.

! Cf. Opus Tertium, cap. 38, where this subject is fully treated. It is discussed
at still greater length in that part of. Bacon’s encyclopaedic work, entitled
Commuma Naturalium; copious cxtracts from which are given by Charles,

PP. 369-389.

144 OPERIS MAJORIS PARS QUARTA.

generantium nihil potest sciri sine geometrica potestate, nunc
volo breviter pertransire a parte materiae illorum, ostendendo
quod necesse est verificare materigm mundi per demonstra-
tiones in lineis geometricis explicandas, si potenter volumus
errores infinitos evacuare. Multitudo vero philosophantium
non solum in forma propria philosophiae, sed in usu theologiae
dicit et asserit, quod una est materia numero in omnibus rebus
et quod solum est diversitas a parte formarum.

! Et arguit ad hoc quod si excludamus per intellectum a
materia coeli et lapidis formas eorum non est assignare per
quod differant quod actus a forma dividit, ut dicit Aristoteles
septimo Metaphysicae. Et in primo Physicorum ? dicit quod
omnia sunt unum in materia sed differunt in forma: et in
secundo Metaphysicae dicit quod nihil est in materia distinc-
tum. Etsi materia plurificaretur sicut forma, quod materia
erit communis et praedicabilis de pluribus sicut forma. Et
allegant quod omne universale naturam formae habet. Nam
partes definitionis ut dicit Aristoteles septimo Metaphysicae
sunt formae?; sed partes definitionis sunt per genus et dif-
ferentiam et componunt speciem; ergo species est forma
tantum sicut genus et differentia. Et constat quod reliqua
duo universalia Porphiriana, id est proprium et accidens, sunt
purae formae, quia sunt de predicamentis accidentium. Ergo
omne universale est forma; et ideo materia non habebit
rationem universalis sed singularis erit et una in numero
omnibus. Et per hujusmodi fundamenta et auctoritates male
translatas nituntur persuadere. Sed hic est error infinitus.
Nullus enim major est in veritatibus speculativis, quia hoc
dato impossibile est servare rerum generationem, et igno-
rabitur totus decursus naturae. Sed quod plus est, si hic
error discutiatur, invenietur valde propinquus haeresi, aut
omnino haereticus, quo nihil magis sit profanum, quia sequitur
necessario quod materia sit Deus et creator. Quod volo ad

* From here to nituntur persuadere omitted in J. It has been restored from O.

2 4j 8 BAN &yvocros Kad’ abrfv. Met. vi. 10, $ 13. Cf. Natural. Awscult. ii. 1,
$$ 11, 12. The passage in Natural. Auscult. i. 4, § 1, appears to refer to the
opinion of others.

* "AAAG roU Aó^yov uépn rà ToU elbovs uóvoy toriv, Met. vi. 10, $ 12; cf. 12,
§§ 4-9; also vii. a, § 8.

MATHEMATICAE IN PHYSICIS UTILITAS. 145

praesens ostendere solum per rationes geometricas ut promisi,
quamquam rationes naturales et metaphysicae sunt copiosae
et efficaces, de quibus alias grandis sermo potest fieri. Et
necesse est propter sensum vulgi, qui violentus est ubique.

Dico ergo quod si materia potest esse una numero in Ifso, it

duobus, eadem ratione in tribus et in infinitis. Nam consimile womens
argumentum facit Aristoteles in capite de vacuo in quarto infinite
physicae, dicens !, quod si aliquid unum et idem potest esse in pod be
duobus, tunc potest esse in tribus, et sic in infinitis; sed quod eat.
potest esse in infinitis habet infinitam potentiam. Ergo materia
est infinitae potentiae quare et essentiae infinitae, ut probabitur,
et ideo erit Deus. Sed consequentiae dictae non possunt con-
tradicere, scilicet quod sequatur quod materia eadem possit
esse in infinitis si essent, et ideo concedunt ei potentiam
infinitam sed negant essentiae infinitatem, quia nihil habet
essentiam infinitam nisi Deus. Et cum arctantur in hac parte
circa infinitatem potentiae, incipiunt verbis vacillare, dicentes
quod potentia materiae est infinita, sicut potentia continui.
Sed istud nihil est, quia haec potentia non est respectu actus
infiniti, nec respectu infinitorum simul et in actu consideran-
dorum, et ideo haec potentia non est actu infinita, sed potentia
tantum. Sed potentia infinita in tantum datur materiae
secundum dictam positionem, ut si essent actu infinita, posset
materia eadem numero esse actualiter in illis infinitis. Ergo
actualiter et intensive habet potentiam. infinitam. Caeterum
potentia continui non est similis potentiae divinae: quia
potentia divina non habet arctationem et limitationem, quan-
tum ad actualem existentiam in. pluribus et in infinitis. Ad
quam non se extendit potentia continui, sed materiae con-
ceditur illa eadem existentia in pluribus, et sic in infinitis, per
auctoritatem et. demonstrationem Aristotelis Quapropter
potentia materiae non est similis potentiae continui sed
divinae.

Caeterum aliter vacilant in hac parte dicentes, quod
potentia materiae est passiva, et potentia divina activa. Hoc
enim excluditur multis modis. Nam potentia passiva dicitur
respectu transmutationis suscipiendae ab agente. Sed potentia

! Nat. Auscult. iv. 8, $ 13.

VOL. I. L

Mathe-
matical
disproof.

F Potentia proportionalis ipsi E.

146 OPERIS MAJORIS PARS QUARTA.

existendi in pluribus non hoc respicit, et ita differunt. Item
potentia existendi in pluribus simul quae non est arctata nec
limitata attestatur summae nobilitati, et ideo datur Deo et
animae quae est in pluribus partibus corporis tota. Sed Deo
et animae non datur propter aliquam rationem patiendi, ergo
nec materiae. Item quaecunque sit haec potentia, sive activa
sive passiva, oportet quod substantia materiae sit infinita si
haec potentia est infinita; et si hoc, tunc materia est Deus
vel aequalis Deo, quia nulla res habet substantiam et poten-
tiam infinitam nisi Deus.

Sit ergo potentia infinita A linea, et linea B sit ejus finita
substantia, et C linea sit potentia aliqua finita, quae sit pars
potentiae infinitae. De
A Potentia infnta. | Omni enim quanto dato
| contingit partem per intel-
lectum abscindere, ut vult
Aristoteles primo Coeli
D |Substantia potentiae C. et Mundi, et D linea sit

B |Substantia ejus finita.

C | Potentia finita pars ipsius 4.

- o — —

E |Substantia aequalis ipsi B substantiae substantia ejus quod est
C potentia; multiplicetur

— ————, ergo D quousque aggre-
G | Potentia major quam F. getur substantia quae sit
aequalis ipsi B, hoc enim
est possibile, quoniam D et 2 sunt finita, et haec substantia sic
aggregata sit E linea. Similiterque multiplicetur potentia C
in tantum ut excrescat potentia proportionalis ipsi E, et sit F
linea, hoc enim est possibile, quia C et D sunt finita, et ideo
potest ad utrumque addi in tantum, ut aggregata sint propor-
tionalia, sicut Cet D. Sed F potentia est finita, quia ex aggre-
gatione finita nascitur, et habet substantiam £ aequalem ipsi
B substantiae, cui correspondet A quod est potentia infinita ;
ergo potentia F finita et A potentia infinita habebunt aequales
substantias. Quare finitum et infinitum aequabuntur, quia
aequalibus substantiis debentur aequales potentiae, et pars
toti aequabitur, quoniam F est pars A sicut C, ut positum fuit
a principio de C, et F crescit ex aggregatione finita C, quare
F erit pars A, et ita pars aequabitur toti.
Et ex hoc ulterius sequetur, quod pars habebit majorem

MATHEMATICAE IN PHYSICIS UTILITAS. 147

essentiam, et plus de essentia quam totum. Quoniam acci-
piatur aliqua potentia finita major ipsa F, et resecetur a
potentia infinita quae est A, et sit G linea. Oportet ergo
quod G potentia, cum sit major quam 7, habeat plus de
substantia, seu fundetur in majori et nobiliori essentia, quam
fundatur F potentia. Sed 7 habuit aequalem essentiam ipsi
A, ut probatum est. Ergo G habebit majorem quam 4; et
ita parti respondet plus de essentia et nobilius quam toti, quod
est impossibile. Et etiam sequetur, quod finitum habebit plus
de essentia sibi respondente quam infinitum ; et omnia haec
sunt impossibilia.

Item nullum infinitum potest habere potentiam finitam.
Ergo per oppositum nullum finitum potest habere potentiam
infinitam. Antecedens probatur per consimilem demonstra-
tionem priori, quia sit 2 linea illud infinitum, et 4 linea sit
illa potentia finita. Accipia-
tur aliquod finitum vel pars
ipsius a et sit c linea. Ergo
habebit minorem potentiam ; |
et sit d linea. Multiplicetur © | Substantia finita pars ipsius a.
ergo d quousque aequetur 4| Potentia ipsius c.
ipsi 6, quod possibile est, quia
utrumque est finitum ; et ideo
tantum potest addi ad d, ut Substantia potentiae e.
aggregatum sit aequale po-
tentiae quae est 4; et sit illud aggregatum e linea. Similiter
ergo multiplicetur c, et addatur ei quousque poterit habere
potentiam illam quae est e, et illud aggregatum sit f linea ;
hoc enim bene possibile est, quoniam c substantia et 4
potentia ejus sunt finitae, et ideo si ad 4 tantum potest
addi, ut fiat e potentia major quam d ad c, tantum potest addi
de substantia ut aggregatum excrescat, cui e potentia erit
proportionalis, et illud aggregatum habebit illam potentiam.
Sed e potentia est aequalis potentiae 4, ut probatum est.
Ergo f quod est finitum, quia ex aggregatione finiti et infiniti
nascitur, habebit potentiam aequalem ipsi a, quod est in-
finitum. Quod patet esse omnino impossibile, et sequetur
ex hoc, quod pars aequetur toti, scilicet 7^ ipsi A, et etiam

L 2

8 | Substantia infinita.

b | Potentia finita. |
|
|

e | Potentia aequalis ipsi 5 potentiae. |

Are the
celestial
spheres
con-
tinuous ?
A line
traversin.
their

148 OPERIS MAJORIS PARS QUARTA.

quod pars est major toto, ut patuit in priori ratione; et quod
finitum habebit majorem potentiam quam infinitum, ut patet
in terminis, et haec omnia sunt impossibilia.

Item si potentia materiae est infinita, sit haec potentia per
A lineam designata infinitam, quae si dividatur in puncto a,
tunc partes divisae sunt aequales, quia utraque ab ipso puncto
a vadit in infinitum. Signetur ergo punctus 5, et puncta c

4 a SS EMLAEEEEEEEX
f d a b c

etd. Partes ergo divisae sunt aequales, sed 6 a f in infinitum
decurrens est major quam a f per a). Ergo ^c linea in in-
finitum extensa, est major quam a f. Ergo est major aequali
af,quod est adc. Ergo pars est major suo toto. Quapropter
impossibile est potentiam materiae esse infinitam. Nec est
haec demonstratio applicanda divinae potentiae, eo quod non
est divisibilis, sicut potentia materiae corporalis. Sicut vero
radices a parte efficientis traxi ad exempla rerum naturalium,
sic similiter possunt aliqua notari quae consequuntur materiam
in rebus mundi, in quibus miranda geometriae potestas
elucescit. Nam si materia mundi una esset numero, oporteret
necessario, quod forma esset una numero, sicut posuerunt
Parmenides et Melissus, contra quos Aristoteles primo libro
Physicae et libro de generatione se opponit. Certo enim ex
unitate materiae numerali sequitur illa potentia falsissima,
quam prius eliminavi per leges fractionum.

CAPITULUM IX.

An corpora se tangant in puncto.

Quoniam autem pro hac positione sunt geometricae falsi-
graphiae, quae omnem hominem possunt perturbare, ideo volo
aliquas inferre. Si enim corpora sint diversa in hoc mundo,
ut coelum et elementum, et imaginemur lineam transire per

® medium eorum, non secabunt illam lineam in diversis punctis,

boundaries quia tunc longitudo linearis esset in medio, et ita superficialis

MATHEMATICAE IN PHYSICIS UTILITAS. 149

latitudo et profunditas corporalis, et sic corpus tertium a coelo is cut in

et elemento esset inter ea, quod falsum est. Ergo in eodem

puncto intersecabunt lineam illam. Sed continua sunt quorum points.

terminus est idem. Ergo sunt continua. Multorum et maxi-
morum virorum fuerunt hic responsiones variae, et omnes
adhaerebant isti parti, quod in diversis punctis intersecarent
vel naturaliter vel mathematice, vel utroque modo, distin-
guentes inter continuitatem naturalem et mathematicam
secundum Averroem in quinto Physicae. Sed istud nihil est;
necesse enim est quod in eodem puncto lineae intersecent se,
ut sit virga ferrea imaginata; sed ille punctus non continuat
corpora secantia, et ideo non sunt continua, sed partes virgae
vel lineae transeuntis, de quarum continuatione non potest
concludi corpora esse continua per quae transit virga ; sed si
in diversis punctis virgae daremus sectionem, tunc necessario
pars virgae, quae est corpus, esset media; et hoc est impossibile,
Item argui potest subtilius, quod quibuscunque corporibus in
hoc mundo positis, si sint diversa et contigua, non continua,
supraponatur vel supponatur tertium corpus, ad quod aequi-
distanter ducantur lineae duae a mediis punctis datorum
corporum. Siergo illae lineae terminentur ad puncta diversa
in tertio corpore, tunc pars illius corporis est media inter eas,
et aequaliter semper distant et appropinquant, et ex altera
parte in medio duorum corporum distabunt per corpus inter-
positum, quod omnino est falsum. Ergo continuabuntur ad
unum punctum in tertio corpore, et eadem ratione ad extremi-
tates suas in conjunctione corporum positorum, quapropter
unum corpus erunt quae posita sunt, quia unus punctus non
potest esse in diversis corporibus. Et hic turbati sunt multi,
nec est tempus renovandi opiniones singulorum, praecipue cum
veritas pateat. Si dicatur quod in eodem puncto corporis
terminabuntur illae lineae nec sint aequidistantes, quia non
distant in aliquo, eo quod corpora simul posita sunt sine medio,
et quia omnis distantia tollitur, oportet quod ad unum punctum
in tertio corpore terminentur, et quoniam duo puncta non
habent aliquid longitudinis, quoniam non sunt quanta, ideo
non faciunt distantiam aliquam sicut nec unus punctus. Unde
tantam indivisionem important duo puncta simul juncta, sicut

two

adjacent

But two
such points
occupy no

more space
than one.

A mathe-
matical
line and

a physical
line differ
only in the
point of
view.

ISO OPERIS MAJORIS PARS QUARTA.

unum per se positum, quia puncto addito puncto non crescit
quantitas, et ideo possunt remanere diversa puncta in ex-
tremitatibus duarum linearum simul junctarum in corporibus
duobus sine medio, quamvis ad unum punctum in tertio
corpore terminentur. Sed si in illis corporibus simul junctis
ducantur duae lineae ab illis punctis infra corpora et descendat
una linea super extremitates earum ad angulos rectos, necesse
est per xiv primi Elementorum Euclidis quod lineae extensae
in corporibus sint una linea continua. Ergo et corpora similiter,
nam talis est sententia illius propositionis.

Et ex hac propositione deceptus fuit Averroes quinto
Physicae, et omnes sequentes ipsum, volentes quod una sit linea
mathematica, et per consequens unum corpus mathematicum,
quamvis diversa sint naturaliter. Nam, ut dicit ibi, contiguitas
naturalis transit in continuitatem mathematicam ; sed hoc est
impossibile, nam quantitas mathematica et naturalis idem sunt
secundum esse, et secundum rem, sed differunt solum secundum
considerationem, quia geometer considerat lineam naturalem,
non prout est in naturali materia, et ideo dicitur mathematica.
Et hanc eandem lineam considerat philosophus naturalis, ut
est in materia naturali, sicut in ferro, vel lapide, vel alia re
naturali. Et quia eadem res est secundum esse, et secundum
veritatem existendi, naturalis et mathematica, ideo si hic esset
linea una vel corpus unum mathematice, tunc eodem modo
esset naturaliter. Dico ergo quod hic sunt lineae secundum
veritatem diversae et corpora similiter, nec hoc repugnat

intentioni Euclidis. Nam non vult quod sit una continua,

sed quod quantum ad angulos rectos faciendos duae tantum
faciunt quantum una, postquam illae duae jacent in eadem
directione longitudinis ac si ibi essent duae partes ejusdem
lineae continuatae; et sic intendit in pluribus aliis locis ubi
accipit unam pro duabus, cum idem faciat ad suum propositum
una sicut duae. Et hoc est quando loquitur de communi
differentia superficierum vel communi sectione, eam enim
vocat unam lineam, cum tamen in veritate sint duae: sed una
obtinet earum potestatem, et ideo facilius loquimur de una,
quam de duabus.

5i tamen objiceretur, quod si quis ponat diversitatem in

MATHEMATICAE IN PHYSICIS UTILITAS. 15I

corporibus, accipiantur igitur duae tabulae planae superficiei
et circularis figurae, et elevetur una ab altera sub eadem
figuratione, tunc aer citius repleret partes exteriores inter eas
quam centrales. Quapropter esset vacuum in partibus interior-
ibus ad tempus. Et hic multae stultitiae solebant dici. Nam
aliqui dixerunt aerem in instanti moveri usque ad centrum ex
lege naturae universalis, ne fieret vacuum; alii quod omnia
corpora tangentia se in aere vel aqua habent superficies
humidas, ut Aristoteles dicit secundo de Anima, et hanc humi-
ditatem aeris vel aquae interceptam posuerunt rarefieri subito
per totum, ne fieret vacuum. Sed hoc quod dicitur, ne fiat
vacuum, est pura negatio!. Nulla vero negatio pura est causa
afhrmationis; et ideo responsiones hujusmodi sunt falsae.
Propter quod dicendum est quod sub eadem figuratione non
potest una ab alia elevari, sed oportet quod declinet una cum
elevatur ab alia, et sic aer ingreditur paulatim. Hoc de plano
potest quilibet experiri in scypho vitreo demisso in vas plenum
aqua; nam pro mundo non potest elevari in eadem figuratione
suarum partium. Cujus causa est, ut aqua ingrediatur ejus
locum paulatim. Et haec est affirmativa ad quam ex conse-
quenti excluditur vacuum.

Si ergo oportet quod sint plures materiae corporales et Refutation
plura corpora in hoc mundo, cum quodlibet corpus est divisibile ot cory of
in infinita, non tamen propter hoc mundus erit compositus Demo-
ex partibus materialibus infinitis, quae vocantur atomi, ut erus.
posuerunt Democritus et Leucippus, quorum positione fuit
Aristoteles magis impeditus et omnes naturales, quam per
aliquid aliud erroneum. Quod tamen per geometricam potes-
tatem eliminatur omnino ; nam nihil fortius potest argui contra
hoc, quam quod tunc diameter quadrati et latus essent com-
mensurabilia, id est, haberent communem mensuram, scilicet
aliquam partem aliquotam pro communi mensura, cujus
contrarium Aristoteles semper docet. Et patet per demonstra-
tionem ex ultima parte septimae propositionis decimi libri
Elementorum, per quam demonstratur, quod si aliqua mensura

! A striking instance of Bacon's positivity. No natural action takes place in
order that some other action may not follow, The remark is repeated in the
next chapter.

152 OPERIS MAJORIS PARS QUARTA.

ut pes vel palmus mensuret costam, non mensurabit diametrum,
nec e contra; ut si diameter sit ex decem pedibus non erit
costa ex aliquot pedibus. Et non solum sequitur ex hac
positione, quod essent commensurabilia, sed aequalia. Quod
patet evidenter in hac figura. Nam si latus habeat decem

atomos, vel duodecim, vel plures,

tunc trahantur tot lineae ab illis

/ atomis ad totidem in opposito
latere, et latera quadrati aequalia
sunt; quapropter tot lineae occu-
pabunt totam superficiem quadrati! ;
et ideo cum diameter transit per
illas lineas, et non possunt plures

Á assignari in quadrato, singulas capiet

atomos a singulis lineis, et ideo non
plures erunt in diametro, quam in
costa, et sic habent partem aliquotam pro communi mensura,

et tot partes habet costa sicut diameter, quorum utrumque
est impossibile.

Fic. 14.

CAPITULUM X*.
De figura mundi.

Proof that — Quoniam vero necesse est corpora mundi esse plura, et
the world is

spherical. divisibilia, et quanta, oportet quod figurationem habeant

debitam, ad hoc ut mundus consistat. Figuratio vero est

passio materiae, et invenitur in rebus ratione materiae, sicut
Revolution et quantitas. Nam figura uno modo est quantitas clausa
ober figure lineis; alio modo dicitur ipsa clausio quantitatis. Necesse
would est vero mundum extra habere figuram sphaericam. Nam
vacuum, Quaecunque alia detur, accidet vacuum vel possibilitas ad

* The fallacy lies in supposing that lines could occupy superficial space ; as

Bacon would have seen if he had tried to occupy the surface of the square with
small circles or squares.

* Cf. Opus Tertium, cap. 40.

MATHEMATICAE IN PHYSICIS UTILITAS. 153

ipsum. Sed natura nec sustinet vacuum, nec possibilitatem
respectu ejus. Si enim esset alicujus figurae angularis, tunc de
necessitate accideret vacuum in moto suo: nam ubi modo esset
unus angulus nihil esset donec alius angulus ibidem veniret !.
Figurae autem aliae quae maxime competerent essent vel ovalis
figurae vel consimiles ei vel lenticularis et ei conformes se-
cundum Aristotelem, libro Coeli et Mundi. Sed negat coelum
habere hujusmodi figuram, sed causam non exprimit. Figura
vero lenticularis est figura illius leguminis quod vocatur lens.
Habet enim laterales superficies gibbosas, deficiens a vera
sphaericitate propter breviorem diametrum quae transit per
illa latera. Si vero esset figurae ovalis, aut pyramidalis
rotundae, aut columnaris, aut alicujus hujusmodi, et moveretur
super breviorem diametrum, adhuc accideret vacuum in actu,
si vero super longiorem, non accideret vacuum in actu, sed
possibile esset vacuum accidere, quoniam tanta esset possi-
bilitas in mundo, quantum ad figuram ut moveretur super
breviorem diametrum, sicut super longiorem. Si vero esset
lenticularis figurae vel casealis, vel hujusmodi, et moveretur
super longiorem diametrum, accideret vacuum in actu, et si
super breviorem, non accideret in actu sed possibilitas relin-
queretur. Nam aeque possibile esset mundo, quantum est de
se, ut moveretur super unam diametrum sicut super aliam.
Nec potest dici quod si esset ovalis figurae moveretur semper
super longiorem, et si lenticularis moveretur super breviorem,
ne vacuum accideret. Refellendum est istud sicut superius,
scilicet quod impossibile est quod pura negatio sit causa
alicujus affirmationis; sed, ne sit vacuum, pura negatio est.
Et ideo oportet quod mundus sit sphaericae figurae, in qua Equality
sola corporali sunt omnes diametri aequales, ut possit libere ober. of
volví secundum omnem diametrum, et sic nullum sequitur
inconveniens. Similiter intra necesse est, ut sit sphaericae
figurae et concavae: nam planae figurae non potest. Quoniam

1 This is from Aristotle, De Coelo, ii. 4 el ydp éora: ebOd-ypappos, covpBnoera
xai rówov fw elvai xal cya xal xévor. KÓxAq "yàp arpedónevov 76 eb0v-ypaypoy
obdéwore Thy abriy ipdge xópar, dAA'! Exov apdrepow ij» a&ipa, viv ob« Cora, kal ob
vüy oüx tor, wéXiw (ora: 3d riy wapdédAafi Taw yout. ‘Opolws 82 why el rc dAAo
cxfjpa yévorro pi) fcas (xov rds de rob péaov "ypappás, olov paxoades )) go«bis.

I54 OPERIS MAJORIS PARS QUARTA.

ducantur a centro terrae tres lineae et una ducatur perpen-
diculariter ad superficiem coeli, ut a 4, illa erit brevior aliis
per xviii primi Elementorum et per xxxii ejusdem. Ergo
coelum non aequaliter distabit a terra: sed oportet ut sit
ejusdem naturae in omni parte. Ergo quaelibet nata est
elongari aequaliter a terra. Nec potest esse convexa interius,

b

a a
CENTRUM TERRAE CENTRUM TERRAE

Fic. 15.

ut patet per viii tertii libri, quae dicit quod a puncto extra
signato si ducantur ad circulum plures lineae, illa quae caderet
in diametrum esset brevior aliis. Ergo relinquitur, quod si
a centro terrae ducantur tres lineae ad convexitatem coeli,
una erit brevior, scilicet illa, quae est perpendicularis super
sphaeram, ut patet in figura, et ideo coelum non aequaliter
distaret a terra, quod tamen oportet ut dictum est. Et iterum
si esset mundus convexae figurae, intra non esset natus
continere omnia: sed mundus natus est continere omnia.
Quod si non potest esse planae figurae, nec convexae, oportet
quod sit concavae, cum non sit alia. Sed concava potest esse
multis modis, aut sphaerica, aut columnaris, aut pyramidalis,
aut lenticularis, aut alia multiplex. Non est autem possibile,
quod sit alicujus nisi sphaericae concavae, propter hoc quod
in hac sola figura sunt omnes lineae aequales, quae ab uno
puncto ducuntur ad superficiem. Non enim est in aliis pos-
sibile dare punctum, a quo omnes lineae ductae ad superficiem
aequentur: nam diametri sunt inaequales. Sed oportet partes
coeli aequaliter distare a terra, propter naturae aequalitatem.
Ergo de necessitate erit sphaericae.

Item inter omnes figuras isoperimetras sphaera ipsa maxime

MATHEMATICAE IN PHYSICIS UTILITAS. 155

capit, sicut proponit viii propositio libri Isoperimetrorum !. Of figures
Superficiales vero figurae dicuntur isoperimetrae, ut triangulus sarfece the
et quadrangulus, et circulus, quando latera trianguli extensa tbe ereatest
in continuum et directum tantum habent in longitudine, content.
quantum latera quatuor quadranguli extensa et quantum
circumferentia circuli si extenderetur, et sic de quibuscunque
figuris superficialibus. Unde dicitur isoperimeter ab ico» quod
est aequale et wepi quod est circum, et petpév quod est men-
sura, quasi aequalis circummensurationis. Et inter omnes
istas superficiales isoperimetras circulus maxime capit, sicut
dicit vii propositio de isoperimetris. Corporales vero tunc
dicuntur isoperimetrae, ut sphaera, cubus, et columna, et
quaecunque, quando superficies sphaerae extensa in con-
tinuum et directum tantum habet in longum et latum
quantum superficies sex ipsius cubi, et quantum superficies
columnae rotundae, et sic de aliis. Sed inter omnes istas
sphaera maxime capit, sicut demonstratur in libro supra-
dicto. Cum ergo coelum debet omnia continere, oportuit
quod esset sphaericae figurae. Item nobilitas mundi, et hujus
figurae dignitas correspondent. Nam haec figura est prima
figurarum corporalium, quia una superficie contenta, omnes
autem aliae habent plures. Ergo competit corpori primo ut
coelo. Item haec est simplicissima, quoniam sine angulis et
cono et lateribus et omni diversitate. Ergo debetur corpori
simplicissimo, quod est coelum. Item aptissima est motui. Spherical
Ergo debetur primo mobili. Item est elongata ab occasionibus adapted
et impedimentis, quia non habet angulum in quem aliquid for motion..
offendat. Ergo maxime competit corpori quod impedimentum
et occasionem offensionis capere non potest. Item est per-
fectissima, quia nihil addi potest ei; sed omnibus aliis potest
aliquid addi. Ergo corpori debetur perfectissimo.

Quod autem corpora contenta in coelo habeant figuram The

. . . - elements
sphaericam, hoc demonstratur de aqua, quae jacet in medio, viui the

! The author of this book is Zenodorus, who probably belongs to the genera-
tion succeeding that of Archimedes. Its principal propositions. fourteen in
number, are to be found in the fifth book of Pappus, and also in Theon's Co»-
mentary on the Almagest of Ptolemy. See Cantor, vol. i. pp. 308-9, and 379-80.
Cantor shows, voL i. pp. 605 and 635 that Zenodorus was known to the Arabs.

e

156 OPERIS MAJORIS PARS QUARTA.

heavens of ut per consequens pateat de aliis. Ducantur lineae undique
MUNI ad superficiem aquae a centro terrae, planum est quod aqua
Water. | Semper currit ad inferiorem locum propter suam gravitatem
ut videmus. Ergo si una illarum esset brevior altera, aqua
curreret ad extremitatem ilius donec aequaretur. Ergo
omnes lineas ductas undique a centro mundi ad superficiem
aquae aequari necesse est. Sed ad planum aequari non
possunt, per xxviii et xxxii primi Elementorum, ut superius
dictum est, nec ad convexam per viii tertii. Ergo oportet,
quod superficies aquae continens terram sit concava, et
non cujuscunque concavitatis, sed sphaericae, quoniam in
sola illa figura omnes diametri sunt aequales. Et haec de-
monstratio non solum tenet de aqua interius, sed exterius.
Nam exterius fluit ad inferiorem locum semper sicut interius.
Et ideo oportet, quod sit convexa exterius, nam neque ad
planam neque concavam exterius possent omnes lineae ductae
a centro esse aequales, secundum formam demonstrationis
prioris, et hoc patet per ex-
perimentum. Nam sit navis
g d, et portus a, et c sit
superficies navis ubi figitur
malus, et 4 sit extremitas
mali, et ducatur c a linea perpendiculariter a portu ad extre-
mitatem mali. Planum ergo est per xix et xviii primi
Elementorum quod a 2 linea est longior quam c a. Ergo si
mare esset planae figurae, tunc oculus existens in c videret
portum melius, quam existens in 6, quoniam 6 plus distat ab
a quam c. Sed per experientiam scitur, quod ille qui est in
summitate mali potest videre portum citius quam ille qui est
in superficie navis. Ergo relinquitur quod aliquid impedit
visum illius qui est in navi. Sed nihil potest esse, nisi tumor
sphaericus aquae. Ergo est sphaericae figurae. Sed si hoc,
tunc terra est sphaericae figurae convexae, nam aliter non
elongaretur aequaliter a coelo, neque appropinquaret centro
mundi aequaliter; sed hoc oportet fieri. Item esset vacuum
ubi se non contingerent: quoniam si esset planae vel concavae
non contingeret concavitatem aeque, ut patet, et ideo vacuum
esset inter eas.

MATHEMATICAE IN PHYSICIS UTILITAS. I57

Similiter de sphaericitate aeris concava intra et extra, Air.
omnino negotiandum est sicut in prima demonstratione de
aqua ; quia aer est gravis! in sphaera sua sicut aqua, ut prius
habitum est, et ideo currit ad inferiorem locum. Et praeterea
vacuum esset inter aerem et aquam, si aer esset alterius figurae.
Nam, si esset planae, tunc non tangeret aerem nisi in puncto,
per tertiam primi libri Theodosii; quia sphaera non tangit
planum nisi in puncto, ut ibi dicitur. Si vero convexae, iterum
non tangit nisi in puncto per duodecimam tertii Euclidis.
Nam signentur duo circuli in sphaera aquae convexa, et aere
convexo, non se tangent illi circuli nisi in uno puncto, sicut
probatur in illa duodecima. Ergo nec corpora in quibus
signantur; nam si corpora se tangerent in pluribus locis, et illi
circuli, ut patet ad sensum. Et ita oportet, quod utroque modo
sit vacuum. Et si esset alterius concavitatis quam sphaerae,
non omnes lineae ducerentur ab uno puncto ad superficiem
corporis aequales. Igitur oportet superficiem aeris esse
sphaericam intra et extra.

Deinde patet per has demonstrationes ultimas de igne, sicut Fire.
de aere. Sed illa quae vadit per descensum ad inferiorem
locum non tenet hic, quia ignis non est gravis in sphaera sua.
Oportet tamen omnes lineas ductas a centro mundi ad super-
ficiem ignis esse aequales, quia ignis est contrarius terrae et
summe leve, et ejusdem naturae in toto et partibus singulis.
Quapropter aequaliter elongatur a loco gravium, et a centro
mundi, et hoc exterius et interius. Ergo oportet quod sit
concavus intra, et convexus extra, et hoc sphaerice, sicut
priora concludunt.

CAPITULUM XI.

Quod plus aquae contineat vas inferiori quam superiori loco
positum.

Sed nunc per figuram aquae magnum naturae miraculum A vessel
ed with

1 The viéw as to the gravity of air deserves notice. It was maintained how-
ever by Aristotle. Cf. De Coelo, iv. 4, $ 5. Ether, or fire, on the contrary,
was regarded as imponderable, as the next paragraph shows.

158 OPERIS MAJORIS PARS QUARTA.

water varies potest suscitari ; quoniam si scyphus continens aquam ponatur
in content . . TP . .
according in loco inferiori, poterit plus capere de aqua, quam in loco

to distance superiori, ut in cellario et solario. Nam propter inclinationem

carth's naturalem aquae ad centrum mundi ubicunque sit, sive in

centre. — loco superiori, sive inferiori, partes ejus semper currunt ad
inferiorem locum ; et ideo per lineas aequales semper distant
a centro, et ideo oportet semper quod pars superior aquae sit
portio unius sphaerae describendae circa centrum mundi, licet
in fundo scyphi retinet figuram vasis, quia ibi solum tangit
vas et non superius. Quare pars suprema figurabitur secundum
legem gravitatis aquae, et hoc est respectu centri mundi, et
ideo superior pars erit portio sphaerae imaginandae circa
centrum mundi. Sed constat quod in loco inferiori erit
portio minoris sphaerae et in superiori portio majoris, quia
magis tunc distabit a centro; nam sphaera superior continebit
inferiorem, ut patet in circulis circa idem centrum. Diameter
autem scyphi erit chorda utriusque portionis, si scyphus
impleatur utrobique quantum potest capere. Ergo illa diameter
resecabit de majori sphaera minorem portionem, et de minori
majorem. Et per xxxviii propositionem triangulorum
Jordani!, in circulis inaequalibus eadem chorda resecat de
majori circulo minorem portionem, et de minori majorem, et
ita erit de sphaeris.

—. Nam signentur illi circuli in sphaeris
illis, et portiones circulorum in por-
tionibus sphaerarum, et patet quod
idem est. Ergo portio aquae super
diametrum scyphi erit major, quando
vas est in inferiori loco, quam quando
est in superiori, et ideo gibbositas
major et tumor altior; quare oportet
quod plus de aqua ibi sit, si scyphus
sit omnino plenus, quam quando est
in superiori loco. Quapropter ad eandem aquam potest plus
infundi de aqua in scyphum, quando est inferius, quam
quando est superius. Nam inferius aqua quae est super

Fic. 17.

! See note on this writer in chap. 16, p. 169.

MATHEMATICAE IN PHYSICIS UTILITAS. 159

diametrum scyphi contrahet se a lateribus vasis, et coan-
gustabit se in portionem minoris sphaerae, quia propinquior
est centro mundi, et ideo chorda ejusdem aquae fiet minor,
quam quando fuit superius. Et erit pars diametri scyphi
ejus chorda, non tota diameter, sed ex utroque latere
abscindetur aliquid de diametro, ut residuum fiat chorda
portionis aquae. Quapropter in lateribus aquae a loco ab-
scissionis diametri usque ad vas erunt duo spatia parva, ubi
poterit plus de aqua 'infundi quam quando est in superiori
loco. Et hoc totum facit inclinatio aquae secundum legem
suae gravitatis figurantis se secundum sphaeram minorem et
majorem respectu centri mundi; cum tamen vulgo studentium
videatur hoc esse omnino impossibile, imo magnis viris qui
geometriae nesciunt potestatem.

CAPITULUM XII.

An figurae quinque corporum regularium mundo con-
veniunt, ut voluerunt Platonici.

Ex istis vero figurationibus sphaericis corporum mundi Plato's
aperitur magnum fundamentum in certificatione rerum natur- correspon.

alium, et evacuantur violentae falsitates. Nam Platonici !, in dence of
quorum tempore viguit geometria, ut Averroes dicit tertio heaven
Coeli et Mundi, aestimaverunt quod corpora mundi principalia, elements to
scilicet coelum et quatuor elementa, figurarentur figuris quinque , cular
corporalibus quae regulares vocantur, et sunt aequiangulae et solids.
aequilaterae et inscriptibiles spherae et circumscriptibiles
eidem, et nullae aliae. Et propter has causas sunt nobilissimae
figurarum praeter sphaeram, quas lator praesentium de facili
potest praesentare, et sunt tres ex superficiebus triangularibus,

et quarta ex quadratis, et quinta ex pentagonis; et non
possunt esse plures, quod est mirabile. Prima habet quatuor

superficies triangulares, et vocatur tetraedrum a rerpás quod

! See Timaeus, 54. It does not appear that Bacon had read Plato.

160 OPERIS MAJORIS PARS QUARTA.

est quatuor, seu pyramis quatuor basium triangularium.
Secunda habet superficies octo triangulares, et ideo vocatur
octaedrum,nam octo purum est Graecum, non Latinum. Tertia
habet viginti superficies triangulares, et vocatur icosaedrum.
ab elxoci quod est viginti. Et non possunt esse plures figurae
regulares ex basibus triangularibus. Nam nullus angulus
corporalis potest valere quatuor rectos superficiales, ut docet
xxi undecimi libri Elementorum. Sed sex anguli triangu-
lorum aequiangulorum valent quatuor rectos: nam tres valent
duos rectos, ut patet ex xxxii propositione primi libri quae
vulgata est. Et ideo sex anguli triangulorum non possunt
componere angulum corporalem ; et ideo nec figura corporalis
potest fieri ex superficiebus triangularibus, quarum sex anguli
semper concurrant ad angulum unum corporalis figurae. Sed
bene potest fieri, quod quinque anguli vel tres triangulorum
constituant minus quam quatuor recti. Et si ex tribus angulis
triangulorum constituatur angulus corporalis, tunc oportet
quod sint quatuor superficies triangulares in corpore illo.
Et si ex angulis quatuor triangulorum fiat angulus corporalis,
tunc oportet quod sint octo trianguli in figura corporali. 5i
vero quinque anguli triangulorum faciunt angulum corporalem,
tunc oportet quod in figura corporali sint viginti superficies
triangulares undique, ut patet ad sensum in figuris corporali-
bus. Ex duobus autem angulis superficialibus non potest fieri
angulus corporalis, quia omnis angulus talis est ad minus ex
tribus superficialibus, ut dicit Euclides in principio xi; et qui-
libet geometer scit hoc. Ergo tantum tria corpora regularia
erunt ex triangulis. Ex quadratis vero non potest esse nisi
unum ; nam angulus quadrati rectus est, et ideo tres tantum
tales congregati possunt facere angulum corporalem, quia si
quartus addatur jam non potest esse angulus corporalis, quia
omnis angulus solidus est minor quatuor rectis. Sed si tres
anguli quadratorum concurrant ad angulum solidum, tunc in
corpore constituto erunt sex superficies quadratae, ut est in
taxillo; et vocatur haec figura cubus et hexaedrum ab é&
Graece, quod est sex Latine. Si vero accipiantur anguli
pentagonorum regularium, tunc tres faciunt angulum solidum,
ct non plures, quia si quatuor acciperentur, jam esset plus

MATHEMATICAE IN PHYSICIS UTILITAS. |. 161

quam quatuor recti, eo quod angulus pentagoni est et rectus
et quinta recti, ut patet ex xxxii propositione primi
Elementorum, et sic essent ibi quatuor recti et quatuor
quintae. Sed omnis angulus corporalis est minor quatuor
rectis. Ergo tantum erit una figura corporalis ex pentagonis
superficiebus, et oportet quod habeat duodecim superficies
pentagonas, sicut patet in fabricatione illius corporis, et hoc
vocatur dodecaedrum, id est, figura corporalis duodecim
basium pentagonarum aequilaterarum.

Et omnes istae figurae corporales regulares fiunt ex super-
ficiebus regularibus quae sunt aequiangulae et aequilaterae.
Non est autem possibile quod ex superficiebus hexagonis fiat
aliqua figura corporalis regularis, quia nullus angulus corporalis
potest fieri ex angulis talium hexagonorum, propter hoc quod
angulus talis hexagoni valet rectum et tertiam recti, ut patet
ex xxxii primi Elementorum. Ergo tres tales faciunt tres
rectos et tres tertias unius recti, sed tres tertiae valent integrum.
In nulla enim re possunt esse nisi tres tertiae. Ergo tres
anguli hexagonorum regularium valent quatuor rectos, sed
nullus corporalis valet quatuor rectos. Ergo nulla figura
corporalis potest fieri ex superficiebus hexagonis, et longe
minus ex heptagonis et octogonis et supra, quia majores
angulos obtinent quam hexagoni.

Quoniam vero dodecaedrum patitur in se inscriptionem
omnium aliarum, ut patet ex quinto decimo libro Elemen-
torum, ideo dederunt Platonici hanc figuram partibus coeli,
propter hoc, quod coelum noscitur omnia continere. Unde
dixerunt partes coeli concurrere in punctum unum secundum
hanc figuram, ut constituatur corpus coeli. Et quia ignis
ascendit in figura pyramidali, ideo dederunt partibus ignis
talem figuram. Quoniam autem octaedrum maxime assimi-
latur pyramidi, et aer praecipue assimilatur igni, dederunt ei
figuram illam. Sed quoniam partes aquae revolvuntur an-
fractibus et fluxibus multifariis, ideo dederunt ei figuram
icosaedrum, quae multiformitate laterum et angulorum
circumvolvitur in sphaera. Partibus vero terrae cubum
dederunt, quia illa figura stabilis est et fixa inter omnes, sicut
terra inter mundi corpora stabilitatem obtinuit et fixionem.

VOL. I. M

'" Aristotle's

objection
that vacua
would be
left.

162 OPERIS MAJORIS PARS QUARTA.

Sed Aristoteles venit contra istos in tertio Coeli et Mundi!,
et probat, quod ex hac figuratione vacuum erit in sphaera
aquae, et in sphaera aeris, et in sphaera coelesti. Nam solus
cubus et pyramis possunt locum replere, quando congregantur
circa punctum unum. Nam replere locum est duobus modis ;
uno, sicut dicimus vulgariter, quod omne corpus replet locum,
nisi sit instantia in ultimo coelo, et sic non accipitur repletio
loci in proposito. Alio modo dicitur esse repletio loci non
solum corporaliter, sed superficialiter, et magis quia paucitas
superficierum implentium sua loca est causa paucitatis cor-
porum replentium sua loca, ut dicit Averroes super tertium
Coeli et Mundi. Replere vero spatium superficiale est implere
quatuor angulos rectos, quia non possunt plures esse circa
punctum unum in superficie, ut patet ex intersectione duarum
linearum ad angulos rectos hoc modo. Et sic quadrata pro-
priissime possunt locum replere superficialem, scilicet quatuor
quadrata, quia .angulus quadrati rectus est, et sex trianguli,
quia sex anguli tales valent quatuor rectos, et tres hexagoni,
quia eorum anguli tres valent quatuor rectos, ut prius tactum
est. Sed pentagoni non possunt locum replere, quia tres
anguli eorum valent tres rectos et tres quintas, et hoc totum
minus est quatuor rectis, et quatuor anguli pentagonorum valent
quatuor rectas et quatuor quintas, quod est plus quatuor rectis,
et ideo haec figura regularis non potest locum replere. Similiter
nec heptagonus, nec aliqua alia, ut patet. Et ideo tantum
tres superficiales locum replent. Et propter hoc paucae erunt
corporales, quae locum replebunt corporaliter, et hujusmodi
repletio corporalis non est per unum corpus, sed quando plura
corpora congregantur circa unum punctum undique, ita ut
impleant spatium corporale circa illud punctum. Et hoc
spatium habet octo angulos corporales, et duodecim angulos
superficiales rectos distinctos secundum rem, licet sint viginti
quatuor secundum rationem, quoniam quilibet angulus cor-
poralis est ex tribus superficialibus, et ideo quoad hoc compu-
tantur ter octo, qui sunt viginti quatuor. Sed saepe iterantur
aliqui, quia hi anguli sunt conjuncti; si enim essent divisi,

1 De Coelo, iii. 8, $ x "OAvs 32 rd wetpdaGar ra dw có para oxnparí(ew dAcyéy
tori, xpivrov pày Sri oupPhoeras ui) dvanAnpotaba: rÓ oy.

MATHEMATICAE IN PHYSICIS UTILITAS. 163

tunc oporteret esse viginti quatuor! secundum veram distinc-
tionem, ut quilibet angulus corporalis ab alio distinctus haberet
tres rectos sibi proprios. Omnia haec patent ex tribus lineis
intersecantibus se ad angulos rectos, ut in tribus festucis vel
aliis. Quoniam vero angulus cubi est ex tribus rectis, ideo
octo tales possunt propriissime replere locum circa punctum
unum. Et ideo in sphaera terrae secundum figurationem nunc
dictam, non erit vacuum, quia octo cubicae partes terrae con-
gregatae circa centrum mundi replent locum totum necessario
circa illud centrum. Angulus vero pyramidis est ex tribus
angulis triangulorum, quapropter valet duos rectos, et ideo
anguli sex tales valent quatuor angulos cubicos, nam utrobique
valent duodecim rectos, et alii sex valent alios quatuor angulos
cubicos. Quapropter concludit Averroes in tertio Coeli et
Mundi, quod duodecim anguli pyramidum congregati circa
punctum unum implebunt totum locum corporaliter, sicut
octo cubici anguli, et ideo in sphaera ignis non est vacuum.
Sed aliae figurae congregatae circa punctum unum non
possunt secundum Aristotelem et Averroem replere locum.
Quotquot enim congregarentur habebunt majus vel minus octo
angulis cubicis, et ideo locum non replebunt. Et ideo in
sphaera aquae et aeris et coeli accidit vacuum necessario
secundum figurationem Platonicorum. Sicut vero cubus in
corporali repletione respondet quadrato in superficiali, quia
cubus sit ex quadratis superficiebus, propter quod utraque
figura propriissime replet locum,sic pyramis respondet triangulo
regulari, quia fit ex triangulis, et utraque figura locum replet.
Sed tertiae figurae, scilicet hexagono superficiali, non respondet
figura corporalis replens locum, quia ex superficialibus hexa-
gonis non potest figura hexagonalis regularis constitui, ut
demonstratum est prius.

Et tamen apis facit domus hexagonas ne vacuum inter- Hexagon
cipiatur; et natura in ventre terrae generat crystallos omnes iD bee ad
hexagonas in unum congregatas. Et sic lapides, qui vocantur in crystal.
irides et in insulis Hiberniae et India dicuntur ab autoribus
inveniri, congregantur in figura hexagona. Et dicuntur lapides
iridis, quia repraesentant colores iridis et arcus coelestis, quando

1 J. has XV.
M 2

If there
were two
universes
& vacuum
would be
left.

164 OPERIS MAJORIS PARS QUARTA.

ponuntur ad radios solares. Et sic est de omnibus generatis
in hoc mundo, quae per superficies suas congregantur, ut
retineant figuras hexagonas, ut vacuum excludatur, et hoc est
mirabile. Sed tamen non est vera loci repletio secundum
quod Aristoteles accipit in hoc loco: nam talis est secundum
omnem situm corporum et superficierum, ut taxilli quatuor
superficialiter secundum omnem situm replent locum, et octo
corporaliter, qualitercunque mutentur anguli vel latera, nam
aequalitas plena est in illis angulis et lateribus. Et sic est de
pyramidalibus corporibus, et de triangulis superficialibus et
quadratis et hexagonis. De aliis non contingit hoc secundum
omnem situm sed secundum aliquem, et ideo hic non com-
putantur. Nam si aliquibus domibus apum erectis aliae
ponantur secundum alium situm, non est loci repletio, sed
vacuum spatium relinquitur, et ideo non sunt de replentibus
locum, ut absolute et simpliciter dicatur repletio. Magna est
ac profunda consideratio de his figuris replentibus locum
propter rerum naturalium figurationem. Sed quantum sufficit
ad praesens in universali de hac figuratione in corporibus
mundi principalibus declaravi.

CAPITULUM XIII!.

An possint esse plures mundi, et an materia mundi sit
extensa in infinitum.

Et transeo ulterius ad duo exempla breviter annotanda in
corporibus mundi, quae fundatur super geometricam potes-
tatem, et sunt adhuc annexa materiae corporali eorum. Nam
Aristoteles dicit primo Coeli et Mundi?, quod mundus occupat
totam suam materiam in uno individuo unius speciei, et sic
de quolibet corpore mundi principali, quoniam unus mundus
est numero, nec possunt plures mundi esse in hac specie,
sicut nec plures soles nec plures lunae, licet multi posuerunt
contrarium. Nam si esset alius mundus, esset sphaericae

! Cf. Opus Tertium, cap. 41. .
* De Coelo, i. 9 t£ dwdhans yap tor: rijs olecias HAns ó was xóopos.

MATHEMATICAE IN PHYSICIS UTILITAS. 165

figurae, sicut iste, et non potest esse distantia inter eos,
quia tunc spatium vacuum sine corpore esset signabile inter
illos, quod falsum est. Quapropter oportet ut se tangerent,
sed non possunt tangere se nisi in puncto uno per xii
tertii Elementorum, ut prius declaratum est per circulos.
Ergo alibi quam in illo puncto erit spatium vacuum inter
eos. Aliud est, quod corporalis materia mundi non est
extensa in infinitum, ut multi posuerunt. Nam geometrica
potestas hoc excludit. Quoniam conjungantur! duae lineae
a et ó angulariter in centro mundi, et a concursu earum
extendantur in infinitum, et tertia uni illarum ducatur aequi-
distanter et terminetur ad aliam, et sit ca. Ergo a et 6
sunt aequales, et o, quae est pars a, et c sunt aequales, quia
ab eodem puncto scilicet o vadunt in infinitum. Sed c linea
aequatur 6 lineae. Ergo o linea aequabitur ipsi a totali,
scilicet pars suo toti, quod est impossibile.

CAPITULUM XIV *,
De unitate temporis.

Multae autem aliae demonstrationes geometricae possent

ad hoc adduci, atque veritates aliae in rebus mundi possent Time con-

notari quasi infinitae, in quibus geometrica virtus elucescit. cemed

not

Sed haec sufficiunt persuasioni, et solum evacuabo duas fal- matter,

ut with

sitates, quae ad unitatem materiae numeralem consequuntur motion re-
ini * presented

secundum opiniones vulgatas. Nam ponunt quod tempus sequi D ecrace

tur ad materiam rerum, et aevum ad formam, et ideo sicut of one

materia est una numero et non plures, sic tempus est unum
numero simul et semel, et sicut forma variatur in rebus, sic
aevum multiplicatur in aeviternis. Unde plura dicuntur esse
aeva, et unum tempus, ut secundum numerum angelorum sit
numerus aevorum. Sed cum probatum est quod materia non
potest esse una, tunc falsum est tempus habere unitatem ab
ea. Deinde tempus non potest sequi, nisi ad subjectum suum.

! The diagram in O. has been omitted as unintelligible.
* Cf. Opus Tertium, cap. 41, which contains an application of the view here
stated to the doctrine of Transubstantiation,

dimension.

Thepresent

moment,
being a

166 OPERIS MAJORIS PARS QUARTA.

Sed motus est subjectum suum, non materia; et subjectum
motus non est materia, sed corpus compositum ex materia
et forma.

Postremo res geometricae nobis ostendunt causam unitatis
in tempore, et demonstrationem addunt super hoc. Nam

point, mày corpus quia habet undique dimensionem, ideo non compatitur

correspon
to any
number of
motions.

secum aliud corpus: ubique enim habet corpus, unde aliud
excludat secundum longum et latum et profundum. Ergo
superficies secundum longum et latum excludet aliam super-
ficiem, sed non secundum profundum, quia sic est indivisibilis
et caret dimensione. Et linea secundum longum excludit
aliam, sed non secundum latum et profundum quia sic non
habet dimensionem. Ergo punctus cum omni careat dimen-
sione, non habet unde excludat aliud a suo loco indivisibili ;
sed imaginato primo puncto in suo loco secundus adveniens
habebit eundem locum in mente, quia non est distantia media,
et sic de tertio puncto, et de infinitis: Motus vero non habet |
nisi linearum dimensionem a priori in posterius secundum longi-
tudinem spatii, et hoc est a praeterito in futurum. Ergo solum
secundum hunc decursum, scilicet a priori in posterius, seu a
praeterito in futurum, unus motus excludet alium, scilicet prior
posteriorem, et praeteritum excludet futurum. Sed comparatio
motus ad praesens est alia quam secundum decursum a
praeterito in futurum. Ergo respectu praesentis nullus motus
habet dimensionem nec divisibilitatem, et ideo non habebit
unde excludat alium a praesenti. Et ideo infinitos secum
potest pati praesentes; et ideo unum tempus praesens sufficit
omnibus motibus praesentibus, et propter hoc habetur hic
vera causa unitatis temporis, et non propter materiam. Deinde
ex istis elici potest unitas vera aevi, sicut temporis. Nam
aevum vel solum habet dimensionem linearum, si ponamus
aevum esse divisibile et habere partes, ut multi aestimant
contra totam philosophiae potestatem, atque contra Augus-
tinum et Dionysium, quanquam Anselmus velit contrarium,
Et si hoc sit verum, tunc! sic est de aevo sicut de tempore,
propter quod erit unum et non plura. Aut aevum erit indi-
visibile, et tunc erit ad aeviterna, sicut locus indivisibilis ad

! nec, J.

MATHEMATICAE IN PHYSICIS UTILITAS. 167

puncta et atomos, et idem numero est locus unius puncti et
plurium, ut prius habitum est. Ergo unum erit aevum omnium
aeviternorum, et hoc est necessarium, et nulli perito in philo-
sophia dubium. Nec est contra sanctos et doctores principales,
sed conveniens sententiae eorum.

CAPITULUM XV.

An motus gravium et levium excludat omnem violentiam.
Et quomodo motus gignat calorem. Itemque de duplici modo
sciendi.

Quoniam vero motus est subjectum temporis, et tempus est In a falling
mensura motus, possumus adhuc videre magnam geometriae object the

potestatem in motibus corporum istius mundi. Aestimant point alone
vero naturales, quod motus gravium deorsum sit naturalis free path.
omnino, et motus levium sursum est similiter omnino naturalis,
ita ut non habeant de violentia. Sed figuratio geometrica
ostendit nobis contrarium. Nam sit d@ » c lignum vel lapis in
aere, et a centrum mundi, g A diameter mundi. Cum ergo
d b c sint semper in suo toto aequaliter distantes descendant
ad centrum per lineas aequidistantes. Ergo d descendet per
lineam 4 e, et 5 per lineam 6 a, et c per lineam c o, quapropter
d cadet extra centrum mundi in diametro 4 g versus coelum,
scilicet in e puncto, et c in o, quare

in hoc descensu Z declinabit a centro

à versus centrum per altitudinem a e,

et c per altitudinem a o. Sed omnis WV
declinatio gravis a centro versus cen- yg

trum est violenta. Ergo 4 et c mo-

ventur violenter, et sic de omnibus

partibus Z 6 c praeter ó quae sola

vadit in centrum. Quapropter mul- FiG. 18.

tum erit hic de violentia. — Caeterum

incessus rectus et naturalis ipsius 2 est per lineam d a, unde si
separetur Z a suo toto caderet in a per rectum incessum, quia
omne grave tendit in centrum. Omnis autem declinatio

168 OPERIS MAJORIS PARS QUARTA.

gravis ab incessu recto est violenta, sed quanto magis d
movetur super lineam 4 e, magis recedit ab incessu recto, ut
patet ad sensum, quia 4 a et d e lineae magis separantur
inferius quam superius, Ergo 4 quanto magis descendit
deorsum, tanto magis movetur per violentiam, et similiter c,
et ideo quaelibet pars ipsius totius d 5 c gravis, praeter ó quae
sola semper descendit secundum incessum rectum. Mani-
festum est ergo quod magna et multiplex violentia est in
motu naturali ipsius gravis. Et ex hoc sequitur quaedam
veritas in rebus naturalibus, scilicet quod motus naturalis
generat calorem; nam quum demonstrata est violentia, et
constat grave naturaliter inclinari deorsum, planum est quod :
duae virtutes sunt in gravi moto deorsum inclinantes ipsum
in partes contrarias. Ergo una distrahit partes gravis in unam
partem, et alia in aliam, et ad has distractiones necesse est
rarefieri partes gravis. Sed rarefactio est dispositio immediata
ad calorem, unde per experientiam scimus quod grave de-
scendens deorsum calescit. Potest ergo hoc hic adverti, sicut
in prioribus, quod causae rerum naturalium debent assignari
per mathematicae potestatem. Et potest homo videre quod
in rebus naturalibus sunt duo modi arguendi, unus per de-
monstrationem quae procedit per causas, et alius per demon-
strationem ad effectum, ut cum prioribus demonstrationibus
probatur per causam, quod violentia accidit gravi in suo motu
naturali, postea demonstratur hoc idem per effectum, scilicet
per generationem caloris. Nam non generaretur calor nisi
per rarefactionem, nec rarefactio ista nisi per virtutes dis-
trahentes grave in partes contrarias, et hae non possunt esse
nisi una naturalis, altera violenta, quapropter grave in suo
motu naturali habet violentiam. Et sic haec conclusio, grave
recipit violentiam in suo motu naturali, probatur per causam
et effectum, Sed causa sola facit scientiam aut longe majorem
quam effectus, quia Aristoteles dicit primo Posteriorum quod
scire opinamur cum causas cognoscimus. Ergo cum demon-
stratio, ut ibidem docet, est syllogismus faciens scire, necesse
est quod demonstratio per causam sit longe potentior, quam
per effectum ; et hoc vult Aristoteles libro Posteriorum !.

! Et... posteriorum, om. in O. Cf. Anal. Post. i. 2, § 1.

MATHEMATICAE IN PHYSICIS UTILITAS. . 169

Quapropter cum in rebus naturalibus demonstratio habetur per
causam per vias mathematicae, et demonstratio per effectum
habetur per vias naturales, plus potest mathematicus in rebus
naturalibus sciendis, quam ipse philosophus naturalis. Et
maxime hoc planum est, quod motus simpliciter violentus,
ut motus gravis sursum, generabit calorem, et longe magis
quam naturalis motus; quia in violenter moto sunt duae
virtutes motrices omnino contrariae, et secundum totum, et
in contrarias partes omnino, ut virtus naturalis gravis tendit
deorsum, et virtus violenta tendit omnino sursum. Et ideo
magna est distinctio partium rei motae violenter, et major
quam in naturali.

CAPITULUM XVI.
De motu Librae.

Et cum jam dictis expedit altius aperire geometricam Researches
potestatem in motibus; et hoc propter intellectum univer- on I ravity.
salem scientiae de ponderibus, quae est pulchra et difficilis
nimis hominibus non habentibus experientiam causarum in
motibus gravium et levium. Dicit ergo Jordanus in libro
de ponderibus!, quod si aequilibris fuerit positio aequalis,

! This was Jordanus Nemorarius, the most original, if we except Leonardo
Fibonacci. of the mathematicians of the thirteenth century. There is good ground
for believing that he is identical with Jordanus Saxo who, on the death of
St. Dominic, 1221, succeeded to the generalship of the order. His principal
works are, (1) De Ponderibus, of which an edition was published in 1533, by Peter
Apianus ; (2) a treatise on Arithmetic, edited in Paris, 1496 and 1514, by Faber
Stapulensis ; (3) Algorithmus Demonstratus, edited by Schoner, of Nuremberg, in
1534; (4) De Numeris Datis, printed in Zeitschrift, Math. Phys. xxxvi histor.
literar. Abtheilung, 1891 ; (5) De Triangulis, printed 1887, by the Copernicus-
verein für Wissenschaft und Kunst of Thorn. Most of these wcrks were
evidently known to Bacon. The treatise, De Ponderibus, which consists of
a short preface followed by thirteen propositions, is interesting as one of the
earliest studies, by a mathematician of great originality, of the mechanics of
a particle forming part of a rigid system. With regard to gravity we find, of
course, the doctrine, still awaiting Galileo's refutation, that heavy bodies fall
more rapidly than light. The arithmetical treatise, containing many algebraic
problems, had also been studied by Bacon, as his fragment on the Principles of
Mathematics clearly shows. (See Cantor, Gesch. der Mathem. vol. ii. pp. 49-54.]

¥70 OPERIS MAJORIS PARS QUARTA.

aequis ponderibus appensis, ab aequalitate non discedet,
et si ab aequidistantia separatur ad aequalitatis situm
revertetur. Et istud videmus ad sensum in lance utraque,
quarum virga sit ex parte utraque aequalis in longitudine
et in pondere, et omnino appendantur pondera aequalia,
et libra aequaliter teneatur per appendiculum, ut stet appen-
diculum ad angulos rectos super regulam librae in centro
revolutionis, nam hic punctus vocatur centrum revolutionis

.& quo appendiculum exit ad angulos aequales. Et dicitur

Gravity of
particles in
the arm of
a balance :
varies with
their
position.

centrum revolutionis, quia quando per violentiam manus
deprimentis alterum ponderum aequalium, aut propter in-
aequalitatem appensorum unum eorum facit nutum, aliud
elevabitur, et hic motus descensus et elevationis describet
circulum unum, cujus ille punctus a quo exit appendiculum
est centrum, et ideo dicitur centrum revolutionis. Quod ut
planius sit fiat figura. Nam sit
regula seu baculus librae a 6, etc d
sit appendiculum, tunc centrum revo-
lutionis a quo exit appendiculum erit
à p d, et in circumferentia istius circuli
appensa movebuntur, nam illud quod
descendet describet circulum infer-
iorem, et ilud quod ascendet de-
scribet circulum superiorem. His
suppositis, arguitur! sic, Cumalterum
brachiorum librae aequalibus appensis nutum faciat per manum
deprimentis, fit, secundum Aristotelem quarto Coeli et Mundi,
gravius, quia grave quanto adquiret magis de loco gravis,
tanto magis adquirit de forma gravitatis, ut ipse dicit. Ergo
quod descendit fit gravius, quantumcunque parum descendat
a situ aequalitatis, et ideo quanto magis descendit, tanto erit
gravius. Ergo fiet inaequale reliquo appenso et ponderosius
eo. Ergo licet fuerint in situ aequalitatis aequalia, tamen
cum recedunt ab illo situ fient inaequalia in pondere ; quare
semper descendet illud quod nutum facit, et aliud semper
ascendet, et ideo nunquam ad situm aequalitatis revertentur.

C

FIG. 19.

1 J.'s reading, argumentor, for arguitur, suggests that what follows is Bacon's
opinion: which it is not.

MATHEMATICAE IN PHYSICIS UTILITAS. 171

Sicut quando duo pondera inaequalia ponuntur in brachiis,
statim recedunt a situ aequalitatis, et nunquam ad eundum
situm revertentur, sed semper descendit quod est ponderosius.
Ergo similiter hic, quod est contra Jordanum et contra
sensum. Item Jordanus dicit, quod inter quaelibet gravia est
velocitatis in descendendo et ponderis eodem ordine sumpta
proportio, sed istud grave quanto magis descendit, tanto fit
ponderosius. Ergo tanto velocius descendit. Ergo nunquam
revertetur per naturam ad situm aequalitatis. Item Jordanus
dicit, quod minus grave secundum situm est, quod descensum
alterius sequitur motu e contrario, id est, quod ascendit
quando descendit, et e contra. Sed appensum nutum faciens
est minus grave secundum situm, ut probabo. Quare sequetur
descensum alterius appensi motu contrario, et ascensum
similiter. Quapropter secundum quod unum descendit, reli-
quum ascendit, et e contra : quare nunquam in situ aequalitatis
quiescent.

Quod autem appensum faciens nutum sit minus grave se-
cundum situm, manifestum est per hoc, quod minus capit de
directo descensu in diametro transeunte per centrum revolutionis
versus centrum mundi: quapropter secundum Jordanum erit
minus grave secundum situm. Et hoc exigit ipsa veritas per
figuram declaranda. Et hujusmodi figuratio solvet objecta, nec
potest habere remedium intellectus nisi per figuram. Descri-
batur ergo circulus super centrum revolutionis, quod est o, in
cujus circumferentia appensa revolventur, et trahatur diameter
a 6 aequidistans horizonti, et lineetur alia diameter intersecans
hanc quae tendat in centrum mundi, et sit d c, et signentur
arcus aequales in utroque semicirculo ab utraque parte diametri
aequidistantis horizonti, et hoc a parte utriusque termini ejus,
et a terminis arcuum ducantur in utroque semicirculo lineae
aequidistantes sibi invicem, et diametro aequidistanti hori-
zonti, quae sunt f A, gp, fg, sr, quae omnes secant diametrum
cadentem in centrum mundi. Oportet ergo secundum Jor-
danum et commentatorem ejus, quod illae lineae aequidistantes
secent de diametro quae vadit in centrum mundi, partes
inaequales, ita ut illa aequidistans, quae propinquior est
diametro aequidistanti horizonti, secet majorem partem

172 OPERIS MAJORIS PARS QUARTA.

diametri alterius, quam remotior aequidistans, ut 7 7 separabit
majorem partem diametri Z7 c quam s 7, ita ut pars diametri
c d c, quae est inter a 6 et / qg sit

major quam pars ejusdem diametri
quae est inter Zg et s 7, et eodem
modo pars diametri 7 c, quae est
inter a 0 et g f, erit major quam
illa quae est inter gp et fz. Et.
secundum hoc oportet quod sumpta
una aequidistante in semicirculo
uno, et alia in alio, quae aequaliter
distant a diametro eis aequidistante,
illae secabunt partes aequales de
diametro descendente i in centrum mundi ut Z2 et gp secabunt
partes aequales de 4 c, et similiter s 7 et f A, sicut dicit vicesima
sexta propositio de triangulis Jordani. Si ergo partes diametri
cadentes in centrum mundi divisae per aequidistantes sunt
inaequales, ita ut illae partes diametri quae dividuntur per
aequidistantes propinquiores diametro aequidistanti horizonti
sint majores ; tunc ergo intelligamus regulam librae jacere in
diametro aequidistante horizonti, et appendiculum sit erectum
in diametro cadente per centrum, ut libra sit in situ aequalitatis
et brachia ejus, deinde postea moveatur libra, et elevetur pars
una librae usque ad primam aequidistantem in semicirculo
superiori, et alia deprimatur usque ad terminum primae
aequidistantis in semicirculo inferiori, ut regula sit in situ Z
lineae, et pars librae altior sit in 4, et reliqua in 5. Si ergo
f descendat usque ad terminum alterius aequidistantis 4,
transibit de diametro cadente in centrum, partem ejus quae
est inter aequidistantes g ^ et f 4, quod minus est quam illa
pars diametri, quae est inter Z g et a 4, ut patet ex praedictis.
Ergo si descenderet usque a caperet plus de descensu recto
in diametro cadente in centrum mundi quam f, dum descendit
in 4; quare £ est gravius secundum situm quam f. Et iterum
7 descendit versus centrum mundi. Sed ? propter declina-
tionem circuli recurvatur a centro, et saltem minus tendit in
centrum, ut patet ad sensum. Ergo relinquitur, quod ex hac
causa adhuc erit minus grave. Et quia sic est, ideo solvitur

FIG. 20.

MATHEMATICAE IN PHYSICIS UTILITAS. 173

prima objectio; nam licet pars regulae! $ descendens est
propinquior centro mundi, ut patet, si linea recta trahatur ab
eo in centrum o, quia illa linea est
brevior quam linea quae trahitur a 7,
ut patet ad sensum, et ita gravior sit
in quantum plus habet de loco deorsum,
tamen quia ? secundum illam rectam
lineam, quae est fo non movetur
versus centrum, sed secundum circu-
lationem circumferentiae circuli, et illa 'P
circulatio facit eam minus capere de
incessu recto in diametro cadente in
centrum quam capiat 7, atque obliquat
et incurvat ipsum f a centro, ut non
ita recte tendat in centrum sicut 4
quando descendit, oportet quod / sit
gravior quam ? dum sunt in tali
situ. Et ideo si dimittantur sibi ipsis 7 descendet, et ejus
descensum sequetur ? motu contrario, scilicet ascendendo
usque ad situm aequalitatis. Et ideo ? non semper descendet,
sed praevalent duae causae gravitatis hic assignatae contra
illam de qua objectio fecit mentionem. Iterum illa gravitas
non cogit, nam modica est et insensibilis, et ideo non operatur
hic, sicut nec si pluma una apponeretur ad alterum appensorum
aequalium, cum sunt in situ aequalitatis, faceret nutum, et
tamen secundum veritatem illud brachium ubi fuerit pluma
est gravis, quia pluma habet aliquid gravitatis. Et ideo
similiter est hic; quia enim brachium descendens, quando est
in ultimo descensu parum distat a situ aequalitatis, ideo valde
modicum et insensibile est quod adquirit de gravitate, et ideo
gravitas acquisita non est computanda.

Fic. ar.

! Jebb's figure (Tab. i. 26) is wrong, as he puts f in the upper instead of the
lower end of the balance. Further, he draws fo and of to the centre of the
circle, in which case both are, of course, equal. The lines should be drawn to
the centre of the earth, as in fig. 21. What is meant is that f is nearer to the
earth's centre than /, and therefore moves with greater force: but that this is
counterbalanced by the fact that the path of p tends to become more horizontal
than that of /; * minus capit de incessu recto in diametro cadente in centrum
quam capiat ¢.’

Oscillation
of balance
due to
atmo-
sphere.

174 OPERIS MAJORIS PARS QUARTA.

Et tunc patet aliud, quod hujusmodi ponderositatem
majorem concludit quod semper velocius descendet ut nun-
quam elevetur. Jam enim patet, quod haec gravitas nihil
facit sensibile, atque duae causae gravitatis praetactae
reperiuntur in brachio altiore. Cum vero in tertio argumento
dicit, quod minus grave est quod descensum alterius sequitur
motu e contrario, scilicet ascendendo, bene concedo. Nam sic
se habet appensum inferius, quia movetur sursum, quando
appensum superius descendit, ut quando sibi ipsis dimittuntur,
et sunt aequalia, sicut positum est. Sed non propter hoc
ascendit plus et plus, nec reliquum descendit quantum potest,
sed solum attingunt situm aequalitatis, et ibi nata sunt
quiescere, propter quod objectio concludit plus quam deberet,
quando vult ex hoc, quod unum ascendit et reliquum de-
scendit, concludere quod transeant situm aequalitatis.

Et si dicatur, quod ibi est motus titubationis et ideo
brachium superius descendit ultra situm aequalitatis et qua
ratione transit parum et multum, quia hic transitus est unius
naturae, et similiter de reliquo brachio ut ascendat semper,
postquam transit situm aequalitatis. Sed dicendum est, quod
hic descensus brachii altioris ultra situm aequalitatis non est
propter naturam ipsius appensi, sed propter reinclinationes
partium aeris impetuosas. Cum enim agr receperit motum,
retinet ipsum bene, et ideo diu titubant partes ejus huc atque
illuc, et non permittunt statim appensum quiescere in loco
aequalitatis !.

1 The remaining portion of Part IV is not divided into chapters, with the
exception of the final section on astrology, which in the Bodleian MS. is divided
as though it were a distinct treatise. "What follows consists first of a disquisi-
tion on Chronology, secondly, of a review of geographical knowledge, and
thirdly, of the treatise referred to. .

In the Opus Tertius, before those subjects are entered upon, there occur some
discussions of matters not treated of in the Ops«s Majus chapters 42-52). These
deal (a) with the question of Vacuum : (5) following on this, with the question
of growth and nutrition: (c) of place and motion with regard to immaterial
beings : (d) of aevum, or created eternity.

MATHEMATICAE IN DIVINIS UTILITAS. 175

MATHEMATICAE IN DIVINIS UTILITAS.

Postquam manifesta est necessitas mathematicae in rebus Connexion

athe-

e. *. e e. "e e. . e. Lo)
hujus mundi et in scientiis humanis nunc potest istud idem matics with
ostendi in divinis. Et hoc est magis considerandum, quia theology.

humana nihil valent nisi applicentur ad divina. Cum igitur
ostensum sit quod philosophia non potest sciri nisi sciatur
mathematica, et omnes sciant quod theologia non potest sciri
nisi sciatur philosophia, necesse est ut theologus sciat mathe-
maticam. Caeterum Deus posuit res creatas in scriptura sua,
qui solus novit potestatem creaturarum quas condidit, nec
potest falsum sentire, nec decet suam veritatem. Ergo cum
omnes res a Deo et angelis et summis coelorum usque ad
terminos eorum ponantur in scriptura, vel in se vel in suis
similibus vel in suis contrariis, et contrariorum est eadem
scientia, ut dicit Aristoteles, et verum est vel in universali
vel in particulari, necesse est theologum scire res hujus mundi,
si textum sacrum debet scire.

Praeterea nos videmus, quod sensus literalis stat in cogni-
tione naturarum et proprietatum creaturarum, ut per con-
venientes aptationes et similitudines eliciantur sensus spirituales.
Nam sic exponunt sancti et omnes sapientes antiqui, et haec
est vera et sincera expositio, quam Spiritus Sanctus docuit.
Quapropter oportet theologum scire optime creaturas. Sed
ostensum est, quod sine mathematica sciri non possunt.
Ergo mathematica omnino est necessaria sacrae scientiae.

Et hoc tertio per propria potest ostendi. Et cum multis Mathe-
modis probabitur quod intendo, primo tamen per occupationes knowledge

sanctorum persuadere conabor, cum exclusione infamiae a triarcl

mathematicae quam multi imprudenter allegant, quia sanc-
torum testimonia non intelligunt. Patriarchae enim et
Prophetae ante diluvium et post invenerunt ipsam et docuerunt
caeteros homines, 1. Chaldaeos, 2. Aegyptios ; et ab Aegyptiis
ad Graecos descendit; et non ita evidenter scribitur quod

1 Cf. O£us Tertium, chap. 54.

Apprecia-
tion of it by

176 OPERIS MAJORIS PARS QUARTA.

sic laboraverunt in aliis scientiis. Sed cum per istos viros
data est nobis lex divina, et fuerunt sanctissimi, non occupa-
verunt se nisi in scientia quae maxime est utilis legi divinae;
ergo mathematica est maxime consona legi divinae. Minor
propositio habet secum suam probationem. Major probatur
per auctoritatem triplicem. Primo per historiographos, et
praecipue per maximum eorum Josephum. Primo enim
Antiquitatum libro in tribus locis de his scientiis faciens
mentionem, expresse narrat totum quod propositio major
proponit Nam dicit, * quod filii Adae invenerunt geometriam,
astronomiam, arithmeticam, et musicam ; et Noe et filii ejus
docuerunt Chaldaeos: deinde Abraham docuit Aegyptios.

! Secundo, verificatur hoc per beatum Hieronymum et

the fathers, Cassiodorum et alios doctores sacros, ut vulgus etiam theo-

logorum non ignorat; et ratificant sancti, quod Josephus
asseverat. Tertio, per philosophorum assertionem. Quoniam
Albumazar quinto libro majoris introductorii in astronomiam
undecima doctrina sive undecimo capitulo refert Sem filium
Noe hujus scientiam alios docuisse, atque in prologo composi-
tionis astrolabii Ptolemaei dicitur, quod a filio Sem, qui divina
memoria commonitus erat, aut fortasse divino nutu commotus,
hujus scientiae studium in orbem derivatum affirmatur. Hoc
idem indicat sanctorum nostrorum post adventum Domini
occupatio, ut Augustini, Cassiodori, Isidori, Hieronymi, Orosii,
Bedae, Origenis, Eusebii Caesariensis. De his enim scripserunt,
et in his se et alios exercitaverunt solum, aut magis quam in
aliis: Cum ergo isti fuerunt doctores sacrae scripturae et
viri sancti, manifestum est, quod hujusmodi scientiae maxime
valent sacrae scientiae professoribus. Quod autem ipsi de his
scripserunt, manifestum est per Cassiodorum et Isidorum, qui

! This passage is much abbreviated in O. Thus: * Secundo verificatur per
doctores sanctos quos recitant sancti: quod Josephus asseverat. Quod autem,
de his scripserunt manifestum est per Cassiodorum et Isidorum quum tractatus
suos de omnibus istis quatuor composuerunt. Augustinus etiam de numeris et
musica libros diversos conscripsit. Sed non solum isti sed alii multi. Et
Cassiodorus dicit, Mathematica dicere valeamus quaecunque docentur, hoc
tamen signum commune propter sui excellentiam proprie vindicavit. Et in
tractatu, &c. O. has many other omissions in this section of the work, which

are supplied by the two Cottonian MSS., Tib. C. v, and Jul. D. v. I have
indicated some of them, but not all.

MATHEMATICAE IN DIVINIS UTILITAS. | 17]

tractatus suos de omnibus istis quatuor composuerunt.
Augustinus etiam de numeris et musica libros diversos
conscripsit ; Hieronymus in libris diversis, et Orosius ad
Augustinum, et Eusebius de mundi locis, quorum certificatio
eruitur ex fontibus astronomiae, sicut certum est, et sequentia
declarabunt. Beda de cursu solis et lunae, et de tota temporis
diversitate, atque Origenes et Eusebius, quae astronomiae
subjacere noscuntur. Non solum vero de his scripserunt, sed
et idoneos docuerunt haec, ut essent acuti contra haereticos,
sicut patet per Cassiodorum in mathematica sexto libro Eccle-
siasticae Historiae; etiam partes geometriae et arithmeticae
disciplinae, ut ibidem dicitur, quae magis a divinis elongantur
quam astronomica et musicalia. Sed non tantum occupaverunt
se scribendo et alios docendo, imo veritates theologicas per
virtutem harum scientiarum exposuerunt ; sicut per omnia
originalia sanctorum sine contradictione manifestum est, ut
evidenter patet in numeris et locis mundi et rebus coelestibus
et aliis quae ad dictas scientias pertinere noscuntur, sicut
patebit inferius.

Sed non solum sic exposuerunt sacra de facto, sed verbo
asserunt has scientias per omnem modum valere rebus divinis,
et super alias scientias extollunt in hac parte. Cassiodorus Cassio-
quidem in praefatione de artibus et disciplinis secularium 99""*
studiorum sic ait, * Mathematicam Latino sermone Doctrinalem
possumus appellare, quo nomine licet omnia doctrinalia dicere
valeamus quaecunque docentur, haec tamen sibi commune
vocabulum propter sui excellentiam proprie vindicavit. Et in
tractatu mathematicae sic ait, ‘ Disciplinales sunt, quae
nunquam opinionibus deceptae fallunt, et ideo tali nomine
nuncupantur. Has dum frequenti meditatione revolvimus,
sensum nostrum acuunt, limumque ignorantiae detegunt, et
ad illam speculativam contemplationem, Domino largiente,
perducunt; quas merito sancti patres legendas persuadent,
quoniam ex magna parte per eas a carnalibus rebus appetitus
abstrahitur, et faciunt desiderare, quae solo Domino largiente
corde possumus respicere. Duplex quidem pars mathematicae
tam a sanctis quam a philosophis ipsis numeris attribuitur
vulgato sermone, videlicet arithmetica de numeris absolute, et

VOL. I. N

178 OPERIS MAJORIS PARS QUARTA.

musica de proportionibus et rationibus caeteris quae in
numeris reperiuntur, prout ad sonum et gestum referuntur ;
quia sonus et gestus sunt praecisum musicae subjectum, dis-
cussi tamen per proportiones numerorum in musicae scientia."

Augustinés Augustinus autem in secundo de Ordine Disciplinae dicit,

view of
arithmetic,

of music,

‘ad divinarum scripturarum neminem aspirare debere sine
scientia potentiae numerorum. Atque in secundo de Doctrina
Christiana dicit, * numerorum imperitia multa facit non intelligi
translate et mystice posita in scripturis"; et ponit exempla
plurima, adjungens. ' quod ita in aliis multis numerorum formis
secreta in sanctis libris ponuntur, quae propter numerorum
imperitiam legentibus clausa sunt. Et ideo propter utilitatem
numerorum maximam Isidorus ! in tractatu arithmeticae dicit,
* Adime seculo computum, et cuncta ignorantia caetera com-
plectitur; nec differre possunt a caeteris animalibus, quae
calculi nesciunt rationem."

Quamvis autem jam communiter cum arithmetica patet
laus musicae, propter hoc quod utraque proportiones quae in
numeris sunt considerat, tamen numeros, ut sunt in sonis,
maxime laudat Augustinus ad Omerium dicens, ‘In omni-
bus rerum motibus quid valeant numeri facilius consideratur
in vocibus, eaque consideratio quibusdam gradatis itineribus
nititur ad superna itinera veritatis, in quibus viis se ostendit
sapientia hilariter, Et in libro Retractationum dicit ?,
‘Sextus maxime innotuit, quoniam in eo res digna cognitione

1 Born in Carthagena, 570. In 601 he became bishop of Seville, succeeding
his brother Leander, the ‘apostle of Spain,’ and held the bishopric till his death
in 636. His great powers were principally devoted to organizing the work of
the Church in Spain. But he was a man of wide learning. and is placed by
Dante (Paradiso, x) in the Sphere of the Sun with Albert, Thomas Aquinas, and
other great theologians. His principal work is a Cyclopaedia, founded on the
works of Martianus Capella and Cassiodorus, entitled Ovigines, in twenty books,
from which much is to be gathered as to the very limited scientific knowledge
of Christendom in the seventh century. The passage here quoted is in lib. iii.
cap. 4. (Cf. Cantor, vol. i. pp. 705-7.) This work continued to be of great
authority throughout the middle ages.

* O. has, ‘Maxime pervenitur a mutabilibus rebus ad immutabiles ac si Dei
invisibilia per ea quae facta sunt conspiciantur. Etin hbro de Doctrina Chris-
tiana posuit exempla de psalterio decachordo, et admittit quod musicam in
pluribus locis et in sanctis scripturis honorabiliter positam invenimus. Cassio-
dorus in tractatu musicae sic ait, Musica disciplina,’ &c.

MATHEMATICAE IN DIVINIS UTILITAS. 179

versatur, quomodo a mutabilibus numeris perveniatur ad
immutabiles, ac si invisibilia Dei per ea quae facta sunt
conspiciantur. Item in libro de Doctrina Christiana dicit,
*Non pauca claudit atque obtegit in sanctis libris rerum
musicarum ignorantia, et ponit exempla in psalterio decachordo
et cythara et hujusmodi, et adjungit, *quod musicam in
plerisque locis in sacris scripturis honorabiliter positam
invenimus. Cassiodorus quidem et in mandatis Dei et moribus
et scriptura sacra et in omnibus rebus creatis eam valere
dijudicat. Unde intractatu musicae sic ait, * Musica disciplina
per omnes actus vitae nostrae diffunditur; primum si creatoris
mandata faciamus, et puris mentibus statutis ab eo regulis
serviamus, musica quippe est scientia bene modulandi. Quod
si nos vitam bona conversatione tractamus tali disciplinae
probamur semper esse sociati. Quando vero iniquitatem
gerimus, musicam non habemus. In ipsa quoque religione
valde permixta est; unde decalogi decachordus, tinnitus
cytharae, tympana, organi melodia, cymbalarum sonus ; ipsum
quoque Psalterium ad instar instrumenti musici nominatum non
dubium est, eo quod in ipso contineatur virtutum coelestium
suavis nimis et grata modulatio; et ut breviter cuncta com-
plectar, quicquid in supernis sive in terrenis rebus convenienter
secundum actoris sui dispositionem geritur, ab hac disciplina
non refertur exceptum. Gratissima vero nimis utiltsque
cognitio, quae sensum nostrum ad superna erigit et aures
modulatione permulcet.'

De utilitate et scientia astronomicorum dicit, ‘ Astronomiam
si casta et moderata mente perquirimus, sensus nostros, ut
veteres dicunt, magna claritate perfundit. Quale enim est
ad coelos animam subjicere! et totam illam machinam super-
nam indagabili ratione discutere, et inspective mentis subtilitate
ex aliqua parte colligere, quod tantae magnitudinis arcana
velaverunt' Et subjungit, ‘Ex quibus, ut mihi videtur,
climata nosse, horarum spatia comprehendere, lunae cursum
pro inquisitione Paschali, ne simplices aliqua confusione tur-
bentur, qua ratione fiat advertere, non videtur absurdum.
Est et alia quoque de talibus non despicienda commoditas, si

! Caelos animo subire, J.
N 2

of astro-
nomy;

of geo-
metry.

Seven
respects in
which
mathe-
matics are
of use to
theology.
(1) Know-
ledge of the
heavens.

180 OPERIS MAJORIS PARS QUARTA.

opportunitatem navigationis, si tempus arandi, si aestatis
caniculam, si autumni suspectas imbres inde discamus. Et
Augustinus in libro secundo de Doctrina Christiana de utilita-
tibus istius scientiae loquens, vult triplicem utilitatem ejus
esse, videlicet, * demonstrationem praesentium, et cognitionem
praeteritorum, et rationabiles conjecturas futurorum. De-
monstratio praesentium in assignatione proprietatum rerum
coelestium consistit. Et praeter demonstrationem praesentium
habet praeteritorum narrationi simile aliquid, eo quod a prae-
senti cognitione motuque siderum in praeterita eorum vestigia
regulariter licet recurrere. Habet etiam regulares conjecturas
futurorum non suspiciosas et ominosas, sed ratas et certas,
ut ait. Et cum sic sentiant sancti de tribus partibus posteri-
oribus mathematicae, necesse est eos de parte prima lauda-
biliter sentire, quae scilicet est geometria. Ex hujus enim
notitia caeterae dependent, cum prima sit omnium et radix
caeterarum. De cujus laude scribens Cassiodorus sic dicit,
*' Etenim si fas est dicere, sancta divinitas, quando creaturae
suae diversas species formulasque dederit, quando cursus
stellarum potentia veneranda distribuit et statutis lineis facit
currere quae moventur, certaque sede quae sunt fixa constituit,
quicquid bene disponitur ac completur, potest disciplinae hujus
qualitatibus applicari."

Et si velimus descendere ad propria studii theologiae in-
veniemus mathematicam omnino necessariam propter septem
magnas causas. Una est notitia coelestium rerum ; nihil enim
est ita conveniens theologiae et ejus professoribus. Nam
theologia est coelestis divinitus; et ideo nulla scientia humana
speculativa conveniet ei in tantum sicut coelestis. Et per
totam scripturam a terrenis revocamur et ad coelestia excita-
mur. Et conversatio nostra secundum Apostolum in coelis
est si sumus vere Christiani, atque aspiramus et credimus nos
fore mansuros corporaliter in coelo et perpetue. Quapropter
nihil deberet tantum sciri a nobis sicut coelum, nec aliquid in
humanis tantum desiderari. Et si nos gaudemus exponere
scripturam, justum est exponi per rerum inferiorum proprie-
tates quae in scriptura ponuntur et aliter sciri non possunt.
Quare similiter cum in scriptura sint multa de coelestibus et

MATHEMATICAE IN DIVINIS UTILITAS. 181

difficilia, necesse est theologum scire coelestia. Praeterea
cum rerum magnitudo excitet nos ad reverentiam creatoris,
et non est comparatio rerum inferiorum ad coelestium magni-
tudinem, tunc cognitio inferiorum non habebit comparationem
superiorum respectu finis, qui est laus et reverentia creatoris..
Dicit enim Avicenna in nono Metaphysicae, ‘ quod ea quae sunt
sub circulo lunae sunt pene nihil comparatione eorum, quae
sunt supra.' Et Ptolemaeus ostendit in Almagesto et omnes
sciunt astronomi, quod tota terra cum omnibus inferioribus se
habet respectu coeli sicut centrum ad circumferentiam. Sed
centrum non habet aliquam quantitatem. ^ Quapropter con-
similiter concludunt de terra respectu coeli, licet in se sit
magnae quantitatis. Et minima stellarum visu notabilium, ut
dicit Alfraganus in principio sui libri, est major terra; sed
minima stellarum respectu coeli non habet quantitatem, de
qua sit vis. Et cum ex octavo Almagesti et ex Alfragano
pateant sex stellarum fixarum magnitudines, quaelibet illarum
quae sunt in prima magnitudine, est aequalis terrae circiter
centies et septies. Et illarum quaelibet quae sunt in sexta mag-
nitudine, est aequalis terrae decies octies. Et sol est centies
septuagies fere major tota terra, sicut probat Ptolemaeus
quinto Almagesti. Et secundum eum una stella non complet
motum suum semel in circuitu coeli nisi in triginta sex millibus
annorum propter coeli magnitudinem, cum tamen stella movea-
tur incredibili velocitate. Sed terra tota posset perambulari
infra tres annos. Quapropter magnitudo inferiorum non habet
comparationem ad coelestia. Similiter nec utilitas; quia tota
utilitas inferiorum causatur ex superioribus. Duplex enim
allatio solis sub obliquo circulo cum aspectibus planetarum
est causa omnium quae fiunt hic inferius.

Si igitur descendamus ad coelestia secundum considera-
tiones theologiae, patet quod theologi quaerunt in sententiis
et tractatibus super sententias, an orbes coelestes sint con-
tinui vel discontinui, et de numero coelorum, maxime propter
nonum et decimum, et de figura eorum et circulis epicyclis
et eccentricis, et motibus in illis, et de differentiis positionum
in coelis, ut de dextro et sinistro, ante et retro, et sursum
et deorsum, et de proprietatibus coelorum, ut de luce et

182 OPERIS MAJORIS PARS QUARTA.

perspicuo et hujusmodi, atque de influentia coelorum in
haec inferiora, et de differentia coeli et naturae elementaris
praecipue propter ignem. Nam Augustinus et alii aliquando
secundum opinionem Platonis nominant coelum esse igneae
naturae. Quaerunt etiam de locis mundi propter paradisum,
an sit sub aequinoctiali circulo vel non; et de inferno ubi
sit; et utrum coelestia habent posse super generabilia et
corruptibilia, et utrum super animam rationalem ; et de fato
et hujusmodi quae ad judicia astronomiae noscuntur pertinere ;
et alia innumerabilia multiplicantur quotidie in quaestionibus
theologiae. Sed non solum tractatus sententiarum, sed
ipse textus sacer cum expositionibus sanctorum hoc requirit.
Nam capitulum primum Genesis multas habet difficultates
propter coelestia, ut ex ipso textu patet, et per expositiones
sanctorum, praecipue Basilii, Ambrosii, Bedae, in libris suis
qui Exemeron vocantur. Et in Josue, propter diei longitu-
dinem, sole stante, praecipue per operationem ad longitudinem
diei, qua retrocessit sol decem lineis ad verbum Isaiae pro-
phetae. Nam videtur esse contradictio in his locis. Atque
cum Salomon dicat in Ecclesiaste quod sol omni die secundum
expositionem Hieronymi in originali flectitur ad aquilonem,
vix aliquis mathematicorum potest hoc intelligere. Quoniam
sciunt quod a solstitio hyemali usque ad solstitium aestivale
flectatur omni die ad aquilonem per gradum unum fere. Sed
in alia medietate anni e converso. Et de altitudine firma-
menti in Ecclesiastico ; et quomodo sol in meridiano exurit
terram, ut ibidem dicitur, indigent astronomica capacitate.
Atque Hyades et Pleiades et Arcturus atque Orion, et interiora
Austri de quibus beatus Job loquitur, habent magnam diffi-
cultatem, praecipue cum dictat beatus Hieronymus super
Isaiam, quod Orion habet xxii stellas, quarum novem primae
sunt in tertia magnitudine, et novem aliae in quarta magni-
tudine, et quatuor residuae in quinta magnitudine, nec plus
dicit. Sed haec sciri non possunt nisi ex octavo Almagesti,
ubi sex gradus magnitudinis stellarum assignantur, et de-
terminantur quae stellae sunt in qualibet illarum. Et quia
infinita sunt alia in scriptura et in expositionibus sanctorum,
quae scientiam coelorum et astronomiae judicia tangunt:

MATHEMATICAE IN DIVINIS UTILITAS. 183

quapropter necesse est theologum bene scire coelestia, tum
propter occupationem quaestionum in sententiis et summis,
tum propter ipsum textum.

Secunda radix astronomiae respectu theologiae et proprie (2) Astro-
respectu textus consistit in locorum mundi consideratione. yeupes
Nam totus textus est plenus his locis, et ideo nihil magnificum Biblical
sciri potest nisi sciantur haec loca. Tota enim series scripturae geography.
decurrit penes regiones, civitates, deserta, montes, maria, et
caetera loca mundi, quorum certitudo non potest haberi nisi
per scientias praedictas, quia harum proprium est distinguere
partes habitabiles a non habitabilibus, et habitabile dividere
in tres partes magnas, Europam, Africam, et Asiam, et istas
tres in septem climata nota, praeter alia climata irregularia
quamplura. Et haec climata certitudinaliter nisi per virtutem
illarum scientiarum nescit quisquam separare in provincias et
regiones et caetera loca, ut inveniantur civitates notae et
famosae, sicut Jerusalem, Babylon, Meroe, Alexandria, Anti-
ochia, Ephesus, Athenae, Tarsus, Roma, et caeterae prae aliis
notatae ab astrologis secundum debitam distantiam ab invicem,
et ab oriente et ab occidente, septentrione et meridie, quibus
inventis poterunt et regiones famosae ab eis denominatae
inveniri, et maria et deserta et montes et omnia quae in sacris
literis continentur. Hic enim est magna utilitas istarum
scientiarum in sacra scriptura. Et forte nihil utilius de philo-
sophia poterit inveniri; quoniam qui ignorat loca mundi, ei
multoties non sapit cortex historiae per loca infinita, et
maxime propter falsitatem multiplicem bibliarum novarum ;
atque per consequens ad intellectus spirituales impedietur
ascendere et non nisi imperfecte poterit eos explicare. Qui
vero imaginationem bonam locorum habuerit, et situm eorum
et distantiam et altitudinem et longitudinem latitudinem et
profundum cognoverit, necnon et diversitatem eorum in calidi-
tate et siccitate, frigiditate et humiditate, colore, sapore, odore,
et pulchritudine, turpitudine, amoenitate, fertilitate, sterilitate,
et aliis conditionibus expertus fuerit, et optime placebit ei
historia literalis, et de facili atque magnifice poterit ingredi ad
intelligentiam sensuum spiritualium. Non enim est dubium
quin viae corporales significent vias spirituales, et loca corpo-

184 OPERIS MAJORIS PARS QUARTA.

ralia significent terminos viarum spiritualium et convenientiam
locorum spiritualium, quoniam locus habet proprietatem
terminandi motum localem et rationem continentiae ; et ideo
istorum locorum cognitio et literam facit, ut dictum est,
intelligi, et vias parat ad intelligentias spirituales: quod multi-
pliciter confirmatur per dicta et facta et scripta sanctorum.
Primo, quia dicit Hieronymus in prologo secundi Parali-
pomenon, ' Sanctam scripturam lucidius intuebitur, qui Judaeam
oculis contemplatus est, et antiquarum urbium memorias,
locorumque vel eadem vocabula vel mutata cognoverit.
Secundo, quia laboraverunt sancti in videndo loca illa et
circumeundo. Propter quod beatus Hieronymus dicit prae-
dicto prologo, *Nobis curae fuit cum eruditissimis Hebrae-
orum hunc laborem subire, ut circumiremus provinciam, quam
universae Christi Ecclesiae sonant. Hoc autem non fecisset,
nisi propter sacrarum literarum intelligentiam. — Tertio, quia
libros multos scripsit de locis mundi, distantiam et situm
eorum et caeteras conditiones magna certitudine determinans.
Orosius etiam ad Augustinum haec loca mirabili utilitate ac
sincera veritate explicat evidenter. Isidorus autem in pluribus
locis regiones et civitates utilius, si potest dici, quam priores
determinat. Cassiodorus autem in climata distinguere non
omittit. Eusebius etiam Caesariensis, ut narrat Hieronymus
in libro de locis, post chirographiam terrae Judaeae et
distinctas tribuum sortes ipsius quoque Jerusalem templique
in ea cum brevissima expositione picturam ad extremum
laboravit, ut congregaret nobis de sacra scriptura omnium
pene urbium, montium, fluminum, viculorum, et diversorum
locorum vocabula, quae vel eadem manent vel immutata vel
aliqua ex parte corrupta. Origenes quidem Adamantius super
Josuam in originali, sicut et in glossa super xviii Josuae
recitatur, loquens de multitudine locorum in scriptura posito-
rum, et inter caeteras laudes locorum istorum, sic nos alloqui-
tur, dicens, ‘Ne cum fastidio haec legatis, et putetis vilem
scripturam ex multis nominibus contextam ; sed scitote in
his contineri majora mysteria quam potest humanus sermo
proferre, vel auditus mortalis audire. Cum ergo nostri sancti
expositores et doctores sacri in istis locis tantum laboraverunt,

MATHEMATICAE IN DIVINIS UTILITAS. 185

et tanta mysteria contineri fatentur, non est dubium quin
eorum cognitio per omnem modum sacrae scripturae est
necessaria. Sed proprium est astrologiae et astronomiae dare
rationes Jocorum mundi et plenam certitudinem. Quapropter
istae scientiae sunt valde necessariae in hac parte. Possunt
autem pulchre verificari in exemplis. Qui enim audit historias
versantes circa Jordanem, Jericho cum planitie sua, montem
Oliveti, vallem Josaphat, Jerusalem, et non habet imagina-
tionem locorum istorum et proprietatem eorum, sensum litera-
lem ignorabit, et ei non immerito non multum sapiet cursus
historiae, atque per consequens sensus spirituales obteguntur.
Qui vero scit longitudines, latitudines, profunditates, altitudines,
varietatem qualitatum, ut calidi, frigidi, sicci et humidi, necnon
et eorum quae consequuntur ad haec quatuor, ut mollis, duri,
grossi, subtilis, asperi, laevis, aridi, liquidi, lubrici, et aliorum
innumerabilium, quae quarto Meteorologicorum determinan-
tur; necnon et colores, et sapores, odores, pulchritudines,
turpitudines, amoenitates, sterilitatem, fertilitatem, naturam
infectivam, corruptivam, et eis contrarias, et caetera quae in
locis considerari habent, potest sensum literalem ad purum
concipere et in eo delectari, atque ad sensus spirituales gloriose
et placide transire.

Paucas enim conditiones locorum praedictorum consider- The
ando, possumus magnificos sensus exprimere moraliter et alle- dug of
gorice et anagogice. Jordanis quidem decurrit ab aquilone Biblical
ad austrum, et jacet in oriente respectu Jerusalem, quae geography.
est in occidente non longe a mari magno posita, et inter
illa duo primo a parte Jordanis est Jericho civitas cum sua
planitie, deinde mons Oliveti, tertio vallis Josaphat, et tunc
sequitur Jerusalem. Mundus autem, dicunt sancti, significatur
per Jordanem secundum rationem interpretationis ejus et
propter ipsius proprietates, quia currit in mare mortuum, quod
est instar inferni, et propter multa alia. Et Jericho carnem
significat, ut volunt sancti. Mons Oliveti significat excel-
lentiam vitae spiritualis propter montis excellentiam, et
dulcedinem devotionis propter Oliveti rationem. Vallis
Josaphat significat humilitatem propter rationem vallis, et
viam coram oculis majestatis, propter hoc quod interpretatio

186 OPERIS MAJORIS PARS QUARTA.

hujus nominis Josaphat est, in conspectu Domini. Et Jerusalem
significat visionem pacis, et moraliter est anima sancta quae
habet pacem cordis; allegorice significat Ecclesiam militan-
tem; anagogice Ecclesiam triumphantem.

Quiigitur a principio vitae suae seu ab ortu nativitatis suae ab
oriente rationis deliberantis seu usu rationis vult devenire saltem
in occidente vitae suae et in senectute ad pacem cordis, et hoc
moraliter ; et ut sit membrum fidele et perfectum Ecclesiae,
sub cujus umbra jaceat in pace contra insultus hostis maligni,
et hoc allegorice; et ut sit ejus conversatio in coelesti Jeru-
salem in hac vita, et transferatur in morte ad illam civitatem
sanctam, ubi sedebit in pulchritudine pacis in tabernaculis
fiduciae vel requie opulenta; debet primo Jordanem, id est,
mundum, aut sibi subjiciendo relinquere, ut sancti seculares,
aut omnino renunciando recedere, ut religiosi. Ibi enim est
primus gradus vitae spiritualis et aliis facilior. Quo facto,
oportet aggredi carnem, quia ipsam non est ita facile vincere
sicut mundum. Est enim pestis familiaris et non relinquens
subjectum. Debet autem ipsam non destruere et cum impetu
frangere, sed paulatim et discrete ejus superbiam domare.
Propter quod consideratur Jericho cum sua planitie; et ideo
debet poenitens plana via procedere, ut rationabile sit ejus
obsequium, ne si carnem stulte obruat, non possit spiritus ad
altiora pertingere. Hoc enim est contra multos ad poeni-
tentiam conversos, qui primo anno vel secundo corpora sua
destruunt, et postea fiunt inutiles, ut nec se nec alios valeant
juvare. Postquam vero homo mundum subjugaverit, et
carnem ut oportet domuerit, tunc et non ante est aptus ut
ascendat ad excellentiam vitae spiritualis et dulcedinem
devotionis. Ex tunc enim potest ascendere ad montem
Oliveti et ad cacumen perfectionis attingere, atque in suavitatem
orationis et contemplationis se immergere. Cum vero fuerit
sufficienter exercitatus in ascensu et circuitu istius celsitudinis,
adhuc! oportet vallem Josaphat transire, hoc est, totam vitam
suam in perfecta humilitate debet concludere, ut sit pauper et
humilis spiritu in conspectu Dei, non in oculis suis vel homi-
num. Multi enim apparent humiles sibi et aliis, et sunt coram

1 J. has, * tunc esset in Jerusalem nisi quod oportet.'

MATHEMATICAE IN DIVINIS UTILITAS. 187

Deo et angelis superbissimi. Quando vero totam compleverit
vitam perfecta humilitate, tunc est in Jerusalem, secundum
ejus sensum triplicem. Habebit enim pacem cordis, quia pax
talis sequitur vitae spiritualis perfectionem. ‘Non enim est
pax impiis, dicit Dominus. Sed sanctis est pax Dei, quae:
exsuperat omnem sensum, et in pace Ecclesiae militantis
quiescit securus, qua pace carent infideles et peccatores in
statu damnationis existentes, quos agitat diabolus et turbat de
peccato in peccatum, et de poena peccati ad novam poenam.
Et! ut dictum est, participabit etiam in hac vita in spe certa
et revelationibus illa beata visione pacis supernae Jerusalem,
quam per gratiam Dei in morte consequetur.

Non solum autem haec loca inter Jordanem et Jerusalem
cognita et historiam declarant et sensus spirituales explicant,
sed alia loca innumerabilia quae inter duos hos terminos reperi-
untur in scriptura. Si quis etiam velit ulterius considerare
alias conditiones enumeratas, multo magis et quasi incompara-
biliter poterit sensus divinos elicere, ut patet intuenti. Sed
modo sufficit innuere quomodo ex paucis multa ex parvis magna
ex planioribus obscura contingat elicere. Sed non possunt loca
mundi sciri, nisi per astronomiam ; quoniam oportet nos primo
scire longitudines et latitudines locorum. — Latitudo est ab
aequinoctiali, et longitudo ab oriente, quatenus sciamus sub
quibus stellis quae loca coaptentur, et quantum sunt a via
solis. Nam secundum haec videmus sensibiliter res hujus
mundi variari, et non solum in naturalibus, sed in moralibus.
Oportet etiam per astronomiam scire, qui planetae dominentur
quibus regionibus; nam secundum hoc potenter immutantur
regiones. Et multa hujusmodi consideranda sunt per astrono-
miam, ut sciamus naturas locorum in scriptura; et non solum
propter loca, sed propter res in eis locatas. Et rerum omnium
cognitio est necessaria, tam propter sensum spiritualem, quam
literalem, ut patet ex dictis.

Tertia radix est de temporibus. Totus enim cursus scrip- (3) Astro-
turae currit per tempora et secula et aetates a principio mundi yerifes
usque ad Christum Dominum, et omnia sunt ordinata propter oid

1 This and the following sentence are omitted in O.

Reduction
of all
Calendars
toChristian
standard.

188 OPERIS MAJORIS PARS QUARTA.

ipsum, ut alius legislator non expectetur, sed quod ille solus
sit salvator mundi per suam legem ; quatenus error Judaeorum
evacuetur de expectatione Messiae; et error Saracenorum de
Mahometo qui secutus est Christum ; et error eorum qui
adhaerebunt adhuc legis latori nefariae qui venturus est, ut
Albumazar docet libro Conjunctionum, qui in veritate erit
Antichristus! ; quatenus etiam omnes sectae paganorum, idolo-
latrarum, Tartarorum, haereticorum, et caeterorum infidelium,
qui per mundum dispersi sunt per sectas pene innumerabiles,
deleantur per certificationem temporis salvatoris, ut nec ante
eum nec post aliquis alius teneatur, per quem salus humani
generis habeatur. Sed nullus potest certificare de temporibus,
nisi astronomus, nec aliqua scientia habet de his certificare
nisi astronomia. Omnes enim mendicant reliquias ejus in hac
parte, ut manifestum est. Et si consideremus inveniemus
multis modis quomodo astronomia est hic necessaria. Nam
tempora ista, quaedam sunt lunaria, quaedam solaria et lunaria,
quaedam habent principium determinatum, ut apud Judaeos
astronomos. Incipiunt enim a lunatione Octobris annum, quia
sunt usi ab antiquo tabulis et canonibus ad occasum solis
civitatis Jerusalem. Sed adhuc gaudent uti eis propter terram
quae data fuit eis a Deo. Quaedam vero habent principium
indeterminatum, ut tempora solemnitatum apud Hebraeos, et
tempora Arabum, et hoc differenter multum. Quaedam vero
tempora sunt solaria, et horum quaedam semper habuerunt
quartum ultra dies integros, ut tempus Graecorum et Latino-
rum; quaedam nunquam, ut tempora Persarum ; quaedam
aliquando sic aliquando non, ut tempora Aegyptiorum. Et
principia annorum variantur apud ipsos, sicut canones astro-
nomiae docent et Almagesti, et alia multa. Cum igitur in
scriptura contineantur anni lunares et solares et Graecorum et
Latinorum et hujusmodi, et volumus omnia tempora reducere
ad annos solares, et ad annos Latinorum, qui sunt anni Christi,
necesse est nobis in sacra historia scire horum temporum
diversitatem, et ut sciamus quid est proprium cuilibet et
quomodo aequantur ad invicem, et quomodo possumus extra-

! What follows to the end of the paragraph is omitted in O.

‘MATHEMATICAE IN DIVINIS UTILITAS. 189

here majus de minori, et contrario, et quodlibet de quolibet.
Sed impossibile est hoc fieri, ut exigit scriptura, nisi per
canones et tabulas et caeteras considerationes astronomiae !.

Caeterum computantur anni a principio mundi secundum
Hebraicam veritatem, et computantur secundum LXX inter-
pretes; sed discordant penitus, et omnes historiae et chronicae
auctores et sancti hic contradicunt sibi invicem, non solum
in toto tempore a principio usque ad Christum, sed in aetatibus
particularibus. Sed diversitas haec non potest certificari, nisi
per aliquam radicem certam. Nulla vero scientia potest hic
invenire nec habet unde cogitet de tanta certitudine nisi
astronomia, cujus est considerare revolutiones certas et ratas
eclipsium et conjunctionum planetarum et caeterarum revolu-
tionum coelestium, stante ordine naturae. Quapropter oportet
quod astronomia apponat hic diligentiam. Et hoc possumus
videre per libros astronomorum. Nam Ptolemaeus in Alma-
gesti certificat nos de tempore a Nabugodonosor usque ad
Alexandrum, et ab eo usque ad Octavianum Augustum, et ab eo
usque ad Adrianum principem. Et Ecclesia tenet quod 41™°?
anno Augusti fuit Dominus natus. Quapropter per hanc
viam certificatur multum tempus a Nabugodonosor usque ad
Christum ?. Et si consideremus sententias Albumazar in libro
Conjunctionum, videbimus quod ipse ponit principium mundi
et primum hominem, scilicet Adam, et ab eo numerat annos
usque ad diluvium, et ponit diem et horam quibus incepit
diluvium, et per revolutiones planetarum et per eorum con-
junctiones determinat sequentia secula, scilicet quando fuit
Nabugodonosor, et quando Alexander, et quando Dominus
Christus, et quando Mahometus, et sic de multis. Et ideo
per artem Albumazar et Ptolemaei et caeterorum mathe-
maticorum oportet resolvere tempora usque ad principium
mundi, ut* sciamus quot anni sint a principio usque ad

! The whole of the foregoing paragraph, except the first two sentences,
omitted in O. 3 Sic in O. J. has xlii.

* This is given somewhat more fully in Op. Tert. ch. 54 (Brewer, p. 208).
The time from the creation of Adam to the Deluge is stated to be 2,226 years,
Y month, 23 days, and 4 hours.

* The following page and half, down to the word dicentes, i is omitted in O.,
but is supplied by the two Cottonian MSS.

Date of
creation.

190 OPERIS MAJORIS PARS QUARTA.

Christum non solum in summa, sed per singulas aetates ac
secula.

Secundo, possumus persuadere de utilitate astronomiae
propter temporis principium determinatum, scilicet an a luna-
tione Octobris seu aequinoctio autumnali, aut ab aequinoctio
vernali. Nam multi voluerunt secundum sententiam vulgi,
quod mundus fuerit creatus circiter aequinoctium vernale ; sed
alii apud aequinoctium autumnale ; quia in veritate secundum
Hebraicam veritatem, annus, quantum ad seriem temporis
naturalem, incipit circiter aequinoctium autumnale. Et hoc
manifeste potest probari per textum Exodi, ubi dicitur, quod
scenopegia celebretur in exitu anni; id est in mense post
exitum anni. Nam 23 habetur sic, * Sollemnitatem quoque
in exitu anni, quando congregaveris omnes fruges de agro.
Ergo post principium novi anni tunc incipit. Et 34 de eodem
dicitur, ‘ Facies sollemnitatem, quando redeunte anni tempore
cuncta conduntur. Et in glossa Hieronymi Ezechielis primo
habetur, quod October est primus mensis anni et Januarius
est quartus. Et Nehemiae primo, ‘Et factum est in mense
Casleu, id est Decembri anno vicesimo '; et secundo, Factum
est in * mense Nisan anno vicesimo. Si enim Nisan, id est
Aprilis, esset caput anni non diceretur anno vicesimo sed
anno primo et vicesimo, ut patet. Item, per praecepta de
seminandis et metendis agris propter quietem septimi anni.
Nam si Nisan, id est Aprilis, sit caput anni, tunc cum
seminatur in Septembri vel Octobri sexti anni, non poterit
meti in septimo anno, quia ferialis est secundum legem,
et sic peribit seges. Item cum totus annus septimus feri-
alis est, tunc si incipiatur annus ab Aprili usque ad Sep-
tembrem non haberent quod comederent, quia fruges sexti
anni non abundabunt nisi pro septimo anno et pro octavo
et pro semine octavi, ut dicit Josephus, et non pro nono
anno. Item per Hieronymum in epistola de solemnitatibus
illud idem patet. Nam dicit sic, ‘In fine anni solaris apud
Hebraeos in septimo mense, quando congregantur fructus
in horrea sive in cellaria, tunc sollemnia celebrare lege
praeceptum est, prima die tubarum, decima die expiatio-
num celebrari debere sabbata. Et a quinto decimo die

MATHEMATICAE IN DIVINIS UTILITAS. I9I

usquedum finiantur octavae tabernaculorum, feriae esse
praecipiuntur.'

Caeterum per Bedam libro temporum, et praecipue per
Josephum et omnes Hebraeos a principio usque nunc patet,
quantum ad initium sollemnitatum, quod Moyses constituit
annum ab Aprili propter Pascha, quod est prima sollemnitas,
et propter mysterium novi temporis, scilicet Christiani, cujus
anni ab incarnatione computantur, quae fuit circiter aequi-
noctium, et in quo tempore nunc gloriosum Pascha celebratur.
Sed in venditione et emptione et caetera gubernatione,
quantum ad anni principium, prioris seculi Moyses decreta
servavit, ut dicit Josephus primo antiquitatum. Prius autem
seculum fuit a Moyse redeundo ad principium mundi. Ergo
cum principium primi anni mundi et principium mundi fuerunt
idem, concludunt isti quod mundus incepit circiter aequinoc-
tium autumnale, ut post spoliationem fructuum veteris anni
incipiat cultura novi. Haec autem alteratio est gravis valde,
et ideo recurrunt homines periti ad scientiam cujus est cer-
tificare tempora, scilicet ad astronomiam. Et illi qui tenent
primam opinionem volunt se tueri per astronomiam, dicentes
quod mundus fuit creatus in meliori dispositione propter
hominis et rerum generationem, et ideo debuerunt planetae
esse in meliori situ suo respectu gubernationis mundi. Qua-
propter ponunt quod sol fuit in medio mundi creatus, ut in
aequinoctiali circulo, ut aequaliter se haberet ad totum mun-
dum. Et in Ariete eum posuerunt non in Libra, quia dicunt
astronomi quod sol ibi habeat suam exaltationem, quae est
major ejus dignitas vel secunda post majorem. Habet enim
quinque dignitates et fortitudines, scilicet, exaltationem,
domum, triplicitatem, terminum, et faciem. Et iterum ponunt,
quod cum oporteat planetas habere eccentricos, necesse fuit
mundo ut lux solis fuisset in Ariete, quia locus augis est longe
nobilior quam alia pars eccentrici. Nam quum sol et luna et
caeteri planetae sunt in augibus suis, tunc sunt fortioris et
melioris operationis in hoc mundo, sicut determinant astronomi,
et sicut experientia docet. Et ex his omnibus sequitur
secundum hos quod mundus incipiebat ab aequinoctio vernali.
Et quod objicitur eis, quod omnia terrae nascentia fuerunt

192 OPERIS MAJORIS PARS QUARTA.

creata in maturitate fructuum, quod non accidit per naturam,
dicunt quod hoc fuit ex vi creatoris non ex vi naturae, cum
tamen adjungant quod in multis regionibus australibus est
calor veris magis conveniens pro fructibus maturandis quam
aestatis. Et non solum in vere, sed iterum in autumno habent
fructus propter temperamentum aequinoctii utriusque. Alii
vero, qui ad plura respiciunt, scilicet ad rationes praedictas de
principio anni et mundi, efficaces et insolubiles eis qui prae-
dictam opinionem tenent, istorum sententias nituntur reprobare
per vias astronomiae. Nam allegant, quod antiqui astronomi
ponunt principium anni circiter principium Octobris, sicut
patet in expositione tabularum, quae Almanac vocantur. Et
dicunt quod Ptolemaeus invenit certitudinaliter augem solis in
Geminis tempore suo. Sed si in principio fuisset in Ariete,
sicut in exaltatione solis, ut in decimo quinto gradu vel decimo
nono, in quibus ponitur solis exaltatio, moveretur aux secundum
motum planetarum, scilicet secundum signa contra motum
primi coeli. Sed hoc non potest esse, quia tunc regiones
habitabiles super quas est aux fierent inhabitabiles per succes-
sum temporis, quando scilicet oppositum augis eveniret super
eas; et e contrario inhabitabiles fierent habitabiles quod est
absurdum: propter quod ponunt quod aux moveatur secundum
motum coeli stellati, non quemcunque imaginatum, sed per
motum Indorum et Thebit, scilicet per descensum et ascensum
polorum ejus, vel per motum capitum Arietis et Librae coeli
stellati in parvo circulo circa capita Arietis et Librae fixa,
quae sunt in coelo nono. Quo quidem motu capita Cancri et
Capricorni moventur progrediendo et regrediendo in superficie
eclipticae zodiaci immobilis nunc ad orientem, nunc ad occi-
dentem, sicut apparet ex imaginatione Thebit, qui super
opera Ptolemaei addidit in hac parte juxta sententias Indorum.
Sic enim assignatur motus octavae sphaerae. Et in hoc
Arzachel in tabulis et canonibus concordat, et Albumazar in
libro Conjunctionum, et omnes astronomi sic modo utuntur.
Sed et sic ponunt augem solis moveri progrediendo et regre-
diendo, et ita non recedit a Geminorum signo, propter quod
non vadit in circuitu terrae, ut oppositum augis aliquando
contingat terras habitabiles.

MATHEMATICAE IN .DIVINIS UTILITAS. 193

Caeterum illi, qui ponunt modo praedicto, scilicet quod sol Position of
fuit creatus in Ariete, dicunt quod paradisus est sub aequi- Paradise.
noctiali propter temperamentum maximum, quia uterque
locus est nobilior mundi, ut ponunt. Sed si aux fuerit ibi in
principio mundi, tunc fuit oppositum augis in loco Librae, qua-
propter in aequinoctio autumnali ejusdem anni fuit sol super
eadem loca. Quare tunc fuit solutum temperamentum, et
bonitas complexionis paradisi et regionis totius aequinoctialis
violata singulis annis, quod est contra proprietatem illorum
locorum secundum positionem istorum. Nam sic factae sunt
inhabitabiles cito propter oppositum augis, quia tunc sol est
prope terram et comburit eam. Sed ipsi volunt quod tem-
peratior locus mundi sit sub aequinoctiali, et maxime in
paradiso, quod stare non potest cum praedictis. Et ideo hi,
qui sic objiciunt, volunt solem fuisse in Libra, quatenus
statim peccatum Adae sequeretur poena, ut separatus a para-
diso non posset pertingere ad ipsum propter combustionem
regionis ultra aequinoctialem. Et ad hanc combustionem
faciendam, statim post ejectionem Adae a paradiso usque
citra aequinoctialem, necesse fuit ut sol foret in Libra, quia
ibi jam constitutus fuerit versus oppositum augis ultra medie-
tatem eccentrici, quatenus statim incipiet combustio, quod non
accidisset in Ariete. Et multae considerationes astronomiae
sunt hic. Et ideo oportet theologum in hac parte scire bene
radices astronomiae.

Et tertio indiget theologus considerationibus astronomiae Longevity
nunc tactis propter longaevitatem Adae et filiorum ejus oF parri
usque post dies Noae, de quibus loquitur scriptura. Nam
mirum est quomodo declinavit aetas humana, cum in prin-
cipio fuit tantae longitudinis et tot tempora transivit. Et
ideo multi imponunt bonitati constellationis coelestis in
principio mundi, et circiter hoc. Et investigant illam boni-
tatem per dignitates planetarum, ponentes, ut dixi, solem esse
in aequinoctiali et in Ariete et in auge, et planetas alios esse
in bonis locis et convenientibus aspectibus, ut fortificaretur
natura humana per bonitatem constellationis a principio,
quatenus vivere posset ita diu. Sed paulatim deficiente
bonitate dicta per mutationes situs planetarum et stellarum

VOL. I. O

Date of
deluge.

194 OPERIS MAJORIS PARS QUARTA.

abbreviata est vita hominis ut ad aliquem terminum veniret
ultra quem non contingat transire; quia omnium natura
constantium est ratio et terminus, ut Aristoteles vult, quem
terminum ponit scriptura circiter octoginta annos in vigore,
sed amplius est labor et dolor. Sed jam tactum est, quo-
modo contra haec objiciunt alii mathematici. Et magna
disputatio est hic ; et forsan invenietur quod declinatio aetatis
non est per recessum a bona mundi dispositione in principio,
sed ob alias causas determinatas, ut suo loco inferius ex-
ponetur.

Et quarto necesse est principium anni certificari propter
diluvium. Nam, ut dicit Josephus, diluvium fuit in Novembri.
Dicit enim haec verba, ' Contigit autem haec passio sex-
centesimo anno nativitatis Noae, mense secundo, qui a Mace-
donibus Dios nuncupatur, ab Hebraeis autem Maresvan.’
Sed Dios, ut dicit Beda libro temporum, est November, non
Maius, ut vulgus aestimat theologorum, et ideo Maresvan
est November, sicut idem Beda dicit. Et est secundus mensis,
quia October est primus in naturali ordine temporis, ut prius
probatum est. Unde Beda dicit, Tisseri enim, qui est October,
qui Maresvan praecedit, propter collectionem frugum et cele-
berrimas festivitates, et hunc Tisseri novum annum appellant
Hebraei. Sic enim Aegypto in annum constituerunt, ut
Tisseri, id est October, esset principium anni. Et ideo
magister in historiis! et quidam glossatores non intellexerunt
Josephum, cum credebant quod Dios et Maresvan essent
Maius. Et ideo omnes sequentes eos decepti sunt propter
Graeca et Hebraica vocabula mensium Graecorum et He-
braeorum, quae non intellexerunt, ut manifestum est inquirenti
eorum opinionem, qui probant principium anni et mundi fuisse
circiter aequinoctium anni autumnale. Et ideo hic cadit
eadem perplexitas, quae prius. Unde necesse est, ut diluvium
fuerit in Novembri, secundum quod probatum est superius
tempus naturaliter incipere ab Octobri. Et Josephus hoc

' This is Peter Comestor (the devourer of books), author of the Historia
Scholastica, and commonly called Magister Historiarum. The Historia Scholastica,

compiled in the latter half of the twelfth century, became the classical text-book
for Biblical students.

MATHEMATICAE IN DIVINIS UTILITAS. I95

evidenter ostendit omni homini, qui scit vocabula Graeca et
Hebraica de mensibus anni.

Non solum vero de principio mundi et anni naturaliter
accidit dubitatio apud theologos; sed de principio diei
naturalis, an scilicet nox praecesserit diem artificialem vel
e contrario. Et hoc est quintum hic inducendum circa
substantiam temporis. Et multi dicunt diem praecessisse
noctem, et exponunt scripturam ut possunt. Sed secundum
Hieronymum super Jonam et super Matthaeum, nox praecessit
diem. Nam, ut ait Alfraganus! in astronomia sua, * Omnes
nationes, quae utuntur mensibus lunaribus, incipiunt diem
ab occasu solis. Sed Hebraei et scriptura utuntur mensi-
bus lunaribus et annis, sicut potest probari modis multis.
Ergo Hebraei et scriptura utuntur die naturali cujus nox
praecedit diem. Et ideo tabulae Hebraeorum astronomicae,
quibus Hebraei usi sunt in certificatione temporum, factae
sunt ad occasum solis civitatis Jerusalem, sicut tabulae
astronomorum Latinorum factae sunt ad meridiem civitatis
Toleti vel alterius. Propter quod in lege determinatur, ut a
vespera dies incipiat. Nam Levitici xxiii dicitur ‘a vespere
ad vesperum celebrabitis sabbata vestra."

Quarta vero radix mathematicae respectu theologiae est (4) De-
penes accidentia et passiones temporum, cujusmodi sunt hnition of
primationes et caeterae aetates lunae et embolismi et hujus- logical
modi. Textus enim et expositiones doctorum requirunt P°"°*
magnam istorum cognitionem, et maxime secundum Hebrae-
orum considerationes tam astronomicas quam usuales. Differt
autem haec radix a praedicta, quod illa consistit penes sub-
stantiam temporum, haec vero penes proprietates et accidentia.
Considerari ergo oportet radicales veritates circa hujusmodi
passiones, antequam convertatur sermo ad scripturam, quia
aliter persuasio esset omnino inintelligibilis. ^ Dico ergo
quod primatio lunae secundum astronomos non dicitur a
visione novae lunae apud Hebraeos, ut aliqui de theologis
dixerunt, quoniam hoc tempus non est aequale, sicut ostendit
Alfraganus. Sed lunatio una aequatur alteri. Aliquando
enim in mane videtur novacula lunae veteris in suo decremento,

1 See note on Alfraganus in the geographical section
O 2

196 OPERIS MAJORIS PARS QUARTA.

et in eodem die in vespere videtur novacula lunae novae, et
aliquando per spatium trium dierum distant, ut experimentum
docet et Alfraganus declarat. Et ideo Hebraei antiquitus per
astronomiam certificaverunt primationem lunae, et cum non
fuerat in visione novae lunae, nec potuit per visum cognosci,
accenderunt faces in Jerusalem in monte alto, ut sciretur quod
tunc fuit tempus primationis, quatenus homines essent parati
facere solemnitates et festa quae habebant expedire. Et
neque consideratur lunatio penes conjunctionem solis et lunae
veram, quoniam hoc tempus non est aequale, sicut certum est
astronomis. Sed considerabitur luna penes conjunctionem
solis et lunae mediam, sicut dicit Alfraganus. Nam hoc tempus
est aequale semper. Nec tamen dicitur prima luna in con-
junctione, sed post conjunctionem, quando luna in tantum
separatur a sole ut sit de se visibilis, licet videri non possit.
Tunc enim est prima accensio lunae, quamvis non videatur
in illa hora. Et haec diversitas accidit propter latitudinem
Junae diversam ab orbe signorum, et secundum quod est in
signis obliqui descensus vel recti, et secundum diversitatem
regionum septentrionalium et meridionalium, ut docet Alfra-
ganus in vicesimo quinto capitulo suilibri. Currit autem aetas
lunae a prima in viginti novem et parum plus. Ex quibus
aetatibus aggregatur tempus lunationis mediae, seu aequalis,
quem vocant astronomi Hebraeorum et Arabum mensem
lunarem, licet aliis multis modis dicatur mensis lunaris. Et
quamvis peritissimi astronomi in tabulis et canonibus ponant
tempus aequalis lunationis esse viginti novem dies et triginta et
unum minuta unius diei, et quinquaginta secunda, ut patet per
Arzachelem in tabulis Toletanis ; tamen Hebraei astronomi
consideraverunt subtilius et melius. Tempus enim dictum
continet viginti novem dies, et duodecim horas, et quadraginta
quatuor minuta unius horae, sicut opus algoristicum expediet.
Sed Hebraei dividunt unam horam in mille octoginta partes,
et quodlibet minutum horae continet octodecim partes horae,
ut patet ex reductione fractionum unius generis ad fractiones
alterius. Et ideo tempus lunationis aequalis! apud Hebraeos,

! The mean synodic period of the moon, i. e. the mean period of its return
to the position in which it is in the same direction with the sun, as determined

MATHEMATICAE IN DIVINIS UTILITAS. 197

secundum quod respondet praecise lunationi Arabum, non
potest esse plus quam viginti novem dies et duodecim horae
et septingenti nonaginta duae partes unius horae. Sed
Arabes in tabulis et canonibus computant diminute, et de-
ficiunt in omni lunatione per tria secunda, et quindecim tertia,
et quadraginta quatuor quarta, quod patet per examinationem
legitimam. Et ideo Hebraei astronomi, volentes complere
lunationem, apposuerunt unam partem, quia minus non
potuerunt ponere secundum hanc divisionem qua usi sunt.
Et ideo computant usque nunc in una lunatione viginti novem
dies et duodecim horas et septingentas nonaginta tres partes
horae. Et longe certior est eorum consideratio quam astro-
nomorum utentium tabulis et canonibus apud alias nationes,
quanquam et plus aliquantulum computant quam praecise
exigat lunatio. Nam excedunt in quatuor tertiis et sexdecim
quartis unius horae. Sed hoc longe minus est quam defectus
Arabum praedictus. Quapropter satis melius computant
Hebraei. Nec est curandum de excessu Hebraeorum prae-
dicto; quoniam in maximo tempore minimus error contingit,
et de quo non est curandum. Menses autem Hebraeorum,
et scripturae usuales diversificantur. Nam unus est triginta
dierum et alius viginti novem, quia vulgus non potest com-
putare nisi per integros dies.

His igitur consideratis propter scripturae et sanctorum Lunar
intellectum, occurrit consideratio ulterior, ut sciamus quod es of
Hebraei utuntur cyclo lunari, cujus consideratione indiget
scriptura exponenda. Nam sicut nos utimur cyclo decem-
-novennali, sic ipsi cyclo lunari, cujus primus annus incipit in
quarto anno nostro. Et ideo falsum dicunt qui non posuerunt
Hebraeos uti cyclo; habent enim embolismos in suo cyclo,
sicut nos in nostro; immo nos habuimus ab eis; et per
embolismos aequant annos lunares solaribus colligendo
undecim dies ter, ut faciant in tertio anno mensem embolis-
malem, id est superexcrescentem. Et nos hunc modum
embolismorum traximus ab eis. Et ideo male dicunt famosi

by calculation from an eclipse observed by the Chaldaeans 720 B. c., and from one
observed in Paris in 1771, is 294, 12^, 447, 2*.8, a result agreeing almost exactly
with the value given by the Jewish astronomers.

198 OPERIS MAJORIS PARS QUARTA.

viri, qui negant Hebraeos usos fuisse cyclo. Et colligunt
Hebraei tredecim cyclos lunares et faciunt tabulam et
canonem ad hoc; qui tredecim cycli continent ducentos
quadraginta septem annos, quia in tanto tempore redeunt
omnes observationes festorum legalium ad idem temporis
principium. Currit igitur observantia legalis penes hoc
multipliciter, necnon alia quamplura. Nam neomeniae et
calendae, in quibus est festum sacrificiorum, et epularum
solemnium, de quibus dicitur primo Regum xx ‘Cras calendae
erunt, et requiretur sessio tua, exigunt ut sciamus quod
mensis lunaris vulgaris incipiat ab occasu solis. Sed lunatio
ipsa non habet principium determinatum. Quare si contingat
luna prima in occasu vel ante in aliqua hora diei naturalis
praecedentis computabitur in vespera sequente novilunium, et
neomenia et calendae et novus mensis, quia jam est luna
prima. Si vero post occasum solis venerit, ut in secunda
hora diei et ultra, non dicetur illa die naturali novilunium
nec neomenia nec calendae, quantum ad initium calendae.
Considerandum tamen quod mensis primus durat ab occasu
solis primae diei usque ad occasum solis tricesimae diei, et
tamen lunatio! non durat nisi a principio noctis usque ad mane
tricesimae diei quantum ad dies integros, licet aliquae frac-
tiones sint ultra. Non igitur incipit secundus mensis ante
occasum solis tricesimae diei, sed lunatio ejus incipit in mane
tricesimae diei, et ideo duae calendae attribuuntur secundo
mensi, in quibus fiebant epulae et sacrificia, scilicet in die
artificiali tricesimae diei mensis primi et in die naturali prima
et tricesima, quia isti duo dies sunt de lunatione secundi,
mensis, licet secundus eorum tantum sit pars mensis secundi.
Propter quod primo Regum xx dicitur, quod sedes David die
secunda post calendas vacua apparuit. Unde accidit quod
menses pares habent semper duos dies epularum, sed menses
impares habent unum tantum. Et ex his patet, quod Ecclesi-
asticus dicit, ‘A luna signum diei festi mensis secundum
nomen ejus est. Et ex his posset videri an luna fuit prima
in principio mundi, vel plena, ut multi dixerunt. Nam Judaei
et scriptura utuntur mensibus lunaribus. Ergo principium

! luna, J., an erroneous reading.

MATHEMATICAE IN DIVINIS UTILITAS. 199

primi mensis et principium mundi fuit idem. Sed mensis
lunaris a primatione lunae incipit. Quapropter in principio
mundi luna prima fuit !.

Et jam dicta necessaria sunt consideranti egressum Noae de Noah’s
arca. Nam glossae involvunt nos in dubitatione gravi, Sit fr?
propter quod magister in historiis deceptus fuit, cum voluit
Noae fuisse egressum xxviii luna eodem die quantum ad
calendas quo intravit. Si enim hoc esset verum, tunc non
tantum per annum, sed per annum et diem ibi fuit, eo quod
annus solaris constat ex diebus ccclxv, qui complentur a prima
die Januarii usque ad ultimam diem Decembris, qui est finis
anni. Et hoc est quod dicit Beda de Temporibus, * Noe cum
ejus familia decima septima die secundi mensis arcam
ingressus et xxvii ejusdem mensis die post diluvium
egressus asseritur. Claret igitur annum solis integrum, id est
ccclxv dierum, esse descriptum, quia videlicet luna, quae
praesentis anni verbi gratia per nonas Maias decima septima
existit, anno sequenti vigesima septima pridie nonas occurret.'
Haec Beda. Quia quota est luna, si undecim addas tota erit
eadem die, anno revoluto. Ut si hodie est prima, eadem dies
revoluto anno erit duodecima. Hoc autem verum est, ut in
pluribus. ^ Tamen aliquando revolutio ejus est tantum
undecima, aliquando tredecima. De xi, verbi gratia, si hodie
pridie nonas Aprilis fuerit prima, eadem die revoluto anno
erit xi. De xiii, verbi gratia, si hodie quinto nonas Maii
fuerit prima, eadem die revoluto anno erit xiii. Numeret
quis, et ita per se inveniet. Ista tota intricatio magistri ex
glossa Strabi exordium sumit. Ut ergo concordemus glossam
Strabi cum Beda dicimus, quod istud Strabi eadem die debet
intelligi eadem feria, ut si dominica intravit, dominica exivit.
Et quod sequitur, si praesenti diei addantur undecim,
praesenti die computato cum xi, bene dicit, et hoc probatur
per quod subdit, ideo post annum xi additis, fuit xxvii dies,
vel xxvii luna. Nam si ipsa dies xxvii excluderetur, non
xxvii, sicut ipse in glossa ponit, sed xxviii fuisse probare-
tur. Et hoc sic apparet. Nam cum xvii luna secundi mensis
in arcam ingressus est, patet quod sequenti anno xvi luna

! Cf. Op. Tert. ch. 54 (Brewer, pp. 214-15).

Date of
law-giving
on Sinai.

202 OPERIS MAJORIS PARS QUARTA.

secundi mensis annus lunaris cccliv dierum expletus est;
a xvii autem die usque ad xxvii sunt xi dies, qui si praedictis
cccliv addantur, fiet annus solaris ccclxv dierum, sicut Beda
superius computavit. Sic ergo egressus est eadem qua in-
gressus fuerat feria, sed non cadem calenda. Et sic uterque
verum dixit. Sed magister tamen dictum Strabi non bene
glossavit. Quare vero xvii luna intra xi debeat concludi,
patet per aliam glossam, quae xvii exclusive decem additis
computat xxvii. Ergo si Strabus computat xi additis tantum
xxvii et iste, x additis, similiter computat xxvii, patet quod
ille inclusive, iste exclusive, intellexerit. Cum autem magister
vult hic excusare se et dare rationem quare dixit egressum
xxvii, cum Beda dicat xxvii, dicens, ' potuit enim esse quod
vespera xxvii lunae egressus sit, jam imminente xxvii,
media vero tempora quolibet nomine extremorum saepe
nominantur'; illud nihil est, quia licet conjunctio solis et
lunae vera vel media omni hora tam diei quam noctis evenire
possit tamen quia Hebraei et Arabes computant secundum
menses lunares, et luna appropriatur nocti, sicut sol diei,
ideo dies et menses a vespera incipiunt semper. Et haec
dicit Beda de temporibus; 'Quacunque hora accendatur
luna, priusquam vespera veniat, non dicetur prima.’ Si vero
post occasum solis accendatur, non prima in praecedenti
vespera, sed tricesima aestimabitur.

Quod etiam super Exodum de adventu filiorum Israel in
solitudine Sinai pro lege Dei recipienda magister dicit, in
exponendo scripturam xxx dies pro mense ponimus; hoc est
falsum. Nam si quilibet numeratur xxx dierum, cum sint
in anno xii menses, erunt in anno lunari ccclx. Sed patet
quod superflue numerantur vi dies. Constat enim quod in
anno lunari non sint nisi cccliv, cum annus solaris lunarem xi
diebus superet, habens ccclxv dies. Ergo in duobus mensi-
bus non sunt nisi lix dies. Et hoc est quod Beda dicit libro
de Temporibus, * Nonnullo moveor scrupulo quomodo majores
nostri diem qua data est lex, quae est iii mensis tertii, quin-
quagesimam ab agni occisione computent, ponentes primi
mensis residuos dies numero xvii, quia xiii priores fuerunt
ante pascha transacti, secundi xxx, tertii iii, qui fiunt simul

MATHEMATICAE IN DIVINIS UTILITAS. 201

dies quinquaginta. Et constet duos menses lunares non lx sed
lix diebus terminari ; at per hoc in summa temporis memorati
non plus quam xlix inveniri. Haec Beda. Igitur secundum
Bedam prima dies Junii non fuit xlvii, imo xlvi, et sic si lex
data fuit quinquagesima die a pascha, non fuit data iii die
mensis Junii, sed iv. Judaei vero dicunt quod die sexta fuit
lex data, et quarta die adventus eorum in solitudine Sinai.
Dixit enim Dominus, * Vade ad populum, et sanctifica eos
hodie et cras, et sint parati in diem tertium. Et ita iste dies
tertius fuit sextus eorum adventus; et secundum hoc quin-
quagesima die fuit lex data, non incipiendo a pascha, nec
a prima die azymorum, sed ab altera die azymorum. Et
hic computus consonat ili de quo habetur Levitici xxiii
*Numerabitis ab altera die sabbati, id est solemnitatis
azymorum, in quo obtulistis manipulos primitiarum septem
hebdomadas plenas usque ad alteram diem expletionis
hebdomadae septimae, id est, quinquaginta dies. Hic igitur
magna involutio invenitur apud lectores propter errorem
magistri in quantitate mensis et in sua computatione, sicut
patet consideranti subtilius, et quia nescitur consideratio
Hebraeorum his temporibus. Et tabula de cyclis lunaribus
multum rectificat observantias legis. Quoniam secundum
illam tabulam necesse est, quod licet principium anni sit
lunatio Octobris secundum veritatem, tamen propter solem-
nitates legis implendas oportet quod triplicem annum habeant ;
unum communem, qui est secundum veritatem annus lunaris,
scilicet habens cccliv dies, et unum diminutum, scilicet qui
habeat cccliii dies; et unum superfluum, qui habeat ccclv
dies; et sic variatur accidentaliter principium anni. Et hoc
necessarium est, quia in die dominica non potest annus inCipere.
Quoniam si in dominica, tunc in xv die mensis septimi esset
dies dominica, et in vigilia illius festi colliguntur rami de
arboribus, quod non licet facere in sabbato. Similiter nec in
die Mercurii nec Veneris potest esse anni principium. Nam si
in die Mercurii, tunc decima dies mensis esset in die Veneris,
in quo non licet aliquid facere, quoniam nec cibum parare, cum
‘sit par sabbato. Quapropter tunc oportet eos facere cibaria.
Majora vero accidunt hic dubitabilia, nisi juvemur magnifice

Dates of
Nativity
and

Passion.

202 OPERIS MAJORIS PARS QUARTA.

per astronomiae potestatem. Nam incidunt quaestiones con-
tra sententias omnium theologorum Latinorum. Sed propter
rerum magnitudinem procedam opponendo ad utramque
partem, et qui potest solvere gaudeat de solutione. Et tamen
nihil contra opiniones communes Latinorum arguam, nisi quod
nescio dissolvere. Utinam inveniam qui solvat, si conclusio
falsa est. Sin autem vera possit esse, tunc non esset solutio
necessaria. Sed nullus tantae auctoritatis est in ecclesia praeter
summum pontificem, qui ausus esset dare sententiam contra
sententias vulgatas in hac parte quamvis essent falsae. Tenet
ergo vulgus Latinorum quod Dominus fuit natus secundo anno
cycli decemnovennalis, et decimo anno cycli solaris, et in his
non est dubitatio, et quod passus fuit viii calendarum Aprilis,
et quod luna fuit xv in die passionis, de quibus est quaestio
magna, atque Latini redarguunt Graecos, qui posuerunt pas-
sum Dominum xiv luna. Hoc magistri dicunt omnes, et
Augustinus, Hieronymus, Beda, dant auctoritates ad hoc.
Contra hoc potenter arguitur. Nam si viii calendarum .
Aprilis fuit passus et luna fuit xv, non potest hoc esse, ut
Beda scribit libro temporum, nisi fuisset xiii annus cycli
decemnovennalis; et hoc est verum. Quia secundum hoc
oportuit quod aureus numerus fuerit xiii, ut luna diceretur
prima in calendario, ubi xiii scribuntur, quatenus ab illo
loco computetur aetas lunae, ut inveniatur xv in viii calen-
darum Aprilis; sicut quilibet potest experiri in calendario.
Sed cum Dominus fuit natus secundo anno cycli, tunc in
fine illius primi cycli habuit xviii annos secundum cyclum,
quibus si xiii qui fluxerunt usque ad passionem addamus
de cyclo secundo, erunt xxxi anni secundum cyclos. Sed
hi anni secundum cyclum non sunt nisi xxix anni aetatis
suae, et de xxx quantum est a nativitate usque ad passionem ;
quoniam prope finem secundi anni ipsius cycli fuit natus,
scilicet ante principium tertii anni per vii dies tantum,
quia annus incipit in circumcisione Domini. Quapropter
in fine primi cycli non habuit Christus annos aetatis suae
nisi xvii et dies vii, quibus si addantur xiii alterius cycli,
erunt triginta; ita quod in xxx fuit passio. Ergo non habuit
Dominus nisi xxix annos, et tantum de trigesimo quantum

MATHEMATICAE IN DIVINIS UTILITAS. 203

est usque ad passionem ; quod est contra evangelium Lucae,
qui dicit * Johannem Baptistam baptizasse Jesum incipientem
quasi xxx annorum. Et iterum secundum fidem evangeli-
orum certum est, quod praedicavit pluribus annis.

Ita Beda nititur probare quod tribus annis et dimidio ultra Theory of
xxx, ut in xxxiv anno fuerit secundum eum passus, id est, Bede.
xviii anno Tiberii Caesaris. Et alia objectio fortior sequitur ;
nam si passus fuerit viii calendarum Aprilis et luna fuerit
xv, tunc, ut prius dictum est, aureus numerus fuit xiii;
sed vulgus Latinorum sequitur beatum Dionysium ? abbatem
Romanum, qui primus in chronicis suis instituit annorum
computationem fieri a Christo, cum prius computabatur a
tempore Dioclesiani sacrilegi, ut Beda scribit, et certum est ;
ita, quod transacto dxxxi anno ab incarnatione vel nativi-
tate incipiebat suum cyclum magnum componere, qui tenet
dxxxii annos, ex multiplicatione cycli decemnovennalis in
solarem procreatus. Et incipit suum cyclum a dxxxii anno
post incarnationem, et non a dxxxiii, quia Dominus fuit
natus secundo anno cycli, et ideo oportuit novum cyclum
incipere a dxxxii, scilicet transacto quingentesimo tricesimo
primo anno a nativitate. Et quod tantum fuit, Beda docet.
Nam dicit, * Dionysius paschales scribit circulos, incipiens ab
anno dominicae incarnationis quingentesimo vicesimo septimo."
Si igitur inveniamus literam tabularum, et revolvamus ab ea
cyclum Dionysii bis et quantum ultra hoc est usque ad annum
praesentem a nativitate Domini, inveniemus viii calendarum
in passione esse in dominica, sicut quilibet potest experiri.
Sed constat ipsum non fuisse passum die dominica, sed die

! Dionysius, commonly styled Exiguus, was the first to substitute the era a.p.
for 4. u.c. He placed the date of the Nativity four years later than that accepted
by previous writers, namely 754 from the foundation of Rome, instead of 750.
His Paschal Cycle of 532 years, resulted from the multipiication of the lunar
cycle of nineteen years, and the solar cycle of twenty-eight years. Bede speak-
ing of the era introduced by him, says (De temporis ratione, cap. xlvii), * Primo
decennovenalis circuli versu temporum ordo praefigitur quem Graeci calculatores
a Diocletiani principis annis observatore. Sed Dionysius venerabilis abbas
Romanae urbis et utriusque linguae, Graecae videlicet et Latinae non ignobili
praeditus scientia, paschales scribens circulos noluit eis, sicut ipse testatur,
memoriam impii et persecutoris innectere, sed magis elegit ab Incarnatione
Domini nostri Jesu Christi annorum tempora praenotare.’

Theory of
Marianus.

204. OPERIS MAJORIS PARS QUARTA.

Veneris. Quapropter multi diligentes in chronicis, sed prae-
cipue Beda, et Marianus Scotus, et Gerlandus! famosus apud
omnes, dubitationem nobis relinquunt maximam penes com-
putationem secundum cyclos Dionysi Nam Beda dicit
computanti, * Gratias age Deo, si annum passionis Domini sic
inveneris. Quare si non invenias, incuriae chronographorum
aut tuae tarditati ascribas, Et in duobus obviant ei, princi-
paliter in hoc, quod posuit Dominum esse natum secundo
anno cycli; et in hoc, quod posuit praecise dxxxi annum
transivisse ab incarnatione vel nativitate Domini.

Marianus ergo in suis chronicis concedit, quod contingere
potest, et verum est, quod sit luna xv in viii calendarum
Aprilis et xiii in annis cycli. Sed tunc vel erit xii annus
aetatis Christi, vel in cclix ; sed neque fuit passus xii anno
aetatis suae, neque in cclix. Quapropter non videtur salvari
posse Dionysius. Et ideo Marianus diligenter attendens
defectus Dionysii, volens adhuc salvare opinionem Augustini
et Hieronymi dicit, quia octavo calendarum Aprilis fuerit
passus, et similiter quod luna fuerit xv, sed non secundo anno
cycli decemnovennalis, sed xviii, ita quod de illo cyclo sint
accipiendi duo anni Christi, ut xviii cycli sit primus annus
Christi, et xix sit secundus, et alter cyclus integer, qui simul
juncti faciunt xxi annum. Et tunc xiii de tertio cyclo ad-
dantur et fient xxxiv secundum cyclum. Sed anni aetatis
Christi sunt pauciores, scilicet xxxii anni et iii menses, et
bene stant cum hoc numero. Et ideo hic Marianus addidit
xxii annos ad tempus Dionysii. Et ideo in computatione

! Bede wrote two works on chronology. The first, De femporibus, was com-
plained of by his disciples as being too short. At their instance, he wrote
several years afterwards the much more elaborate treatise, De temporum
ratione. i]

Marianus Scotus was an Irish monk of the eleventh century who entered an
Irish monastery at Cologne, and lived subsequently in Fulda and in Maintz.
He is the author of an universal chronicle beginning with the Christian era, and
continued to the year of his death in 1082. He considered the Dionysian date
of the Nativity to be twenty-two years too late. Marianus is not to be con-
founded with the abbot of St. Peter's, Ratisbon, a contemporary of the same namc.

Gerlandus was a student in the Benedictine monastery of Besancon, of
which he became prior in 1131. He wrote a Computus (i.e. a work on the

rectification of the Calendar), and also an arithmetical treatise, mentioned by
Cantor, vol. i. p. 769.

MATHEMATICAE IN DIVINIS UTILITAS. 205

nostra a Christo, si volumus sequi Marianum, addemus
semper xxii annos plures quam computet ecclesia secundum
Dionysium. Sed secundum Bedam et secundum computa-
tionem certam annorum imperatorum, manifeste patet Mari-
anum esse superfluum. Nam secundum eum a nativitate
Christi usque ad cyclum Dionysii sunt dliii; quia ad dxxxi
jam 'addit xxii. Sed superius patuit quod ab incarnatione
Christi usque ad Dionysium non fuerunt tot, sed dxxxi.
Quantumcunque enim largius computentur anni impera-
torum, inveniemus quod ipse superfluit in xxii annis, vel
in xxi,vel ad minus in xx, et ideo non est imitandus.
Patet etiam per beatum Augustinum Marianum esse super-
fluum. Dicit enim Augustinus decimo octavo libro de Civi-
tate Dei, sic computantur ccclxv anni a passione Christi usque
in consulatum Honorii et Euticiani. Ergo iste annus, scilicet
consulatus Honorii et Euticiani, a nativitate est cccxcvii,
addendo annos a nativitate usque ad passionem, scilicet xxxii
annos secundum Marianum et iii menses secundum superiorem
computationem ; sed secundum computationem Mariani, sicut
ipse in chronicis suis posuit, ccccxix fuit. Constat ergo eum
esse superfluum xxii annis. Nam si ex ccccxix annis xxii
dempseris, remanent cccxcvii.

Gerlandus autem famosus, quem omnes computistae sequun- Theory of
tur et astronomi in tractando ea quae ad computum pertinent, 9*'/^dss.
videns Dionysium non posse salvari nec sequentes ejus, nolens
etiam Augustino et Hieronymo adhaerere de calenda pas-
sionis, sed beato Theophilo, qui fuit vicinus apostolis, ponenti
quod decimo calendarum fuit Dominus passus, dempsit de
computatione Dionysii vii annos, et posuit Dominum fuisse
passum nono anno cycli. Nam cum Dionysius posuit Dominum
natum secundo anno et dempsit unum annum cycli a nativitate
demit Gerlandus illum i et ii usque ad viii inclusive. Et ideo
Dominus fuit secundum eum xi annorum, completo illo
cyclo, quibus si addatur unus cyclus integer et v anni, quia
v est aureus numerus ut xv luna sit ibi, erunt xxxv anni
secundum cyclos, et isti bene stant cum annis nativitatis
Domini. Sed sicut Marianus fuit superfluus, sic Gerlandus
est diminutus. Nam per computationem superius suppositam

The
Passion
was on the
fourteenth
day of the
moon.

206 OPERIS MAJORIS PARS QUARTA.

secundum Bedam, et secundum annos imperatorum, a nativitate
Domini sunt tantum dxxxi vel circiter, ita quod ad minus
defecit Gerlandus in v annis, quantumcunque largius annos
imperatorum computemus.

Magister vero in historiis dubitationibus aliorum apponit
novum dubitabile. Nam. cum dicit in fine capituli de coena
Domini, ‘si revolvamus tabulam computi, inveniemus lunam
xxii in calendis Aprilis et diem Veneris in tempore passionis :
ergo viii calendas Aprilis fuit xv luna et dies Veneris, multi-
pliciter oberrat. Nam si sua sententia esset vera, tunc numerus
aureus esset xiii, et tunc, sicut prius tactum est, fuisset passus
ante xxx annos completos, quod est falsum. Item si tabulam
revolvamus, ut magister dicit, inveniemus G esse literam domi-
nicalem in tempore passionis, et G esse in viii calendarum.
Quare fuit passus in dominica,quod est falsum et contra
evangelium. Sed multi, ut Beda scribit, et maxime Victorius,
ut patet in epistola sua ad Papam Hilarium de paschali
observatione, dicunt Christum fuisse passum vii calendarum
Aprilis et resurrexisse v. Sed tunc, ut Beda dicit, oportet
quod fuerit annus secundus cycli decemnovennalis, quia binarius
erit numerus aureus, supponendo quod Dominus fuerit passus
xv luna, sicut in prioribus semper suppositum est. Sed quia
xv anno Tiberii posuit Dominum passum, ut ex ejus opus-
culis patet, ideo merito redarguitur a Beda et aliis.

Haec igitur secundum considerationem chronographorum
discussa sunt, quae omnia sequuntur ex hoc, quod supponitur
lunam fuisse xv in die passionis. Sed astronomi solliciti in
hac parte non possunt invenire xv lunam nec viii calen-
darum in tempore passionis, nec x nec vii, ita ut ibidem
inveniatur dies Veneris, quod oportet secundum Evangelia,
nec etiam a xxx anno Domini usque ad finem vitae suae
possunt invenire in aliqua calendarum. Quapropter summa
dubitatio accidit in hac parte. Nam diligenter haec discussi
tam per me quam secundum consensum peritorum in astro-
nomia. Sed de xiv luna bene invenitur. Quapropter multa
secundum scripturam sunt mihi et multis insolubilia in hac
parte in contrarium, per quae ostenditur quod fuit passus xiv
luna, sicut Graeci ponunt et Hebraei concordant. Nam dicitur

MATHEMATICAE IN DIVINIS UTILITAS. 207

in Matthaeo ‘Non in die festo. Sed dies festus est dies
azymorum, qui instabat, et dies azymorum est xv. Ergo ante
fuit occisus. Item Joannes xviii, ‘Non introierunt in praetorium
ut non contaminarentur, sed manducarent Pascha.’ Ergo in
vespera proximo ventura manducarunt Pascha; si igitur
accipitur ibi Pascha pro agno paschali, in vespera illa in-
cipiebat xv dies, et fuit luna xv, et tunc computabatur.
Ergo ante illam vesperam fuit xiv luna. Quare occisus fuit
Dominus xiv luna, sicut agnus paschalis in lege. Cum
autem dicitur, quod Pascha ibi non sumitur dicto modo, sed
aliter, hoc non potest habere auctoritatem ex scriptura, et
ideo eadem facilitate contemnitur secundum Hieronymum,
qua probatur. Caeterum cum dicunt Pascha hic accipi pro
azymis, hoc esse non potest Nam immundi, licet prohi-
beantur edere Pascha, id est agnum paschalem, non tamen
prohibebantur edere azyma, si post comestionem agni fierent
immundi. Immo si aliquis fermentum comederet. dicit lex,
Exodi xii, quod periret de coetu Israel. Praeterea, nec in-
veniebatur fermentum in domibus eorum in illis diebus, quare
tunc non comederent panem per vii dies, quod est omnino
absurdum. Et ideo non habet haec responsio locum. Item
Joannes xix, ‘Erat autem parasceve Paschae. Ergo eadem
die ad vesperam paraverunt Pascha. Sed quando paraverunt
Pascha incipiebat xvluna. Ergo cum fuit passus ante, fuit xiv.
Item Joannes eodem, * Ibi ergo, propter parasceven Judae-
orum, quia juxta erat monumentum, posuerunt Jesum.' Ideo
enim acceleraverunt sepelire, ne in die xv sepelirent, nam in
die azymorum non sepelissent eum, quia nullum sepeliebant
in praecipuis festis, sicut sunt Pascha, Pentecoste, Scenopegia,
et hujusmodi. Item Lucae xxiii, ‘Et revertentes mulieres,
scilicet in die crucifixionis, * paraverunt aromata, et sabbato
quidem siluerunt secundum mandatum.' Ergo illo die non
fuit dies azymorum, sed xiv; non enim licuit eis parare
aromata in die azymorum. Nam Exodi xii de prima et
ultima die azymorum dicitur, * Nihil operis facietis in eis
exceptis his, quae ad vescendum pertinent' Qua ratione
enim siluissent die sabbato propter mandatum, eadem ratione
siluissent in die Veneris, si fuisset dies azymorum. Nam

From this

with proper

astro-
nomical
tables we
should be
able to fix
the date.

208 OPERIS MAJORIS PARS QUARTA.

praeceptum cadit super utrumque, licet sabbatum sit sanctius.
Et Augustinus libro de quaestionibus novi et veteris testa-
menti dicit, quod fuerit passus xiv luna. Haec autem et
multa alia hic adduci possunt cum exclusione falsarum respon-
sionum.

Sed haec nunc sufficiant ut excitemur ad duo, scilicet ut
sciamus quota luna Dominus fuit passus, an xiv vel xv, et
si una illarum stabiliatur, tunc inveniatur dies passionis per
tabulas astronomiae, ut tactum est. Sed haec omnia habent
summam difficultatem, magis tamen propter hoc, quod theologi
ignorant astronomiam et. computum, et hujusmodi, quam
propter difficultatem rei in se. Si enim essent periti in his,
pro certo bene invenirent aetatem lunae et diem passionis, et
mutarent multas sententias quas solemnizant. Nam peri-
tissimi in istorum consideratione tenent quod Dominus fuit
passus xiv luna. Et hoc verificato, facile est invenire
calendas per tabulas speciales ad hoc compositas. Quatenus
vero excitatio mentis fiat ad hoc, ponam hic unam tabulam,
in qua secundum tabulas primationum inventa est oppositio
solis et lunae per omnes annos Domini usque ad xxxviii, ut
scilicet videatur in quo anno accidit in Martio circiter passio-
nem Domini, et in quo in Aprili. Non tamen propter certifi-
cationem hujus rei pono hanc tabulam, sed pro exemplo, ut
videatur modus persuadendi in hac parte ; nam certificatio est
valde difficilis propter hoc, quod motus coelorum non sunt
omnino certificati, nec tabulae qualescunque sufficiunt in hoc
casu. Multi enim in astronomia periti laboraverunt hic, ut
has oppositiones solis et lunae invenirent, et non potuerunt
invenire annum passionis a xxx in xxxv, ubi in Martio
esset oppositio in die Veneris, nec dies ante oppositionem nec
proximus post, ita quod cum passione concordaret. Nec ego
potui invenire adhuc. Ubi tamen poterit oppositio cum die
Veneris inveniri secundum tabulam praesentem !, patebit per
ejus expositionem.

1 This is evidently not the table referred to in Opus Tertium, chap. 54 (Brewer,
P. 215). He says in that passage, * ( Hebraei] posuerunt unam tabulam ex tredecim
cyclis talibus (i.e. cyclis lunaribus?, qua revoluta complentur omnes, et omnia
redeunt ad idem temporis principium. Et hic cyclus cum canonibus suis et
expositionibus est apud eos loci computi et kalendarii apud nos quantum ad

- =— =
eee’

k. Lo

sionis signum, et similiter in alia.
Dies proximus post oppositionem.

Dies oppositionis (et ideo pas-

oo o | Dies proximus ante oppositionem.

E
E
a
E
i :
E 8
ad § 3
x .
Se 3 ry -
2 B B -
'a © L
f b -
4 -
g April.
n April.
e April.

—— | — | ———— | ————— | LIllÉl———

57 52 April.

c f a -
5 | lb b 6 | a 5 | 40 | April.
6 a e f g 15 28 | April.
^^"l.el^.e.lnale April
7 g c d e o pn.
S e f g a 48
Principium cycli alia 9 d c d e 20
via, sc. rationis. —dp—— | ——|———|—— 8
IO c g a b 16
II b c d e 32
I2 Eg g a b M
13 f C d e 16
I4 e g a b
I5 d e f g 36
16 | b alb 24 | April
17 a ki e f 12 Mart
18 g b c d 44 April
19 f e f g£ 32
Principium cycli se- | 20 d b c d 1
cundum computistas. 21 c e f g 5
22 b b c d °
23 a f a
24 f a 3 c °
25 e e f g 48
26 d b c d r
27 c f g a
a c
g g
f c
Hic.
April.
Mart.
| April

f 1747 y, Ta d4- ^4 ^e

MATHEMATICAE IN DIVINIS UTILITAS. 209

Tabulae explicatio.

Prima igitur linea in prima tabula inferius occurrens tenet
annos Domini usque ad xxxviii; quia certum est infra hos
ipsum subiisse passionem. Secunda linea habet omnes literas
feriarum sextarum, quae contigerunt in illis xxxviii annis.
Tertia linea tenet dies proximos ante oppositionem solis et
lunae. Quarta, diem oppositionis. Quinta, diem post op-
positionem immediate. Sexta, diem sequentem, et sumitur
hic oppositio solis et lunae media. Septima linea cum sibi
annexis tenet tempus transactum de Martio ante diem pas-
sionis. Reliqua vero tabula negotiatur circa Aprilem, ut
inveniatur oppositio in Aprili circiter diem passionis, excepto
quod xvii anno et xxxvi accidit in Martio. Sciendum autem
quod hae tabulae factae sunt ad meridiem civitatis Novariae,
licet fuerit facta Parisius ; sed causa fuit, magis enim secreta
est, et meridies ibi praecedit meridiem Parisius per xxv
minuta unius horae. Si igitur de tempore habito subtraxe-
rimus xxv minuta, relinquetur tempus oppositionis post
medium diem civitatis Parisius. Secundum ergo hanc tabulam
passus fuit Dominus iii nonas Aprilis die Veneris in opposi-
tione solis et lunae mediae xv anno cycli decemnovennalis
et xiv cycli solaris, anno xxxiii ab incarnatione secundum
cyclum Dionysii, et hoc est, xxxii secundum veram aetatem
Domini. Et istud in tabula secunda accidit super b literam
in directo xxxiii anni post duos dies de Aprili et xvii horas,
et xvi minuta, et xxxiii secunda, | tertia, xxiv quarta, et sic
sapientissimi in his considerationibus aestimaverunt, qui
multa. Et hanc tabulam literis Hebraicis misi in Ofere Majori cum ejus expo-
sitione et canonibus suis, secundum quod pertinet ad computum eorum. He
refers to this table again in the following chapter, p. 220. The table given in
the Opus Majus is the one spoken of in the Opus Tertium, p. 223.

What seems probable is that Bacon included with the Opus Majus the
whole or part of a work written by him in 1263, entitled Computus, of which
a good description will be found in Charles's work on Bacon, pp. 336-8. The
Computus contains a full discussion of the solar and lunar year and month, of the
lunar cycle of nineteen years and its insufficiency ; and a series of tables com-
paring the Mahommedan and Christian calendars.

The table here given contained in the first edition several errors which have
been corrected by collation of O. with Tib.

VOL. I. P

210 OPERIS MAJORIS PARS QUARTA.

multum laboraverunt ad hoc probandum. Unde secundum
eos, quod viii calendas Aprilis passus fuerit, non est
opinio ecclesiae certificata, sed vulgata, sicut multa alia
vulgantur, quae indigent majori certificatione. Si igitur
oppositio media et xiv luna ab accensione concurrant in
unum in passione, res manifesta est secundum hanc tabulam
et secundum aestimationem sapientum. Si vero oppositio
praecessit in passione xiv lunam per diem integrum, oporteret
recurrere ad tabulam accensionis novae lunae factam con-
similiter huic, et tunc magis excluderetur dubitatio. Sed
hujus rei certificatio, sicut aliorum quae scribo, desiderat
Vestrae Celsitudinis assensum, quatenus periti in hujusmodi
veritatem firmiter stabilirent. _Occasionem vero dedi in hoc
capitulo qualiter ad hujus rei certificationem poterimus
pervenire, et nego me in praesenti tractatu de tanta difficultate
certificasse.

A M Dictum est, quod septem sunt radices mathematicae, quibus
throws necesse est uti mathematica. Una est de coelestibus. Alia
light ?? de locis mundi. Tertia de temporibus quantum ad substan-
theological tiam. Quarta de passionibus et accidentibus temporum, de
questons. Quibus dictum est. Nunc volo afferre quintam radicem, et
est de figurationibus geometricis penes lineas, angulos, et
figuras tam corporales quam superficiales. Impossibile enim
est quod sensus spiritualis sciatur, nisi fuerit literalis scitus.
Sed sensus literalis sciri non potest, nisi homo sciat significata
terminorum et rerum significatarum proprietates. Nam in
illis consistit profunditas sensus literalis, et ex eis extrahitur
sensuum spiritualium altitudo per convenientes adaptationes
et similitudines, sicut sancti docent, et patet ex proprietate
scripturae, et omnes sapientes antiqui sic tractaverunt scrip-
The Ark. turam. Cum igitur opera artificialia, ut arca Noae, et taber-
naculum cum vasis suis et omnibus, atque templum Salomonis
et Ezechielis et Esdrae et hujusmodi alia pene innumerabilia
ponantur in scriptura, non est possibile ut literalis sensus
sciatur, nisi homo ad sensum habeat haec opera depicta, sed
magis figurata corporaliter; et sic sancti et sapientes antiqui
usi sunt picturis et figurationibus variis, ut veritas literalis ad

MATHEMATICAE IN DIVINIS UTILITAS. 2II

oculum pateret, et per consequens spiritualis. Nam in veste
Aaron, ut dicit scriptura, erat descriptus orbis terrarum et Aaron's
parentum magnalia. Et ego vidi Aaron sic figuratum cum "ens
veste sua. Sed nullus posset de hujusmodi corporum figu-
ratione cogitare nec ordinare, nisi optime sciret libros Elemen-
torum Euclidis et Theodosii et Millei! et aliorum geometrarum.
Nam propter horum ignorantiam apud theologos non solum
decipiuntur in maximis, sed in minimis. Dicunt enim cum
magistro in historiis quod sphaerulae candelabri fuerunt
corpora circularia, non habentes plenam sphaericitatem. Sed
non dicuntur sphaerulae diminutive propter hoc, sed quia
fuerunt parvae sphaerae, habentes tamen completam defini-
tionem sphaerae Euclidis et "Theodosii. Nam Hebraei in
Gallico suo itllas sphaerulas vocant pomeas a rotunditate
pomali et sphaerica, et sic de aliis infinitis. O quam ineffa-
bilis luceret pulchritudo sapientiae divinae et abundaret
utilitas infinita, si haec geometricalia, quae continentur in
scriptura, figurationibus corporalibus ante nostros oculos
ponerentur. Nam sic mundi malitia diluvio gratiae deleta,
attolleremur in sublimi cum Noe et filiis et omnibus ani-
mantibus suis locis et ordinibus collocatis. Et cum exercitu
Domini in deserto excubaremus circa tabernaculum Dei, et
mensam propositionis, et altare, et sancta sanctorum, ac
cherubim obumbrantia propitiatorium, et caetera illius antiqui The tabe-
populi insignia tanquam praesentia videremus. Deinde temple.
tabernaculi vaeillantis instabilitate vacuata fixum Domini
templum Salomonica sapientia fabricatum intraremus. Et
cum Ezechiele in spiritu exultationis ad sensum intueremur,
quod ipse tantum spiritualiter intellexit, ut tandem reparata
nova Jerusalem cum Esdra et Nehemia intraremus majorem
domum pleniori gloria decorandam. Certe ipsa visio sensi-
bilis esset pulchra, sed pulchrior quando figuram nostrae
veritatis videremus praesentialiter, pulcherrima vero quando

1 Milleius is the Arabic transformation of Menelaus of Alexandria, a mathe-
matician and astronomer of the first century A.D. Two of his astronomical
observations, made in the first year of Trajan, are mentioned in the Almagest
(vii. 3). His work on Spherical Trigonometry (for his discussion of spherical

triangles may be so called) is not extant in the Greek original, but has been
preserved in Hebrew and Arabic translations. It was edited by Halley in 1758.

P2

The rain-
bow.

212 OPERIS MAJORIS PARS QUARTA.

scripturae intellectum spiritualem et literalem contemplantes
gauderemus visibilibus instrumentis excitati, quod scimus
omnia nunc in ecclesia Dei esse completa, quae ipsa corpora
sensibilia nostris oculis exhiberent. Et ideo nihil reputo
dignius studioso in sapientia Dei, quam hujusmodi figurationes
geometricas ante ejus oculos exhiberi. Utinam jubeat
dominus quod haec fiant. Et sunt quatuor homines vel tres,
qui ad haec sufficerent, sed sunt peritissimi Latinorum; et
merito debent esse periti, quoniam ineffabilis difficultas hic
latet propter obscuritatem textus sacri, et propter contra-
rietates sanctorum et diversitates caeterorum expositorum.
Sed aliter patet geometrica utilitas respectu sapientiae
divinae, tam in textu quam in questionibus ; et non solum in
his, sed in comparationibus pulchris respectu gratiae et gloriae
et poenae futurae, et cautela vitiorum. De quolibet ponam
aliquod exemplum. Et pro omnibus in generali revocemus
ad memoriam, quod nihil sciri potest de rebus hujus mundi
sine geometrica potestate, ut prius probatum est. Et rerum
ccgnitio necessaria est in scriptura propter sensum literalem
et spiritualem, ut superius expositum est. Nam proculdubio
tota rerum mundi veritas jacet in sensu literali, ut dictum est,
et maxime rerum geometricarum, quia nihil est nobis ad
plenum intelligibile, nisi figuraliter ante oculos nostros dis-
ponatur; et ideo in scriptura Dei tota rerum sapientia
figurationibus geometricis certificanda continetur et longe
melius quam ipsa philosophia possit exprimere. Nec mirum,
cum ipse Deus auctor totius sapientiae suam ordinavit scrip-
turam. Quare pro infinitis exemplis volo unum ad praesens
afferre. Nam Aristoteles magis omnibus philosophantibus
nos involvit suis obscuritatibus in tractando de iride, ut nihil
per eum quod dignum sit intelligamus, immo multa falsa in
translatione Latinorum continentur, sicut ex interpretum
varietate contendimus Nam quod in codicibus Latinorum
habetur, quod iris non accidit ad radios lunae nisi in quinqua-
ginta annis bis, manifeste falsum est, sicut quilibet potest in
plenilunio quando pluit experiri, dummodo claritas lunae non
impediatur per nubium densitatem. Et Avicenna dux ac
princeps philosophiae post Aristotelem, ut clamant omnes,

MATHEMATICAE IN DIVINIS UTILITAS. 213

seipsum ignorasse iridis naturam humiliter confessus est. Et
sic de omnibus philosophis certum est, quod nullus potuit
scientiam iridis obtinere. Nec mirum, cum sacram scripturam
non ita diligenter perscrutati sunt ; sicut fuerat eis necesse.
Nam omnes philosophi ignoraverunt causam finalem iridis.
Sed finis imponit necessitatem eis quae sunt ad finem, ut
Aristoteles dicit secundo Physicorum, et certum est in omnibus.
Finem autem, propter quem est iris, solus textus Dei explicat
evidenter, scilicet, cum dicitur, ‘Arcum meum ponam in
nubibus coeli, &c. Ex quo habetur, quod contra diluvium
et abundantiam aquarum est arcus Dei ordinatus. Ergo
oportet, quod quandocunque apparet hic arcus in coelo, sit
valida consumptio humiditatum aquearum ; et hoc est verum.
Nam nubes resolvuntur abundanter, et rorationes fiunt in-
finitae, sicut philosophi dicunt, et nos videmus in magna parte.
Sed consumptio humiditatis aqueae non est nisi propter
aliquid quod habeat virtutem consumendi. Nihil autem in
generatione iridis invenimus nisi radios solis et nubes.
Nubium congregatio est causa materialis; ergo radiorum
projectio est causa efficiens. Sed radii incidentes non possunt
magnas et mirabiles operationes perficere, quia non concurrunt
ad invicem ; concursus autem virtutum exigitur ad hoc, quod
valida operatio educatur. Sed concursus non potest fieri nisi
per reflexionem et fractionem. Quapropter oportet, quod
iris generetur per infinitas reflexiones vel fractiones in stilli-
cidiis infinitis sine intervallo cadentibus, ut sic tam colorum
quam figurae veritas per hujusmodi multiplicationes penes
figuras, angulos, ac lineas inveniatur, et non per diversitatem
materiae nubis ut in textu Latinorum continetur et omnes
credunt, sicut certis experimentis explicabo cum de scientiis
experimentalibus faciam mentionem. Sicut ergo philosophi
propter ignorantiam scripturae sacrae non potuerunt scire
veritatem iridis, sic eodem modo impossibile est philosopho
infideli attingere ad plenam certitudinem creaturae alicujus

! Lunar Rainbow. Aristotle's words are (Meteorologicorum, iii. cap. 2): &v 79
wavoeAnvy yap yeréaba: dva-yan 10 péddov (a«a0ai, xal Tóre árareAAosays f bvroóogs:
biómep dy £recir bip rà wevrixovra dis lveréyoper uórov. Bacon had good cause
to complain of Aristotelian translation.

Explana-
tion of
Ecclesiasti-
cus, cap. 43.
v. 4.

214. OPERIS MAJORIS PARS QUARTA.

propter scripturae ignorantiam. Nam in veritate quaelibet
creatura ibi accipitur secundum ultimam sui dignitatem,
scilicet secundum veram definitionem et descriptionem ejus,
quia Deus fecit creaturas quas posuit in scriptura, et solus
ipse scit eas sicut sunt. Cum igitur geometrica potestas
requiratur ad cognitionem omnis creaturae corporalis, non
est dubium quin ineffabili modo valeat sapientiae divinae
propter rerum cognitionem.

Sed rediens spiritualiter ad propositum pono exemplum de
Scriptura, quae dicit, ‘sol tripliciter exurit montes!, &c. Nam
et incidunt radii infiniti ad omne punctum montis, propter
quod infiniti exeunt a quolibet puncto solis, et lux est causa
caloris maxime cum congregatur, ut sensibiliter scimus, et
infiniti reflectuntura superficie montis, quia a denso fit reflexio,
et congregantur in omni puncto aeris, et distrahunt omne
punctum aeris, rarefacientes aerem prope montes, et sic
secundo calefaciunt montes. Et per medium nubium fran-
guntur radii duplici fractione, primo in superficie nubium
versus solem, dein in aere inter nubes et montes. Et per
hanc duplicem fractionem est necesse omnes radios solis
venientes ab uno puncto concurrere ad invicem in punctum
unum in monte vel aere prope montes, praecipue in bene altis
montibus et Alpibus?. Et sic fiet calor in montibus, licet non
in altissimis; quoniam montes qui ascendunt usque ad nubes
vel prope sicut sunt montes Italiae et Hispaniae, et mons
Caucasi et Caspiae et alii innumerabiles, habent frigus magnum
et nives quasi perpetuas; quia nimis accedunt ad medium
interstitium aeris, qui est locus frigidissimus in hoc mundo.
Et sic a singulis punctis solis radii venientes ac dupliciter
fracti incedunt et augmentant calefactionem montium. Et
haec omnia patent per figurationes mathematicas, sicut ac-
cidit de beryllo rotundo vel crystallo, vel urinali, vel quo-
cunque perspicuo grossiori aere. Quando enim haec corpora

1 This passage in the Revised Version is given thus: ‘A man blowing a

furnace is in works of heat; but the sun three times more, burning up the

mountains :’ a rendering which would dispense with Bacon's laborious attempt
to explain £ripliater.

* The following sentence seems to imply that Alps are spoken of in the sense
usual in Switzerland, of the lower mountain pastures.

MATHEMATICAE IN DIVINIS UTILITAS. 215

occurrunt radiis solaribus, accidit per duplicem fractionem
quod possit ad oculum et ad tactum eligi punctus aeris post
hujusmodi corpus, in quo stuppa sicca vel aliquid bene com-
bustibile accendatur, ut prius habitum est. Et haec triplex
calefactio potest vocari triplex combustio, de qua loquitur
scriptura ; vel aliter possumus dicere quod facit unam montium
combustionem de tribus de quibus scriptura intendit, cum
dicit, ‘sol tripliciter exurit montes. Nam alio modo con-
sideratur combustio penes varietatem angulorum, quia multi-
plicatio lucis vel est ad angulos rectos, vel obliquos, vel nullos.
Si ad obliquos, est fortis actio; si ad rectos, fortior est per
xvii primi Elementorum Euclidis et per alias vias; si ad
nullos, fortissima propter omnimodam aequalitatem, ut prius
habitum est. Sed ab omni puncto solis ad quodlibet punctum
montis objecti soli veniunt radii, et infiniti cadunt ad angulos
rectos, infiniti ad obliquos, ut manifestum est. Quamvis autem
superficies montium non est ubique polita et lenis, nec sphaerica,
tamen in multis partibus ejus est hujusmodi, et infinities per
portiunculas diversas, et ideo ratione sphaericitatis hujusmodi
accidit casus ad nullos angulos, et ideo est triplex incidentia.
Quapropter accidit triplex radiorum casus penes angulum et
privationem anguli. Et in omnibus modis est calefactio per
casum lucis et congregationem. — Quapropter secundus modus
combustionis, de quo loquitur scriptura, potest hac via nunc
dicta assignari. Tertio vero casus lucis variatur penes figuras,
nam cadit in sphaerica figura et pyramidali cujus conus est
in sole et basis in monte, atque in pyramidali cujus conus est
in puncto montis et basis in sole. Et omnibus his tribus
modis figuratur multiplicatio lucis a sole in monte, ut certum
est ex supradictis. Sed multiplicatio lucis sphaerica licet
possit esse fortis, tamen pyramidalis, cujus conus est in sole,
est fortior; et pyramidalis, cujus conus est in puncto montis,
est fortissima, quia, ut dictum est per illam pyramidem a tota
superficie solis objecta monti venit lux ad quodlibet punctum
montis, quoniam basis illius pyramidis est superficies solis, et
infinitae tales pyramides veniunt ab eadem solis superficie,
sicut manifestum est figuranti. Et natura non requirit plures
figuras in multiplicatione lucis, nec in alicujus virtutis vel

Symbolic
meaning of
direct, re-

216 OPERIS MAJORIS PARS QUARTA.

speciei multiplicatione, ut a quocunque agente fiat species mul-
tiplicanda, ut certum est scienti naturae vias per geometricam
potestatem. Et per has tres multiplicationes figuratas oritur
combustio tertia, de qua loquitur scriptura. Sed haec sciri
non possunt, nisi homo optime sciat potestatem geometricam.

Propter vero quaestiones pono unum exemplum pro mille,
ubi geometrica requiritur potestas, licet vulgus non advertat.
Nam de luce et multiplicatione ejus multa quaerunt theologi,
scilicet utrum sit substantia vel accidens, utrum sit corpus in
medio, utrum subito vel successive feratur in medio et caetera.
Sed haec nullo modo sciri possunt sine eis quae dicta sunt de
multiplicatione secundum lineas angulos et figuras. Nam
multiplicatio lucis est sicut multiplicatio omnis alterius
speciei cujuscunque agentis. Lux enim in medio est species
lucis quae est in corpore luminoso. Et ideo regulae, quae
dictae sunt de speciei multiplicatione sumptae generaliter,
intelliguntur in luce et in qualibet specie determinata. Cum
ergo multiplicatio speciei absolute consideratae requirat
maximam geometriae potestatem, ut prius ostensum est
abundanter, manifestum est quod ad lucis multiplicationem
intelligendam | eadem geometriae potestas necessaria est,
quamvis theologi non utantur.

Deinde de spiritualibus rebus exprimendis per res geome-
tricas pono exemplum in gratia et gloria et salvandis ac

fracted, and damnandis, ut videamus quomodo lineae rectae, fractae, et

reflected
rays.

reflexae, valeant hujusmodi spiritualibus adaptari. Et cum
gratiae infusio maxime manifestatur per lucis multiplicationem,
expedit per omnem modum ut per multiplicationes lucis cor-
porales manifestentur nobis proprietates gratiae in bonis, et
repulsa ejus in malis. Nam in bonis perfectis infusio gratiae
comparatur luci directe incidenti et perpendiculari, quoniam
non reflectunt a se gratiam, nec frangunt per declinationem ab
incessu recto, qui attenditur secundum viam perfectionis vitae.
Sed infusio gratiae in imperfectos, licet bonos, comparatur
luci fractae; nam propter imperfectiones eorum non tenet
gratia in eis incessum omnino rectum. Peccatores autem, qui
sunt in peccato mortali, reflectunt et repellunt a se gratiam
Dei, et ideo gratia apud eos comparatur luci repulsae seu

———— M — ———m ——— — —— —— — ee —— — — oe ——-— -— — ——— -—

MATHEMATICAE IN DIVINIS UTILITAS. 217

reflexae. Sed sicut corporum, a quibus reflectitur lux, quaedam
sunt aspera, a quibus.lux reflexa dissipatur nec apparet ; et
quaedam sunt polita et aequalis superficiei et laevis, a quibus
fit reflexio sensibilis, ut patet in speculis; sic peccatores
existentes in mortali peccato sunt dupliciter. Quidam enim
sunt, qui sic repellunt gratiam, quod nihil boni apparet in eis,
sed apud se et apud proximos manifestum est quod dissipatur
totus gratiae effectus in eis, et isti sunt aperte mali qui peccata
sua non abscondunt. Alii vero sunt, qui licet boni non sint,
tamen occultant peccata sua, et apparent boni in conspectu
hominum, ut hypocritae. Et potest aliter fieri comparatio
ista. Nam peccatores in hac vita comparantur corporibus
reflectentibus, ut dictum est, et homines in gratia in hac vita
comparantur illis quibus est fractio lucis propter imperfectiones
humanae fragilitatis, quia quantumcunque sit homo perfectus
in hac vita, tamen habet multas obliquitates, et imperfecta est
caritas in eo et notitia Dei. Sed existentes in patria com-
parantur illis rebus quae recipiunt lucem penitus secundum
rectum incessum omni exclusa declinatione, quantum possibile
est creaturae, et quantum exigit ordo divinae justitiae, qui
reddit unicuique secundum quod meruit. Quoniam vero
damnati omnino carent gratia et gloria Dei, et glorificati
ratione imperfectionis meriti in multis atque ex lege creationis
(cum omnis creatura habeat imperfectionem respectu gloriae
conditoris) sunt quodammodo imperfecti, potest fieri tertia
comparatio secundum statum damnatorum et glorificatorum
et Dei, quatenus apud damnatos teneat omnino comparatio
lucis reflexae, et apud glorificatos valeat similitudo lucis
fractae, et divinae gloriae summa rectitudo et perfectio noten-
tur, quomodo melius probatur trinitas personarum et unitas,
per incessum lucis directum, secundum quod possumus et
secundum quod licet nos exemplificare per creaturas ea quae
sunt apud creatorem.

Et quod valde notandum est adjungam, scilicet quod im- Geo-

TE oe . . . . metrical

possibile est beatam trinitatem et essentiae unitatem aptius ,,mpo] of
a nobis repraesentari in exemplo creaturae sensibilis quam per Trinity.
res geometricas. Nam in solo triangulo inter omnes res factas
invenitur unitas essentiae cum distinctione trium occupantium

Symbolic
sense of
rational

an
irrational
numbers.

And of

propaga-
tion of rays.

218 OPERIS MAJORIS PARS QUARTA.

eandem essentiam. | Quoniam idem spatium numero et totum
capit quilibet de angulis trianguli, ut patet ad sensum, et
tamen veraciter sunt anguli distincti, quod est mirabile in
creatura, nec alibi reperitur nisi in summa trinitate. Et cum
super datam lineam necesse est triangulum aequilaterum col-
locare, ut prima propositio Euclidis denunciat, quid magis
proprie potest assumi ut intelligamus quod data persona
Dei patris necesse est trinitatem personarum aequalium -
exhiberi ?

Haec et hujusmodi multa possunt ex geometricis ad sapien-
tiam salutarem pertrahi, et maxime de decimo libro, ubi
rationalitas et communicatio quantitatum declaretur. Nam
haec et ad divina et ad virtutum figurationes cum exclusione
vitiorum utiliter et praeclare possunt adaptari. Nam quic-
quid de rationabilibus quantitatibus continetur ibi potest
pulchre et proprie ad vitam rationabilem, quae in virtute
consistit, facile pertractari. Et quod de irrationabilibus quan-
titatibus exponitur potest moribus irrationabilibus et bestialibus
peccatorum conformari. Quicquid etiam de communicatione
quantitatum dicitur potest convenienter trahi ad actus caritatis.
Et quod de incommunicatione proponitur, ad odium et
divisionem animorum noscitur pertinere. Sed longiorem ser-
monem haec requirunt. De cautela vero peccatorum magnum
adjutorium est per considerationem hujusmodi geometricarum
multiplicationum. Nam cum res delectabiles hujus mundi
sint nobis sicut muscipula, quibus capiamur ad peccatum, ut
in libro Sapientiae scribitur; et sicut est in hamo diaboli, qua
strangulemur, nisi quantum Deus dignatur nos custodire, et
sensus nostri super res delectabiles delati nuntiant intellectui
occasionem peccati ; primum et principale remedium quod in
homine sit est ut in quinque sensus suos species rerum delec-
tabilium, ut mulierum, et ciborum, et divitiarum, in quibus
humana cupiditas aestuat et ambitio superba gloriatur,
non recipiat secundum multiplicationem principalem ; nam
accidentalis sufficit homini ad damnationem, quando recipitur
avide et abundanter. Sed magis adhuc cavenda est multipli-
catio recta sensibilis quam fracta vel reflexa, propter fortiorem
actionem prius expositam. Maxime vero, ne species delecta-

MATHEMATICAE IN DIVINIS UTILITAS. 219

bilis recta cadat ad angulos aequales in sensum, quia tunc
fortissima est, praecipue si conus pyramidis brevis occurrat.
Sic Eva recepit speciem soni serpentis et pomi visibilis et
suavis odoris. Et Adam allectus est ut se et totum genus
humanum specierum sensibilium multiplicatione damnaret.
Sic David sanctus propheta per speciem Betsabeae deceptus
de adulterio cecidit in homicidium. Sic senes presbyteri
quos judicavit Daniel specie mulieris decepti sunt. Et certum
est omnem hominem decipi speciebus rerum hujus mundi;
quia secundum Johannem, * omne quod est in mundo, vel est
concupiscentia carnis, vel concupiscentia oculorum, vel superbia
vitae, a quorum amore nullus se potest abstinere, qui gaudet
in sensu specierum quae veniunt a rebus. Nam capitur sicut
bestia. Et ideo homines sanctitati vacantes avertunt sensus
ab omnibus rerum delectabilium speciebus quantum possunt,
et maxime de illis quae pertinent ad sensum tactus et gustus,
quae sunt gulae et luxuriae, ut non solum non tangant, sed
nec videant nec audiant de his fieri mentionem, ne species
multiplicata in sensus spiritum cogat servire carnis illecebris;
et praecipue cavent ne prope sint, ut vitent pyramides breviores,
atque multiplicationes principales et rectas et ad angulos
aequales, ut praedixi. Et haec maxime cavenda sunt quando
oportet vel in confessione vel ob aliam aliquam causam loqui
cum mulieribus. Nam omnes homines quantumcunque sanctos
species fortes in hac parte turbarent, etsi non vincerent quos
Deus custodire dignatur.

Jam dictum est de quinque radicibus mathematicae respectu (6) Sixfold
scripturae; nunc remanent nobis duae aliae, scilicet numeri et RA
musicalia. Quoniam vero sancti abundanter ostendunt utili- metic in
tatem istorum respectu theologiae, et magis exprimunt horum theology
comparationes et laudes respectu divinorum quam de prioribus,
ideo plura de aliis tetigi, et de his solum innuam quasdam
vias, quarum explicatio in libris sanctorum copiose invenitur.
Numeri vero ad sensum scripturae valent quatuor modis. Nam
non est numerus in scriptura positus, quin accipiatur in sensu
literali secundum omnes ejus proprietates arithmeticas, qua-
tenus per congruas similitudines eliciantur sensus spirituales,
sicut sancti infinitis quasi modis manifestant. Secundo, propter

220 OPERIS MAJORIS PARS QUARTA.

historias sciendas et certificandas necesse est theologum
abundare in potestate numerandi, ut sciat omnes modos
algoristicos, non solum in integris sed in fractionibus, quatenus
sciat numerare, addere, minuere, mediare, multiplicare, dividere,
et radices extrahere, tam fractiones quam integra; et iterum
quod non solum sciat vulgares fractiones penes medietates,
tertias, quartas, quintas, et sic in infinitum ; sed quod sciat
astronomicas fractiones per minuta, secunda, tertia, quarta,
quinta, et sic in infinitum; quia in his historialibus oportet
recurrere ad motum solis et lunae, in quibus tales fractiones
considerantur principaliter, de quibus satis exemplificatum est
superius. Et non solum oportet fractiones Latinorum scire
et Arabum, sed Hebraeorum, qui frangunt unam horam in
mlxxx partes de quibus tactum est prius. Caeterum illum,
qui uti debet his, scire necesse est reducere diversa genera
fractionum ad invicem ; quia si inter integra accidant septem
quintae, et decem septimae, et viginti octavae, et hujusmodi
infinitis modis, non potest homo se expedire, ni istas diver-
sitates fractionum reducat ad unum genus fractionis, ut sic
reducantur ad integra. Sed in his fractionibus et integris
utendis magna est subtilitas, et pulchra sapientiae lumina
relucescunt, praecipue cum per haec tota sapientia divina et
humana dirigitur et rectificatur, secundum quod auctoritates
Cassiodori et Isidori prius manifeste expresserunt, qui crude-
liter nos redarguunt ex eo, quod omnes ignorantes numerorum
potestatem asserunt non differre a brutis animalibus, quae nec
divina nec humana cognoscunt. Tertio, valet consideratio
numerorum in scriptura, scilicet in divisione et distributione
sortium praedarum et portionum facienda sacerdotibus, Levitis,
principibus, et singulis, secundum quod Moyses peritissimus
in numerationibus algoristicis distribuit unicuique quod suum
est, infinitam quasi multiplicationem rerum distribuens in
partes certissimas operibus algoristicis propriissimis tam in
fractionibus quam in integris. Et nullus literalem sensum,
nec per consequens spiritualem potest elicere, ut exigit dig-
nitas scripturae, nisi operum horum sciat rationem et noscat
operationes numerandi per quas Moyses et alii in scriptura
procedunt.

ST 030-0 —

MATHEMATICAE IN DIVINIS UTILITAS. 22I

Quarto!, necesse est optime scire rationes numerandi propter Arith-
corruptionem numerorum in scriptura, quia quasi infinitis efic*
modis corrumpuntur ; fere enim omnes numeri sunt corrupti. received
Quae corruptio ad veritatem reduci non potest, nisi per Bible t
omnimodam numerandi potestatem tam in fractionibus quam
in integris. Fere enim aut pro majori parte omnes numeri in
sacro textu et in libris sanctorum sunt scriptorum et cor-
rectorum vitio depravati, de quibus pauca exempla subjungam
pro infinitis: Nam undecimo capitulo Genesis habetur,

' Vixit Arphaxat, postquam genuit Sale, ccciii annis. Sed
in Hebraeo habentur cccciii anni. De Graeco vero non
potest haberi veritas, quia inter Arphaxat et Sale interponit
Cainan, quem nos non habemus, sicut nec Hebraeus. Et
in eodem capitulo, ‘Vixit Reu xxxii annos' secundum
Hebraeum et antiquos codices Latinorum. Sed in exemplari
vulgato habentur xxxv, ut historiae veritas continuari non
possit. Et xviii capitulo in penultima parte ejus, * Quid si
minus quinquaginta justis quinque fuerint, delebis propter
quinque. Sic Hebraeus, sic antiqui libri habent. Moderni
autem posuerunt xlv propter sensum planiorem. Sed non
licet sine sede apostolica mutare textum quem recepit et jussit
per omnes ecclesias derivari. Et xxxvii capitulo, * Joseph
cum esset xvii annorum ' secundum Hebraeum et Graecum.
Sed moderni habent xvi, et quod in eodem capitulo non
sit venditus xxx argenteis, sed xx, probatum est superius
multiplici testimonio. Et in Exodi xiv capitulo, ‘tulitque
sexcentos currus, secundum Hebraeum et Graecum et
Josephum et antiquos codices. Sed pars glossae truncata fere
in omnibus libris facit quod exemplar vulgatum habet ccc
currus. Nam communiter habetur hoc tantum in glossa
‘contra fidem trinitatis pugnaturus. Unde propter nomen
trinitatis abraserunt sexcentos et posuerunt ccc. Sed in
pluribus antiquis glossatis invenitur sic, ' contra fidem trinitatis
numero senario se armavit pugnaturus. Et ideo secundum

! This paragraph supplies further illustrations of the corruption of the Paris
text of the Bible, spoken of on p. 77, and also in the Opus Minus (Brewer,
Pp. 330-349). It is also one of many proofs of the care with which Bacon had
collated the Septuagint and the Hebrew text.

Properties
of number
three.

222 OPERIS MAJORIS PARS QUARTA.

glossam possunt ibi esse sexcenti. Et Exodi xxxii habetur
in Hebraeo et Graeco ‘quasi tria millia, Sed exemplar vul-
gatum habet viginti tria millia. Et dicit magister in historiis
quod hoc est de antiqua translatione. Sed antiqua translatio
est LXX interpretum, et est de Graeco, Graecus autem non
habet hoc, sed sicut Hebraeus. Et hic error habet apparen-
tiam ex prima ad Cor. x. Sed non est intelligendum pro
hoc loco, ut patet in textu et in glossa. Quoniam cum dicit,
* Neque idololatrae efficiamini, &c. quod ad hunc locum per-
tinent, non ponit numerum interfectorum. Sed statim cum
dicit, ‘ Neque fornicemur’ &c. sequitur, ‘et ceciderunt viginti
tria millia, quod intelligitur secundum glossam de his, qui for-
nicati sunt cum Madianitis, ut legitur xxv Numerorum.
Nolo plura exempla aggregare ad praesens, cum non sit ex
principali intentione corruptionem textus probare. Sed haec
ideo intuli, ut videatur necessitas computandi in scriptura,
quatenus sciamus verificare corruptiones numerorum.

Et adhuc potest quinta ratio de numerorum utilitate signari.
Nam unitas in se ducta cubice, id est, ter, ut semel unum
semel non multiplicat essentiam, sed eadem manet licet aequa- —
litate trium laterum deducatur. Et sic familiari exemplo
theologi notant beatam Trinitatem. Quamvis autem multiplex
numeri perfectio inveniatur secundum quod denarius dicitur
esse perfectus, et septenarius, et senarius, tamen maxime
ternarius sibi vindicat perfectionem ; quoniam perfectio
praecipua quae numeris aliis attribuitur est quod omnes partes
aliquotae simul sumptae reddant suum totum, ut patet in
senario. Sed in ternario solo accidit, quod pars aliquota et
non aliquota simul sumptae reddunt ipsum, scilicet unitas et
binarius, quod non potest in alio inveniri. Atque cum in
omni numero sint duo, scilicet discretio partium et unitas
congregationis earum, qua numerus dicitur esse unus; nec
aliquid aliud facit numerum nisi haec duo; ista praecise re-
periuntur in ternario. Per binarium enim est discretio, et per
unitatem ipsa unitas habetur. Et ideo tota perfectio numeri
in ternario et non in alio reperitur. Et propter hoc hic
numerus convenit creatori magis quam alius. Et sicut ab
unitate omnis multitudo procedit, sic ab ipso Deo. Et arith-

MATHEMATICAE IN DIVINIS UTILITAS. 223

metica docet in fine suo omnes medietates investigari in Three
proportionibus numerorum. Nam nec geometra nec musicus Proponi on.
nec astrologus de his tractat, sed supponit quod arithmetica,
quae est scientia numerorum, edocet. Theologi autem
nituntur has medietates ad proprietates divinarum persona-
rum exaltare, et praecipue Ricardus de Sancto Victore in
libro de trinitate, qui liber magnam habet difficultatem ob
istarum medietatum ignorantiam apud vulgus. Et multi
propter eandem abutuntur comparationibus istarum medie-
tatum ad divina. Triplex vero est medietas, scilicet arith- .
metica, geometrica, musica. Arithmetica vero consistit in
identitate differentiarum primi ad secundum, et secundi ad
tertium, ut quatuor, tria, duo. Nam unitas sola est differentia
hinc inde, et huic simile reperitur in divinis personis. Nam
differentia Patris ad Filium est quod Pater dat Filio et non
accipit ab eo; Filius autem e converso. Similiter inter Filium
et Spiritum Sanctum est consimilis differentia. Nam Filius
dat Spiritui Sancto et non accipit ab eo; Spiritus autem
Sanctus e converso accipit ab eo et non dat ei. Et cum geo-
metrica medietas sit, quando est eadem proportio primi ad
secundum, et secundi ad tertium, ut inter viii, iv, ii, ratio
hujus medietatis per omnimodam aequalitatem et unitatem
essentiae in tribus personis reperitur, et in omnibus essentia-
libus, quae sunt potentia, sapientia, bonitas. Nam credimus
et firmiter tenemus quod qualis est Pater talis est Filius, et
talis Spiritus Sanctus. Harmonica seu musica medietas con-
sistit in identitate proportionis primi ad tertium, et differentiae
primi et secundi ad differentiam secundi et tertii, ut vi, iv,
iii. Nam dupla proportio est inter primum et ultimum ;
similiter inter binarium, qui est differentia primi et secundi,
et unitatem, quae est differentia secundi et tertii Et
sic per similitudinem in personis divinis reperitur. Nam
quae est proportio Patris ad Spiritum Sanctum quantum
aequalitas ; sic est inter differentiam Patris et Filii, et inter
differentiam Filii et Spiritus Sancti. Nam inter Patrem et
Filium est differentia, quod Pater dat et non accipit, Filius
accipit et non dat; et haec eadem est inter Filium et Spiritum
Sanctum, ut patet Sic igitur breviter assignantur hae

Dimen-
sions of
heavenly
bodies.

224 OPERIS MAJORIS PARS QUARTA.

medietates, quamquam et aliter a multis assignentur, quos
non possum intelligere; quia videtur mihi quod non possunt
secundum arithmeticae judicium salvari. Sed non est tem-
poris praesentis opiniones singulorum explicare.

Et sexta ratio de utilitate arithmeticae potest sumi in
scriptura penes res hujus mundi, quibus ipsa utitur. Nam
altitudinem et magnitudinem et spissitudinem et numerum
coelorum et stellarum tangit et requirit certificationem
istorum Et sancti in expositionibus suis multa loquuntur.
Nam Hieronymus dicit super Isaiam, quod Orion habet xxii

. stellas, quarum ix primae sunt in tertia magnitudine, et ix

Terrestrial
arc corre-
sponding
toa
degree,

residuae in quarta, et iv ultimae in quinta magnitudine, et
non exponit se. Oportet ergo theologum haec non ignorare.
Sed specialiter arithmetica rectificat in his, et ideo volo hic
has veritates magnificas aperire per numeros, quatenus
pulchre et utiliter apparet comparatio numerorum. Ad hoc
autem considerandum necesse est ponere aliquam radicem
notam. Haec autem est quantitas arcus terrae, quae re-
spondet uni gradui in coelo, secundum quod docet Alfraganus
capitulo viii.

Et Averroes consentit in fine secundi Coeli et Mundi. Isti
vero dant modum certificandi hoc in numero milliariorum et
partium ejus. Ptolemaeus autem quinta Almagesti dictione
procedit per viam demonstrationis diffuse in quantitate alti-
tudinum solis et lunae et in eorum magnitudine. Sed non
dat quantitatem certam per numerum milliariorum ; nec de
aliis corporibus coelestibus determinat quantitatem. Oportet
igitur supponere, quod cubitus aequalis et geometricus con-
tineat pedem et dimidium, et milliare continet 4,000 cubi-
torum, et sic accipit Alfraganus in sua consideratione. Omnis
autem circulus sphaerae potest dividi in 360 partes, quae
gradus vocantur. Intelligamus igitur maximum circulum in
sphaera coelesti, qui transeat per centrum et dividat sphaeram
in duas partes aequales. Dico ergo quod uni gradui! istius

! The first attempt to compare angular astronomical magnitudes with terrestrial
distances was that of Eratosthenes (B.c. 276-196), who found that when the
sun was vertical at Syene, it was one-fiftieth part of a great circle (i. e. 7? 12^)
from the zenith at Alexandria. The distance between the two places was

MATHEMATICAE IN DIVINIS UTILITAS. 225

circuli in coelo respondebunt multa milliaria in terra, cujus
experientiam innuit Alfraganus in hoc, quod accepta in aliquo
loco elevatione poli super horizonta, si perambuletur ad
septentrionem vel meridiem, usquequo elevatior polus appareat
vel depressior per gradum unum, invenitur quantitas milliari-
orum terrae, quae respondeat uni gradui in coelo. Nam si in
nocte clara stellata quis per foramina quadrantis vel astrolabii
vel alterius instrumenti perspexerit stellam nauticam et ipsum
polum, et notaverit gradus quos attingit extremitas virgae in
dorso astrolabii vel filum in quadrante, processeritque in terra
ad septentrionem donec in altera nocte stellata viderit eundem
polum elevari plus super horizonta per unum gradum, ille
arcus terrae, quem perambulaverit, respondebit uni gradui, et
erit ei similis, ut sumuntur arcus similes in sphaeris diversis
secundum Theodosium, sed non erunt propter hoc aequales.
Cum autem per semidiametrum terrae, quae continet 3,250 Dimen-

milliaria, doceat 21° capitulo mensurari diametros orbium 2 2A,
coelestium et distantias augium et oppositorum earum, oportet
quod veram quantitatem semidiametri accipiat. Nam aliter
magnus accideret error in distantiis augium, eo quod quantitas
semidiametri terrae multotiens replicata faceret magnum
errorem in illis distantiis, nisi praecise sumeretur. Cum
igitur fatendum est Alfraganum percepisse hunc errorem,
manifestum est quod ipse accipit veram semidiametri quanti-
tatem, scilicet 3,250, et veram diametrum, scilicet 6,500. Ergo
oportet quod supponat radicem veram et completam, quae
est in quantitate arcus terrae respectu gradus coeli, licet non
exprimat eam perfecte. Quapropter ipse supponit quod sit
56 milliaria, et duo tertiae milliarii, et 27 nonagesimae, et una
sexcentesima tricesima, vel 56 milliaria et 2,984 cubiti et

regarded as 5,000 stadia. But the uncertainty as to the Greek measures of
length, and the coarseness of their astronomical instruments ‘independently
of the fact that Alexandria and Syene are not on the same meridian), make it
impossible to deduce any precise result from this observation. The Arabian
instruments were better, but were obviously insufficient as a basis for solving
the problem here discussed by Bacon, of the Earth's magnitude.

It may be noted here that in the oldest MSS. of the Opus Majus, as well as in
those of a later date, Arabic numerals are very commonly employed in dealing
with large numbers.

VOL. I. Q

226 OPERIS MAJORIS PARS QUARTA.

quinque septimae unius cubiti. Et ideo, si quis bene con-
sideret, ipse respectu diametri et semidiametri, quibus utitur,
omittit octavo capitulo in hac radice, quae est quantitas arcus
terrae respectu gradus in coelo, 50! sexcentesimas tricesimas
unius milliarii, sive quod idem est, 317 cubitos, et tertiam
cubiti, 28 sexagesimas tertias unius cubiti, quoniam non
exprimit ibi nisi quod arcus iste terrae est 56 milliaria et
duae tertiae unius milliaris. Sed licet radicem plenam sup-
ponat, tamen fractiones aliquas omittit propter taedium
numerorum. Mos enim ejus est in libris suis multotiens
omittere fractiones et similiter faciunt alii autores. Si igitur
volumus huic quantitati diametri, scilicet 6,500 qua utitur,
adaptare radicem, dicemus quod arcus terrae respondens uni
gradui in coelo continet 56 milliaria, et duas tertias unius
milliaris, 27 nonagesimas milliarii, et unam sexcentesimam
tricesimam. Et si volumus computare per cubitos, erit arcus
terrae respondens uni gradui in coelo 56 milliaria, et duo
millia cubitorum, nongenti octoginta quatuor cubiti, et 8
sexagesimae tertiae unius cubiti, quae 8 sexagesimac tertiae
sunt plus quam una octava cubiti per unam quingentesimam
quartam unius cubiti, quod de facili patet. Nam octo sexa-
gesimae tertiae valent 64 quingentesimas quartas, et 63
quingentesimae quartae sunt octava totius; ergo 64 quin-
gentesimae quartae excedunt octavam in una quingentesima
quarta; et ita octo sexagesimae tertiae unius cubiti ex-
cedunt octavam ejus in una quingentesima quarta. Et si
triplicaverimus diametrum hanc 6,500 et ejus septimam
addiderimus, habebitur circumferentia totius terrae, et erit
praecise viginti millia milliariorum quadringenti et viginti octo
milliaria, et duo millia ducenti octoginta quinque cubiti, et
quinque septimae unius cubiti; vel penes alias fractiones,
erit numerus hic vigesies mille quadringenti viginti octo
milliaria, et quatuor septimae unius milliarii. Et secundum
hoc tota terrae superficies erit centies trigesies bis mille
millia milliaria sexcenties mille milliaria. Et secundum hanc
radicem perfecte computatam erit quarta terrae habens
33,150,000 milliaria in sua superficie. Et octava terrae
1 The omission is greater than Bacon states; i. e. it is $$$ of a mile.

MATHEMATICAE IN DIVINIS UTILITAS. 227

habebit 4,143,750 milliaria. His enim duabus quantitatibus
indigemus, sicut et caeteris praedictis.

His visis, consideranda est altitudo coelestium, et similiter Dimen-
magnitudo et spissitudo. Nam Alfraganus dicit xxi capi- Sonsof the
tulo, quod Ptolemaeus et alii sapientes posuerunt medie- spheres.
tatem semidiametri terrae esse quantitatem qua metiti sunt
longitudines a centro terrae, et posuerunt corpus terrae
quantitatem qua mensuraverunt corpora stellarum. Et hoc
satis patet ex demonstrationibus Ptolemaei quinta dictione
Almagesti. Sententiat ergo Alfraganus ex comparatione
semidiametri terrae ad semidiametrum orbis stelati, quod
distantia orbis stellati a centro terrae est vigesies millies
centies decies aequalis medietati diametri terrae, quod est
sexaginta quinque mille millia trecenta quinquaginta septem
millia quingenta milliaria, quod si duplicetur, erit diameter
totius orbis stellati scilicet 130,715,000 milliaria. Et cum
. multiplicatur hoc in tria et septimam diametri erit rotunditas
maximi circuli in coelo stellato, scilicet 410,818,57 r milliaria,
et tres septimae milliarii, hoc est, 1,714 cubitt, et 2 septimae
cubiti. Et si hunc numerum diviserimus in 360 pastes, una
pars, scilicet quae erit quantitatis unius gradus coeli stellati,
habebit milliaria 1,141,162 et 251 trecentesimas sexagesimas
milliarii, hoc est 2,788 cubiti, et octo nonae unius cubiti Et
si duxerimus diametrum in rotunditatem, erit superficies tetius
coeli stellati, 53,700,149,508,265,000, videlicet, quinquagesies
ter millesies millesies millesies millesies mille millaria, septin-
gentesies millesies millesies millesies mille milliaria, centies
quadragesies novies millesies millesies mille milliaria, quin-
gentesies octies millesies mille milliaria, ducenties sexagesies
quinque millia milliaria! Semidiameter autem coeli stellati
est longitudo longior orbis Saturni, quia junguntur sine
medio. Sed ejus longitudo propinquior terrae est 46,816,250
milliaria, quod est longitudo longior orbis Jovis, cujus longi-

! The manipulation of these large numbers is interesting; and they may,
perhaps, to some extent account for the contentment of the ancient and medi-
aeval mind with a limited universe. Archimedes, in his Psasssmstes, had assigned
a wider limit for the diameter of the universe; viz. ten thousand million stadia,

or one thousand million miles, as against one hundred and thirty million in the
computation of Alfraganus and Bacon.

Q2

228 OPERIS MAJORIS PARS QUARTA.

tudo propinquior est 28,847,000 milliaria, quod est longitudo
longior orbis Martis, cujus longitudo propinquior est 3,965,000
milliaria, quod est longitudo longior orbis solis, cujus longitudo
propinquior est 3,640,000, quod est longitudo longior Veneris,
cujus longitudo propinquior est 542,570, quod est longitudo
longior Mercurii, cujus longitudo propinquior est 208,541 et
duae tertiae milliarii, et hoc est 2,666 cubiti et duae tertiae
cubiti, et haec est longitudo longior Lunae, et haec, ut dicit
Alfraganus, est 64 vicibus et sexta vicis unius aequalis medie-
tati diametri terrae, et longitudo propinquior Lunae est 109,037
et medietas milliarii, hoc est, 2,000 cubiti, et haec est 33 vicibus
et semis et medietate decimae, id est, una vicesima unius vicis
aequalis medietati diametri terrae. Diametri quidem singu-
lorum orbium habentur per duplum semidiametri ; rotunditas
cujuslibet habetur per triplicationem diametri cum additione
septimae partis, et tota superficies cujuslibet orbis habetur per
ductum diametri suae in rotunditatem suam, ut exemplificatum
est in terra et in orbe stellato. Et quilibet potest haec experiri
per computationem, et ideo omitto haec propter prolixitatem.
Quoniam vero subtracta longitudine propiore a longiore
remanet spissitudo orbis, ideo patet, quod spissitudo orbis
Lunae est 99,504 milliaria, et spissitudo Mercurii 334,209, et
Veneris 3,097,250, et Solis 325,000, et Martis 24,882,0co, et
Jovis 17,969,250, et Saturni 18,541,250. Haec ex radicibus
Alfragani et Ptolemaei in Almagesti sumuntur.

Sciendum vero quod in omnibus istis altitudinibus sumitur
distantia a centro terrae. Unde licet sapientes aliquando
dicant longitudines has fieri a terra, intelligunt tamen quod
a centro terrae, quia medietas terrae nihil facit sensibile.
Cum ergo longitudo propinquior orbis Lunae sit 109,037 mil-
liaria et medietas milliaris, subtracta medietate diametri terrae,
quod est 3,250, a numero praedicto integrorum milliariorum,
scilicet 109,037, relicta medietate, residuum distantiae orbis
Lunae a terra erit 105,787. Et ponantur 20 milliaria pro
dieta. Ergo si iste numerus dividatur per 20 exibit numerus
dietarum 5,289, et restant 7 milliaria. Et si istae dietae divi-
dantur per 365 dies unius anni, exibunt anni 14, et restant
dietae 179, quae si dividantur per 30 quae sunt dies mensis

MATHEMATICAE IN DIVINIS UTILITAS. 229

perfecti, exibunt menses perfecti 7, et restat unus mensis im-
perfectus, id est, 29 dierum. Patet igitur quod sumendo
dietam in 20 milliaribus posset homo pertransire spatium
usque ad orbem Lunae in 14 annis et quinque mensibus
perfectis et uno mense imperfecto, et adhuc restarent 7 mil-
liaria et medietas milliarii, quae a principio relicta fuit.

De nono vero coelo et decimo nihil potest per instrumenta Height of
sensibilia sciri in altitudine et spissitudine et magnitudine, sicut *le"ds
de aliis coelis, ut de spissitudine octavi coeli quia haec omnia
latent sensum, et ideo super haec cessat certificatio quantitatum
et altitudinum, et spissitudinum. Et per longitudinem pro-
pinquiorem Lunae est manifesta longitudo longior orbis ignis,
sed longitudo longior aeris non est nota. Nam philosophi
haec neglexerunt, quia non est utilitatis notabilis Quantum
tamen est usque ad locum nubium verificaverunt, quoniam
demonstratur in libro de Crepusculis! quod altitudo illa est
per 51 milliaria et duas tertias. Plinius? autem secundo
Naturalium recitat nubes elevari stadiis 400 et goo secundum
diversa philosophorum testimonia. Ergo ad minus extenditur
aer in tantum et plus; quamvis Albumazar et quidam alii
aestimant vapores non elevari nisi per duo milliaria et decimam
et tertiam milliarii. Et Ptolemaeus in libro de Dispositione
Sphaerae dicit, quod decem stadiis est ultima elevatio vaporum.
Et Martianus in Astronomia in hoc concordat. Nam montem
altissimum ponunt decem stadiis elevari, ut Olympum, in

! This book is generally attributed to Alhazen, and, like the treatise on Optics
of the same author, was translated into Latin from Arabic by Gerard of Cremona.
It is an attempt to determine with geometrical precision (a) the position of the
Sun with reference to the horizon when evening twilight ceases or morning
twilight begins: (6) assuming twilight to be caused by solar rays passing through
terrestrial vapours, the height above the Earth to which these vapours rise,
He found that at the extreme limit of twilight the Sun was between nineteen
and twenty degrees below the horizon. From this datum, and from the three
data of the Earth's radius, the Sun's radius, and the distance of the Earth from
the Sun (as given in the current astronomy;, he concluded that the extreme
altitude of terrestrial vapours was somewhat less than fifty-two miles.

' Pliny (Hist. Nat. ii. 33) makes the limit of cloud vary from 4o to goo
stadia; the stadium being estimated at 125 paces or 625 feet. Bacon, in the
following sentences, shows himself aware of the extreme uncertainty of these
measures of length, But the estimate of the stadium hardly varied to the
extent stated by him.

230 OPERIS MAJORIS PARS QUARTA.

cujus cacumine non invenitur ventus nec vapor, quod probant
homines per experientiam. Sed quoniam Aristoteles! libro
Meteorologicorum vult vapores elevari usque ad confinium
aeris et ignis, ideo tenenda est sententia saltem libri de Cre-
pusculis, et aliae glossandae sunt per diversam quantitatem
stadii et milliaris. Nam aliquando invenitur, quod stadium
est octava pars milliaris, et alias quod est longe plus, et
similiter de quantitate milliaris est magna diversitas; scitur
enim quod montes Italiae et alii, ut Caucasus, in cujus cacu-
mine apparent radii solis usque ad tertiam partem noctis,
habent plus quam octies 125 pedes, et ideo habent plus quam
octo stadia, secundum quod stadium dicitur esse 125 pedum.
Et ideo alibi inveni in expositione libri de Ormesta Mundi,
quod stadium continet duas leucas, et duas partes unius
leucae, et sic unum stadium continet quinque milliaria et
tertiam milliarii. Per hujusmodi ergo diversitates solvuntur
praedicta. Quod autem certius est de altitudine maxima
montium est, quod est octo milliaria, secundum quod docetur
libro de Crepusculis, et ideo apud librum Ptolemaei potest
esse falsitas translationis vel scripturae, quando altitudo
maxima ponitur in octo stadiis.

Postquam jam habemus coelorum altitudines, planum est
nos habere et stellarum secundum considerationes Ptolemaei
et omnium mathematicorum. Nam longitudo propinquior
Lunae est longitudo orbis ejus, et longior longitudo similiter
est una, et sic de aliis. Sed de magnitudinibus et spissitu-
dinibus stellarum non est notum per hanc viam. Qui igitur
posset invenire diametros, de facili inveniret rotunditatem
et totam superficiem per doctrinam quam prius tetigi in
orbibus. Antiqui vero quidam, ut Martianus in sua Astro-
logia, nisi sunt invenire diametrum Solis et Lunae per fluxum
aquae per foramen vasis, dum oritur stella, et dum volvitur
totus orbis coeli; et ita per illas duas aquas inveniebant
quanto arcui diameter corporis stellae subtenditur.

! Aristotle observes, Meteorolog. i. 3, $ 10, that clouds form in a region not too
near the heavenly bodies to be dissipated by their heat, nor too near the Earth
to be affected by the rays of heat reflected from its surface. Tívorra: ydp ai
Tay vepay dOpoices ov Afpyovaw fjóg ka 7d oxí(ea0a: «ls dyaves al darives.

MATHEMATICAE IN DIVINIS UTILITAS. 231

Instrumenta autem aquae erant, sicut nunc fiunt quaedam Measure-
horologia. Sumunt enim caldarium in fundo habens foramen apparent
unum, et illud implent aqua, ita tamen quod in exitu primae diameters
guttae per foramen incipiat Sol oriri, et in occasu Solis con- planete
siderabant quantum aquae exierat, quam dividunt in duodecim
partes secundum numerum duodecim horarum, et ideo lapsus
cujuslibet partis per dictum foramen est revolutio quindecim
graduum, quae facit unam horam diei. Volentes igitur per hoc
quantitatem Solis vel Lunae accipere, prima parte Solis oriente
primam guttam aquae diurnae exire permittunt, et ultima
parte Solis orta, foramen obturant. Quae igitur est proportio
aquae nunc elapsae ad totam aquam diurnam, eadem est
diametri Solis sive arcus coeli huic correspondentis ad totum
arcum diei. Alii vero per astrolabium vel quadrantem con-
sideraverunt quantum movetur regula, dum extremitates Solis
et Lunae aspiciuntur, et considerant tunc, quod quae est
proportio illius arcus in instrumento ad totam circumferentiam
ejus, eadem est proportio stellae ad circumferentiam coeli.

Sed isti modi non habent sufficientem certitudinem. Et
propter hoc Averroes dicit in fine secundi Coeli et Mundi, quod
investigatur quantitas diametrorum stellarum per instrumen-
tum, quod dicitur, habens duas regulas. Illud enim instru-
mentum terminat angulum, quem respicit diameter stellae, et
hoc instrumentum continetur ex duabus regulis ad modum
circini ad quantitatem quatuor cubitorum, et sunt in extremi-
tatibus earum primae perforatae, ut videantur duae extremi-
tates Solis vel Lunae. Per angulum enim inter duas regulas,
quando notus est, scitur diameter stellae quoniam est basis
illius anguli. Et hoc instrumentum invenit Abrachis !, ut vult
Ptolemaeus quinta dictione Almagesti xiv capitulo. Ptole-
maeus vero abhorruit primos modos propter insufficientiam,
et hunc modum Abrachis invenit habere defectum. Nam
secundum hoc instrumentum Abrachis aestimavit diametrum

! Abrachis, the Arabian transformation of Hipparchus. It may be remarked,
as an illustration of the imperfection of the astronomical instruments used by
the ancients, that Archimedes, who constructed an instrument for measuring the
apparent diameter of the Sun, had to content himself with the conclusion that

it was not less than $$$ and not more than $41; in other words, he left a margin
of error of nearly six minutes.

The true
diameter
of the
Moon.

232 OPERIS MAJORIS PARS QUARTA.

Lunae in omni longitudine sua esse aequalem secundum
aspectum diametro Solis propter aequalitatem angulorum.
Sed Ptolemaeus consideravit. quod diameter Lunae non
aequatur secundum aspectum diametro Solis, nisi quando
Luna est in longitudine sua maxima. Et hoc est quando
Luna est in auge epicycli, et epicyclus in auge eccentrici, et
hoc est iterum quando est plena. Tunc enim angulis aequalibus
diametri Solis et Lunae subtenduntur secundum aspectum.
Sed quando Luna est in longitudine alia non est sic, et ideo
quantitas anguli non certificatur apud existentiam Lunae in
quocunque loco; quod ideo fit, quoniam tabula elevatur a
regula, et oculus est super superficiem regulae, et ideo non
recte protenditur oculus ad foramen tabulae, sed obliquatur
aliquantulum, et deberet tunc accipi quod est inter duo fora-
mina, et accipitur quod est inter duas regulas, et ideo est
dubitatio de quantitate anguli. Et propter hoc Ptolemaeus
voluit certificare quantitates angulorum per eclipses Lunares,
et descendit ad diversas eclipses, in quibus manifestat pro-
positum. Certificatur igitur per instrumentum et per eclipses
quantitas anguli cui subtenditur diameter Lunae quando est
in longitudine sua maxima et plena. Et ideo per quantitatem
anguli certificatur diameter Lunae!, et per triplicationem
diametri cum additione partis septimae certificatur quantitas
rotunditatis Lunae, et per ductum diametri in rotunditatem
certificatur tota superficies Lunae, et totum ejus corpus.

Et quoniam medietas diametri terrae est radix ad hoc, ut
Ptolemaeus utitur xv capitulo dictionis praedictae, ideo per-
cipitur quantitas diametri Lunae per comparationem ejus ad
diametrum terrae, et quantitas corporis Lunae per compara-
tionem ad quantitatem corporis terrae. Et ideo Ptolemaeus
in xvi capitulo concludit per demonstrationem suam et
figurationem quod secundum quantitatem qua erit diameter
Lunae pars una, erit diameter terrae tres partes et duae
quintae fere. Diameter igitur terrae erit in longitudine triplum
diametri Lunae, et duae quintae ejus. Et ideo si a diametro

! Bacon passes from the apparent to the real diameter of the Moon without
explaining how the latter is found, i.e. from the Moon's mean horizontal
parallax.

MATHEMATICAE IN DIVINIS UTILITAS. 233

terrae, quae est 6,500 milliaria, separaverimus diametrum
Lunae, per computationem erit diameter Lunae praecise 1,911
milliaria, et tres quartae unius milliaris, et una decima septima
unius quartae ; et triplicata diametro cum adcitione septimae
partis habebimus ejus rotunditatem, quae erit 6,006 milliaria,
et sex decimae septimae quartae partis unius milliaris; et
ducendo diametrum in circumferentiam habebimus totum
corpus Lunae quod erit 45,927,882 milliaria, et hoc erit quasi
una de xxxix partibus totius terrae, sicut docet Ptolemaeus.
Nam secundum quantitatem qua erit corpus Lunae pars una,
erit magnitudo corporis terrae trigintuplum nocuplum et
quarta ejus fere; quoniam cum quantitas diametri Lunae
fuit pars una, quantitas diametri Terrae fuit tres partes et duae
quintae. Si igitur istae quantitates ducantur in se cubice et
corporaliter, patet quod unum ductum in se cubice non est
nisi unum, sed tria et duae quintae ducta in se cubice faciunt
trigintuplum nocuplum et quartam fere. Quapropter corpus
terrae erit trigintuplum et quarta fere respectu corporis Lunae.
Et hoc patet, quia quantitas praedicta de corpore Terrae
investigata superius est trigintupla nocupla ad quantitatem
corporis Lunae et fere quarta, ut patet consideranti.
Quantitas autem diametri Solis et totius corporis ejus
dependet secundum Ptolemaeum a duobus, scilicet a quantitate

The
diameter
and other

diametri Lunae et a quantitate semidiametri Terrae. Nam dimensions

longitudinem Solis a Terra ostendit per longitudinem Lunae
jam notam, et per angulos quibus diametri Lunae et Solis
subtenduntur apud aspectum, cum fuerit Luna in longitudine
sua maxima in plenilunio. Tunc enim videtur corpus Lunae
cooperire totum Solem nec plus, et ideo tunc dicitur Sol
eidem angulo subtendi apud aspectum cui subtenditur Luna.
Nec considerat longitudinem Solis diversam, quia propter
superfluam distantiam non accidit diversitas in aspectu, sive
Sol sit in longitudine propinquiore, sive longiore. Et invenit
per has considerationes, quod secundum illam quantitatem
qua diameter Lunae est pars una, et diameter Terrae tres
partes et duae quintae fere, erit diameter Solis 18 partes et
4 quintae unius partis. Diameter ergo Solis erit decuplum
octuplum ad diametrum Lunae, et quatuor quintae ejus;

of the Sun.

Dimen-
sions of
the planets.

234 OPERIS MAJORIS PARS QUARTA.

eritque diameter Solis ad diametrum Terrae quintuplum et
medietas ejus fere. Si ergo per diametrum Terrae notam,
quae est 6,500, sumpserimus diametrum Solis erit 35,941
milliaria, et 12 decimae septimae unius quartae. Et si haec
quantitas triplicetur cum additione septimae partis, erit quau-
titas rotunditatis Solis 119,803 milliaria et una tertia, et 12
decimae septimae unius quartae. Et si duxerimus diametrum
in rotunditatem erit tota superficies Solis 292,783,785,375 mil-
liaria. Et si quantitas diametri Solis respectu diametri Lunae
sumpta multiplicetur in se cubice, erit hic cubus sexies mille
et sexcentuplum et quadragintuplum et quadruplum respectu
corporis Lunae, et medietas ejus fere; et ideo secundum
quantitatem, quae est corpus Lunae pars una, erit magnitudo
corporis Solis respectu Lunae sexies mille sexcentuplum
quadragintuplum et quadruplum et medietas ejus fere. Quod
si diameter Solis comparata ad diametrum Terrae ducatur in
se cubice, fiet cubus qui erit centuplum et septuagesimum
fere. Et ideo Sol est centies septuagesies fere major corpore
Terrae. Et istud quod dicit fere exponitur a Thebit in libro
suo, qui intitulatur, De iis quae indigent expositione antequam
legatur Almagestum. Sed nec omnino praecise. Nam dicit
quod Sol est centies sexagesies sexies aequalis Terrae. Et
Alfraganus xxii capitulo sui libri addit super hoc dictum
Thebit quartam et octavam Terrae, quas prius determinavi
propter hunc locum certificandum. Est igitur Sol major tota
Terra centies sexagesies cum quarta et octava Terrae super-
additis. Et istud est praecisa quantitas Solis secundum
considerationes auctorum.

Ptolemaeus vero non determinavit nisi quantitatem Solis et
Lunae. Sed Alfraganus dicit xxii capitulo consimilem
modum esse in aliis, quem Ptolemaeus accepit in his. Nam
secundum quod jnvenit quod diameter Lunae, quando est in
longitudine sua maxima et plena, est in aspectu aequalis
diametro Solis, similiter est cum alii planetae sunt in medio
longitudinum suarum, diametri eorum habent comparationem
ad diametrum Solis in quantitate certa. Diameter enim
Mercurii in aspectu est xv pars diametri Solis, et Veneris est
decima pars diametri Solis, Martis est xx, Jovis xii, Saturni

MATHEMATICAE IN DIVINIS UTILITAS. 235

xviii pars diametri Solis; quoniam diameter corporis Mer-
curii est vicesima octava pars diametri Terrae, et diameter
Veneris est! tertia pars diametri Terrae et tertia partis, et
diameter Martis est similis diametro Terrae semel et sexta,
diameter Jovis est aequalis diametro Terrae quater et semis
et xvi vicis unius, et diameter Saturni est aequalis diametro
Terrae quater et semis, quod est 29,250 milliaria. Ex quibus
sequitur quod corpus Mercurii est una pars de 22 millibus
partibus Terrae, et Venus est 39 pars Terrae secundum
Alfraganum, sed secundum Thebit libro dicto est una de 32
partibus Terrae, et Mars est similis Terrae semel et semis et
medietas octavae unius vicis, et Jupiter est aequalis Terrae
nonagesies quinquies et Saturnus est similis Terrae nonagesies
et semel. Et si quis per diametrum Terrae quantitatem dia-
metri cujuslibet in milliaribus et per quantitatem diametri
velit circumferentiam invenire, et per utramque totam super-
ficiem in milliaribus, facile est per praedicta.

De stellis autem fixis 1,022 dat Alfraganus eandem artem. The fixed
Nam tot sunt notae sapientibus de his quae sunt a septentrione stars.
usque ad ultimam, quae apparuit eis in climate tertio. Nam
per instrumenta possunt quantitates istarum certificari. Sed
harum 1,022 sunt sex gradus, et differentiae magnitudinum,
secundum quod Ptolemaeus viii Almagesti, et Thebit in libro
memorato, et Alfraganus et alii sapientes docent. Sunt igitur
sex magnitudines, et prima est major inter alias, et sic per

1 The omission in J.'s edition of the diameter of Venus in terms of the Earth's
diameter has made the subsequent estimates of the size of the planets unin-
telligible. I have restored the reading as given in Tib. In Jul the whole
passage relating to this subject is omitted.

It will be observed that the expression im aspectu is used for the apparent
diameter of the planets in terms of the Sun's apparent diameter. Then follows
the statement of their real diameter in terms of that of the Earth. Throughout
this estimate Bacon follows very closely that of Alfraganus, as given in his
Elementa Astronomica, cap. 22 (ed. Golius, Amsterdam, 1669). Alfraganus
however gives the size of Venus as yy of the Earth. Supposing her diameter as
I to 3j, this would make her cubical dimension yy of the Earth, nearly, and this is
the estimate of Alfraganus ; ‘moles Veneris est pars una de Terrae partibus 37.’

It may be interesting to compare these results with those of modern astronomy,
in which, taking the Earth's diameter as unity, that of the Moon is -27, of Mer-
cury -4, of Venus .97, of Mars -5, of Jupiter 11-5, and of Saturn 4-25. The Sun
is 110, which contrasts strongly with Bacon's estimate of 5.5. But Bacon's
view of the lunar diameter is near the truth.

236 OPERIS MAJORIS PARS QUARTA.

consequens ordinate. 'In prima vero magnitudine sunt xv
stellae fixae, ut sunt Canis et Vultur cadens, et cor Leonis et
hujusmodi, quarum cujusque diameter in aspectu est xx pars
diametri Solis, et cujuslibet istarum diameter est aequalis
diametro Terrae quater et semis. Et ideo quaelibet illarum
est aequalis Terrae centies et septies secundum Alfraganum.
Et ex mensura harum stellarum patet quantitas aliarum. Sunt
ergo in magnitudine secunda xlv stellae, ut sex stellae Ursae
majoris et duae stellae Ursae minoris, et unaquaeque istarum
est aequalis Terrae nonagesies. Et in magnitudine tertia sunt
208, ut aliquae stellae Ursae minoris, secundum Ptolemaeum,
et multae aliae, et harum quaelibet est aequalis Terrae septua-
gesies et bis. Et in quarta magnitudine sunt 474, ut 4 stellae
Ursae minoris et multae aliae, et quaelibet istarum est aequalis
Terrae quinquagesies quater. Et in magnitudine quinta sunt
217 quarum quaelibet est aequalis Terrae trigesies sexies. Et
in magnitudine sexta sunt 62, quarum quaelibet est decies
octies major tota Terra. Deinde sunt stellae aliae infinitae,
quarum quantitas non potest sciri per instrumenta, et tamen
sunt visu notabiles, et ideo habent quantitatem sensibilem
respectu coeli, sicut pars respectu totius. Sed Terra non
habet aliquam quantitatem sensibilem respectu coeli, sicut
probat Ptolemaeus in principio Almagesti, et certum est hoc,
quoniam se habet sicut centrum ad circumferentiam circuli.
Quapropter quaelibet istarum stellarum visu notabilium est
major tota terra, et hoc dicit Alfraganus capitulo iv. Ex his
igitur omnibus, quae dicta sunt de magnitudinibus corporum,
patet quod majus omnibus, exceptis orbibus omnibus praeter
orbem Terrae, est Sol; deinde secundo stellae primae mag-
nitudinis, tertio Jupiter, quarto Saturnus, quinto reliquae
stellae fixae omnes secundum gradus et ordines suos, sexto
Mars, septimo stellae fixae visu notabiles, octava Terra, nono
Venus, decimo Luna, undecimo Mercurius.

(7) Im- Musicalia? vero secundum quod sancti determinant neces-
pore of , This recognition of numerous stars other than those included in the cata-

theology. logue of Hipparchus is noteworthy.
3 This subject is more fully treated in Opus Tertium, chapters 59-64. Besides
music properly so called, the discussion includes gesture, accentuation, aspira-
tion, punctuation, and prosody.

MATHEMATICAE IN DIVINIS UTILITAS. 237

saria sunt theologiae in multis. Nam licet non oportet
propter scientiam scripturae quod habeat theologus usum
cantus et instrumentorum et aliarum rerum musicalium,
tamen debet scire rationem omnium istorum, ut sciat naturas
et proprietates harum rerum et operum, secundum quod
musica speculativa et practica docent. Scriptura enim plena
est vocabulis musicalibus, sicut jubilare, exultare, cantare,
psallere, cythara, cymbala, et hujusmodi diversi generis.
Praeterea continet in se multa genera canticorum tam in novo
quam in veteri testamento. Item multa genera metrorum
continentur in textu sacro Hebraico, quae sancti notant in
expositionibus suis multipliciter. Sed musicae est dare
causas et rationes horum, licet grammaticus doceat, quia
est de his. Praeterea tota pronuntiatio scripturae consistit
penes accentus, longitudines, et brevitates, et penes cola,
commata, periodos; et haec omnia pertinent causaliter ad
musicam, quia horum omnium musicus dicit propter quid,
grammaticus vero quia est tantum. Sic enim auctores philo-
sophiae determinant, et Augustinus in musicalibus de his
determinat. Nam musica alia vertitur circa audibile, alia
circa visibile ut auctores determinant; quae vero est circa
audibilia habet partes duas; una est circa vocem humanam,
alia circa instrumenta. Quae vero est circa vocem humanam
est quadruplex. Nam alia est melica, ut in cantu; alia
metrica, quae considerat naturam et proprietates omnium
carminum et metrorum et pedum; tertia est rhythmica, quae
omnem varietatem proportionum in rhythmis considerat ;
quarta est prosaica, quae accentus et alia praedicta considerat
in sermone prosaico. Nam accentus est quidam cantus; unde
dicitur accentus ab accino, accinis, quia omnes syllabae habeat
suum sonum proprium elevatum aut depressum aut com-
positum, et omnes syllabae unius dictionis adaptantur sive
accantantur uni syllabae supra quam residet sonus principalis.
Et sic longitudo et brevitas et caetera omnia quae in recta
pronuntiatione requiruntur ad musicam reducuntur, et de eis
determinant auctores musicae, sicut patet apud Censorinum
de accentibus et apud Martianum et apud multos. Et haec
patent per Isidorum et Cassiodorum in musicalibus. Et

Distinction
of mathe-
matics
from
magic.

238 OPERIS MAJORIS PARS QUARTA.

Augustinus reducit metra et pedes et hujusmodi ad musicalia.
Horum igitur omnium potestatem deberet theologus perfectus
habere, quia in sensu literali et spirituali istorum naturae et
proprietates requiruntur, ut sancti multipliciter determinant.
Musica vero in instrumentis determinat compositionem in-
strumentorum et usum. Et ideo cum scriptura sit plena
hujusmodi instrumentis, oportet theologum perfectum scire
saltem in universali compositiones instrumentorum, et scire
quomodo usus eorum habeat fieri propter sensus mysticos
infinitos praeter literales. Musica vero consistens circa visibile
necessaria est; et quod sit talis, patet ex libro de ortu
scientiarum. Nam quicquid potest conformari sono motibus
consimilibus et figurationibus competentibus, ut fiat delectatio
plena non solum audiendo sed videndo, pertinet ad musicam.
Et ideo exultationes et omnes flexus corporum ad gestum
reducuntur, qui est una radix musicae, quoniam haec con-
formatur sono motibus consimilibus et configurationibus com-
petentibus, ut vult auctor libri praefati. Et ideo Aristoteles
dicit septimo Metaphysicae quod ars saltandi non vadit in
finem suum sine alia arte, et hoe est sine altera specie musicae
cui ars saltandi configuratur. Exultationes igitur et caeteri
flexus corporum, quos et quas exercuerunt Maria soror
Moysi, et Delbora et aliae cantatrices, et David et caeteri
cantores de quibus scriptura multipliciter tractat, debent
sciri a theologis, ut omnes proprietates eorum sciant ex-
primere, quatenus sensus spirituales angelicae devotionis
eructent. Et quamvis sic appareat satis ut nunc oportet
quod istae scientiae sint necessariae respectu theologiae et
philosophiae, tamen longe major est earum utilitas con-
sideranda per alias vias magnificas quae pertinent ad sapien-
tiam non solum absolute, sed ut ipsa debet ecclesiam Dei
regere, et caetera tria aliquotiens tacta procurare, ut inferius
tangetur.

Manifestato quomodo mathematica necessaria est sapien-
tiae tam divinae quam humanae, adhuc necesse est ad certi-
ficationem praecedentium, ut evacuentur quaedam cavilla-
tiones in contrarium et exponantur quaedam dicta sanctorum,

JUDICIA ASTRONOMIAE. 239

ut omnis dubitatio tollatur circa mathematicae utilitatem.
Et illud in quo maxime percutitur mathematica est propter
judicia astronomiae. Quoniam igitur contentio multorum
ignorantium philosophiae potestatem et maximam utilitatem
theologiae, tam relate quam absolute reprobantium mathe-
maticorum considerationes, impedit studium sapientiae et
laedit gravissime in hac parte; ideo volo in praesenti veri-
ficare intentionem eorum, et evacuare infamiam verae mathe-
maticae. "Theologi igitur multa invenerunt a sanctis effusa
contra mathematicos, et aliqui eorum propter ignorantiam
mathematicae verae et mathematicae falsae nesciunt dis-
tinguere veram a falsa, et ideo tanquam auctoritate sanctorum
culpant veram cum falsa. Vocabulum enim verae mathe-
maticae scribi per 7 aspiratum, et ab hoc nomine mathests
media correpta !, quod scientiam designat, derivari a multis
refertur auctoribus, et certum est ex Graeco; quia matheo
verbum idem est quod disco, et s»a/Aefes est discipulus, et
mathests disciplina. Unde mathematica est disciplinalis
scientia et doctrinalis, sicut Cassiodorus dixit superius. Sed
vocabulum falsae mathematicae sine aspiratione scribi as-
seritur ab eisdem auctoribus et a mathesi media producta,
quod divinationem notat, descendere, vel quod certius est,
a mantos vel a mantia, quae sunt idem quod divinatio, sicut
Hieronymus dicit in originali ix Isaiae. Quicquid vero sit

! Bacon corrected this error in his later writings. Of the true mathematica
he says, * Haec scribitur cum aspiratione et dicitur a mathesis, quae est disciplina,
quae habet mediam productam, ut in mea grammatica Graeca exposui; licet
totum vulgus Latinorum credat quod media sit correpta, secundum quod fiunt
versus falsi, Scire facit Mathesis, sed divinare Mathesis.'

This passage is from the unpublished MSS. on Mathematics (Brit. Mus. Sloane,
MSS. 2156, fol. 72, c), a section of the encyclopaedic work projected by Bacon, but
in all probability never completed. A similar passage will be found in his com-
mentaries on the apocryphal Secretum Secretorum (Bodleian, Tanner MSS.,
116). ‘Mantia vero Graece est divinatio Latine qua magia ac mathematici
utuntur, secundum quod haec nomina, mathematica et mathematicus, derivantur
a matesi media correpta, quae matesis est magica imponens necessitatem rebus
contingentibus et libero arbitrio. Contra quam et contra matematicos ab ea
dictos egregie beati Augustinus et Gregorius in Omeliis de Epiphania disputant
et alibi . . . ut Aristoteles, Avicenna, Ptolemaeus et omnes alii veraciter philoso-
phantes. Sed tamen hi veri judicatores difüntur mathematici a mathesi media
producta quae et per aspirationem scribitur."

240 OPERIS MAJORIS PARS QUARTA.

de hac scriptura et derivatione, tamen falsa mathematica est
ars magica. Nam numerantur quinque species artis magicae,
scilicet mantice, mathematica, maleficium, praestigium, sorti-
legium.

Mathematica ergo est secunda pars artis magicae. Haec
sibi usurpat considerationem coelestium characteribus, car-
minibus, conjurationibus, sacrificiis superstitionis, et fraudibus
variis deformatam. Et ponit per virtutem constellationum
omnia de necessitate contingere, nihil ad utrumlibet, nihil
a casu nec fortuna, nihil a consilio, de bonitate tamen essentiae,
et in adjutorium constellationum efficacius ordinavit singulis
constellationibus propria figmenta characterum et aliorum
praedictorum. Et haec expresse asseruntur in libris magicis.
Unde haec scientia ista omnia ponit per coelum de necessitate
contingere, et praesumit per hanc necessitatem infallibiliter
de omnibus judicare futuris. Sed ista mathematica damnata
est non solum a sanctis, sed a philosophis, ut dicit Isidorus in
tractatu astrologiae, asserens unam partem astronomiae esse
superstitiosam, scilicet quae est magica, et dicitur mathe-
matica falsidica. Unde Aristoteles et Plato, testante Isidoro,
eam damnaverunt ; et Plinius! per diversa loca Naturalis
Historiae eam saepius percutiens propter errores quos haec
fantasia scripsit in naturalibus et medicinalibus, tandem eam
nimis abhorrens xxx libro originem illius aperit, et quo-
modo totum mundum defoedavit evidenter ostendit. Tullius
etiam in libro Divinationum magis in particulari ad ejus
malitiam descendens ostendit quod cultum divinum destruxit,
rempublicam violavit, et medicinam infecit et naturalem
philosophiam et omnes bonas artes subvertit. Ptolemaeus
etiam et Aristoteles et Avicenna et Messehalac et Haly et

! The introduction to the thirtieth book of Pliny's Natural History discusses
the origin of magic. It arose, he says, at a very remote period of history, from
the threefold root of medicine, religion, and mathematic. Every country was
infested by it, but specially the East. Zoroaster may be looked upon as its
founder. Osthanes introduced it into Greece at the time of the Persian war,
when it spread like wild-fire; although Greek philosophers in thc course of
their travels had already looked into it. Pliny proceeds to trace its progress in
Italy, Gaul, and Britain. For Cicero's accouut and criticism of Chaldaean astro-
logy see De Divinatione, lib. ii. cap. 42-47.

JUDICIA ASTRONOMIAE. 241

Albumazar, qui prae aliis majori auctoritate de his locuti
sunt, necessitatem absolutam in rebus inferioribus non ponunt
per virtutem coeli, quia liberum arbitrium non subjacet rebus
naturalibus, nec aestimant judicium debere fieri infallibile,
immo nec aliquam libero arbitrio ponunt necessitatem, cum
nec rebus naturalibus eam ascribant, ut patebit. Et ideo
philosophi universaliter damnant istorum falsorum mathe-
maticorum insanias.

Nec solum damnant quantum ad principale, scilicet propter Incanta-
errorem quem habent de coelestibus, sed quia mathematici tions and
isti daemones advocant in adjutorium coelestium disposi- of spirits.
tionum per conjurationes et sacrificia, quod est omnino ne-
fandum, atque nihilominus maculant suas considerationes in
coelestibus per circulos et figuras et characteres vanissimos
et carmina stultissima, et orationes irrationabiles in quibus
confidunt. Praeterea fraudes operum adjungunt, scilicet per
consensum, per tenebras, per instrumenta sophistica, per sub-
tilitatem motionis manualis, in quibus sciunt illusionem esse,
et multa stultis miranda faciunt per haec in quibus virtus
coeli nihil operatur, et ideo sibimetipsis contradicentes, quod
coelo attribuunt coram aliis, apud seipsos sciunt non habere
veritatem. Similiter licet alias in quibusdam conjurationibus
et sacrificiis et carminibus et characteribus et figuris variis
confidunt tanquam cooperantibus constellationi secundum
eorum judicium, tamen pluries fraudulenter ista componunt
secundum species fraudis predictas, et coram sibi credentibus
ascribunt plurima constellationi, respectu quorum ipsa nullam
habet potestatem. Et hoc eos non latet. Propter igitur has
stultitias mathematicae sophisticae philosophi eam damna-
verunt, et sancti ac viri catholici haec percipientes eam simul
cum philosophis reprobaverunt.

Sed praecipua ratio sanctorum fuit ad hoc, quod tales Christian
mathematici impediverunt a principio ingressum fidei in hunc mirae
mundum, quia non solum imbuti hac fantasia erraverunt in to magic.
fide et finxerunt mores suos in coelestibus, tanquam per
coelestia et caetera dicta de necessitate fierent iracundi vel
mansueti, casti vel luxuriosi, et sic de aliis; sed opera
miraculosa fidem Christi probantia ascripserunt isti mathe-

VOL. I. R

True
mathe-
maticians
have
always

242 OPERIS MAJORIS PARS QUARTA.

maticae, dicentes, Christianos esse mathematicos et magos
populum seducentes. Sicut enim ipsi per hanc daemoniacam
calliditatem potuerunt multa coram populo rudi facere per
quae detinebant eos ad errores et dominabantur eis, sic
imposuerunt apostolis et martyribus et .caeteris praedi-
catoribus fidei quod non ex parte Dei fecerunt vera
miracula, sed per artem magicam qua ipsimet usi sunt. Et
ideo hanc mathematicam et ejus professores sancti et ecclesia
penitus damnaverunt.

Sed veri mathematici, quos in hac parte vocamus astrono-
mos et astrologos !, quia indifferenter a Ptolemaeo et Avicenna
et aliis pluribus sic vocantur, non redarguuntur de sacrificiis

condemned COnjurationibus carminibus characteribus, ut etiam plebs

these
errors.

Proofs
from Hali,

studentium non ignorat, sed solum super judicio infallibili et
rerum necessario eventu notantur, Non autem possumus
eorum sententiam deprehendere nisi ex libris eorum testimonia
propria eruamus, ut sic vel errantes damnemus ex propriis
verbis, vel excusatos a dentibus vulgi imperiti liberos extra-
hamus. Quoniam igitur maxime imponitur eis error judicii,
tamquam infallibiliter velint cum divina certitudine contendere,
ut plebs cis imponit, adducantur philosophi nobiliores,
scilicet Aristoteles, Avicenna, Ptolemaeus, Hali commentator
ejus et Messehalac, Albumazar, quibus magis incumbit hoc
onus. In universali igitur considerando quid secundum
philosophos tenendum sit hic, Ptolemaeus in principio Centi-
logii pronuntiat dicens, * Astronomus non debet dicere rem
specialiter sed universaliter, ut qui eminus videt aliquam rem,’
et addit, : judicia quae trado tibi sunt inter necessarium et
impossibile."

Et dicit Hali super hunc locum, ‘ Hoc ideo dixit, quia haec
scientia non est nisi per probationem et opinionem ; quia
materia ad quam pertinet opus totum stellarum convertibilis

4 [n his mathematical treatise, Bacon speaks of astrology as the speculative
side, astronomy as the practical side of the science. *Astrologia componitur ex
hoc nomine Astron, quod est stella, et hoc nomine Logos, quod est verbum vel
ratio vel sermo, quia est sermo de stellis. Astronomia vero dicitur lex stellarum,
et Nomos est lex. Unde quia lex universaliter sonat in practicam, ut in morali
philosophia lex est ipsa practica, ita similiter Astronomia est practica Astrologiae."
(Sloane MS. 2156, fol. 82, c.)

JUDICIA ASTRONOMIAE. 243

est ad unum et ad aliud. Propter quod capitulo lix Centi-
logii secundum unam translationem dicit, ‘cum interrogatus
fueris de absente, non judices de eo mortem, donec removeas
ab eo ebrietatem ; nec vulnus, donec tollas ab eo sanguinis
minutionem ; nec substantiam adquisitam, donec pecuniam
sibi commissam removeas; est enim in omnibus idem
judicium. Et dicit Hali, ‘ qui tractat de judiciis, judicat per
formas quae sunt prope veritatem, quia non invenitur in forti-
tudine judiciorum partitio vel differentia inter sopitum et
mortuum, et inter vulneratum et minutum, nec inter illum
cui commissa est pecunia et illum qui adquisivit': et addit
exemplum, ‘quod patre suo se abscondente cum aliis a facie
imperatoris, astrologus visitans eum quotidie praecepit poni
concham maximam aeneam plenam aqua, supra quam pone-
retur scabellum, consuluitque ei ut desuper sederet in majori
parte diei; et hoc ideo praecepit, ut faceret errare astrologos
imperatoris in existentia absconditorum. — Dixerunt enim
quod esset in medio maris propter similitudinem aquae con-
chae, cui superinsederat. Distinguere enim inter hoc et illud
non poterant propter continentis et contenti similitudinem.
Aqua enim undique continebatur, et vasis concavitas alvei
marini concavitatem expressit."

Similiter Ptolemaeus in libro de Dispositione Sphaerae From
dicit, ‘quod judicationes astronomi de rebus inferioribus non Fem.
sunt inventae ex scientia artificiali, quare sunt fines earum
necessariae, sed sunt ex eis quae sunt secundum plurimum.'
Et iterum dicit, ‘astronomi affirmaverunt illud non secundum
viam artificialem, nec secundum ingenium determinatum, sed
per convenientiam cadentem super rem propinquiorem.’
Et tertio dicit, * quod manifestum est quod illud quod affir-
mant non est affirmatum nisi secundum rem plurimam, non
secundum viam artificialem et non est res faciens illud
necessarium. Propter illud ergo cadet multotiens error in
eis, ut affirmat. Et Ptolemaeus in primo capitulo! quadri-

! The works entitled Cextiloginm and Quadripartstum, to which frequent
reference is made in the Opus Mayus, are both of them astrological works.
The Greek text of both was printed in Nuremberg in 1535; the title of the first
being KAavdiov IIroAepaíov BiBXiov 5 xapwés, of the second, KAaviiov IIroA«paíou

R2

244 OPERIS MAJORIS PARS QUARTA.

partiti dicit, *hujus autem tam excellentis artis occulta
profunditas ejusque tam augusta et incomprehensibilis exer-
citatio, ut ab humano ingenio eam impossibile sit penitus
amplecti, ex ineffabili subtilitate, ejusque admiranda quasi
quadam divinitate videtur contingere. Longe enim ab
humano sensu remota est, et corpoream transcendens naturam
quasi ultra hominem eminus transcenditur. ^ Et tertio
capitulo dicit *quod ex nimia ipsius artis profunditate
quicunque error incidit, Quapropter secundum Ptolemaeum,
cui nunc temporis maxime ascribitur ratio judicandi, mani-
festum est quod astrologus non potest dare plenam certi-
tudinem suorum judiciorum, praecipue in singulis. Quod
etiam non solum ex his liquidum est, sed ex aliis ejus
sermonibus, quibus licet innuat possibilitatem judicandi de
multis cum rationabili certitudine, tamen tantam difficultatem
simpliciter arti inesse pronuntiat, ut facile pateat ipsum penitus
definire, quod non debet astronomus de sufficienti certitudine
in singulis gloriari. Unde quadripartiti primo capitulo dicit,
* quamvis enim res haec in tantum sit ardua, ut nullatenus ad
finem omnino perduci valeat, non tamen videtur conveniens
desistendum, sed potius ea quae possibilitati nostrae non
repugnant exponere dignum judicavimus. Et post pauca
intendit, ‘quod talis artis est difficilis et laboriosa assecutio,
ut absque diuturna exercitatione penitusque secularibus libera
po8npoructjs TerpdBiBAor ovrrá£evs. The Latin translation used by Bacon was
probably from the Arabic; but, so far as I have read the Greek original, its
meaning is preserved in the translation with fair accuracy. The passage here
referred to begins, ob yap éori Üvrarór tov imorüjuova Tas nepucds. l&éas T&v
wpa^rpárom dvayyciAra, Go ep o5 4 ala09ais Béxerar Ti pepuciyy l8éay ToU alabnrot,

. » pévot ydp ol tvOvorGrres wpoAé-yovat xal ra pepuxd.

Ptolemy (supposing him to be the author of those treatises) takes it for
granted that there is a force diffused from the eternal Aether upon the elements,
and through them on the earth and the living things contained in it, “Or pir
(he says in the opening of the Tefrabiblow) &aBíSora, wat duxveiral vis Bóvajus
dsó Tís al0epáSovs xal alBíow Qéceos . . . wücw dy ivapylíoraror xai &' bAlyor
gavein, We should not reject astrology, he observes, on account of the numerous
errors made in particular judgements, any more than we should reject the art
of navigation because sailors often blunder. Some of the mistakes are due
to the inherent difficulty of the subject, some to the imperfect knowledge
and skill of those who teach it. In any case the study of astronomical con-

junctions rests upon certain facts, even though the inferences from the facts
be erroneous.

*

JUDICIA ASTRONOMIAE. 245

et infructuosis expedita curis ad hanc nequaquam valeat quis
aspirare. Et quia liberis a curis aliis et studiosis est bona
spes proficiendi in hac scientia, ideo in secundo capitulo dicit,
'nobis quidem minime videtur consentaneum, si aliunde
error inciderit, artem a nobis penitus excludere. Et adducit
exemplum, dicens, * Nautae enim maris scopulos minus
providentes, si quo decepti errore naufragium patiantur,
restitutis navium armamentis de pristina non deficientes
salute alacri mente spe confirmatione naves conscendunt.
Ad hunc etiam modum nos hanc astrorum scientiam firmam
et certam et in sua veritate immobiliter persistentem, quan-
tum possibilitas humani permittit ingenii, assequi studeamus,
ut in benevolentiam tam studentium quam aliorum reducere
conemur, quatenus artis ipsius observata dignitate, ea ducente,
quae futura sunt praevideant, quae autem sua impossibilitate
ars ipsa prohibet relinquantur Et tertio vult capitulo,
* quamvis quicunque hic error incidit negligentia praetermitti
aut oblivione deleri inconveniens penitus reputandum est.’
Et post pauca, ‘cum autem evidentissime constat. hanc
futurorum praenotionem non cum errore teneri, nec omnes
illius species erroribus implicari, quid demum ex hac effi-
cacia, quibus etiam modis quae innovantur repelli valeant,
diligentius restat aperire. Sin autem singula tradere non
valeat, quantum tamen possibilitas contulit exhibere non
fugiat. Quod si minimum id reperietur, minoris profectus
ut in brevius redigatur non censemus. Et ponit exemplum,
*licet enim physica non omni homini sit salutis occasio, cum
sit tamen quorundam, appetenda sua utilitate videtur.'

Ex quibus verbis et consimilibus manifestum est, quod
de intentione Ptolemaei non est quod astrologus det in
particulari certum judicium et sufficiens in singulis; sed
in universali, et medium inter necessarium et impossibile, et
non in omnibus potest determinatum dare judicium. Propter
quod Avicenna, qui opera Ptolemaei complevit, ut ipsemet From Avi-
recitat in prologo libri Sufficientiae, manifestat in decimo cepa and
Metaphysicae, quod astrologus non potest certificare in
omnibus nec debet, propter instabilitatem materiae generabilis
et corruptibilis, quae non in omnibus semper obedit virtuti

What the
fathers con-
demn is
the com-
pulsion
attributed
to stellar
influence.

246 OPERIS MAJORIS PARS QUARTA.

coelesti, ut dicit Messehalac ponens exemplum de magnete,
quia virtus ejus non habet potestatem super ferrum nisi in
debita distantia et in aliis conditionibus quae exiguntur ad
attractionem fuerit adaptatum.

Et iterum sciunt, quod ordinatio divina potest omnia
mutare secundum sui voluntatem, et propter hoc adjungunt
semper in suis sententiis in fine hoc verbum, quod ‘sic erit, si
Deus voluerit. Caeterum ipsimet sciunt et testantur, quod
anima rationalis potest multum mutare et impedire de
effectibus stellarum, ut de infirmitatibus, et de pestilentiis
frigoris et caloris, et fame, et multis, secundum quod
Ptolemaeus in Centilogio dicit et docet. Et Hali exponit
ipsum; et Isaac in libro febrium evidenter ostendit; et
Aristoteles in libro Secretorum confirmat et declarat hoc
idem.. Nam quando praeviderint haec mala, possunt prae-
parare remedia. Unde dicit Isaac, quod ‘non accidit malum
homini, nisi sit detentus ignorantia scientiae coelestis, et ponit
exemplum in pestilentiis et in infirmitatibus et in voluntariis,
in quibus haec scientia potest dare remedia, si complete
sciretur. Ex his igitur manifestum est, quod philosophi non
ponunt eventum rerum inevitabilem per coelestia in omnibus,
nec infallibile judicium in singulis, sed secundum possibili-
tatem hujus scientiae ; praecipue cum etiam addunt quod alia
scientia, quae experimentalis vocatur, certius adhuc judicat
quam astronomia vulgata. Ita docet Ptolemaeus in libro de
Dispositione Sphaerae, et patet de hac in sequentibus.

His igitur et hujusmodi diligenter consideratis, manifestum
est quod veri mathematici et astronomi seu astrologi, qui
philosophi sunt, non ponunt necessitatem et infallibile judicium
in rebus contingentibus de futuro. Et ideo quicunque eis
haec attribuunt, manifeste de ignorantia philosophiae con-
vincuntur, et veritatem reprobant quam ignorant. Unde in
duobus peccant, videlicet quod ea quae ignorant tractant, et
nihilominus in veritatem blasphemant. Sed illi qui sic vera
tuentur ut falsa reprobant condemnant mathematicos magicos,
qui non philosophantur sed tam philosophiae quam fidei
contradicunt, sicut a principio tactum est. Et ideo sancti
contra hos locuti sunt, et non contra veros mathematicos.

JUDICIA ASTRONOMIAE. 247

Quod manifestum est per obviationes sanctorum. Nihil enim
reprobant nisi quod per stellas necessitas rerum contingentium
et maxime morum et actuum humanorum fiat, ac infallibile in
omnibus judicium. Sed soli mathematici magici haec ponunt,
et veri mathematici non sic dicunt. Quapropter quicquid
Basilius in Hexaemeron, et Ambrosius in Hexaemeron, et
Augustinus et Gregorius in homilia Epiphaniae et Augustinus
super Psalmos Ixi et xci,et super Joannem et multis locis ipse
et alii doctores dicunt contra mathematicos, totum est directe
contra eos qui fingunt necessitatem imponi eis quae sunt ad
utrumlibet, et praecipue eis quae a libero arbitrio proficis-
cuntur, qui soli sunt mathematici falsidici vel fraudulenti,
superstitiosi non philosophi, ut manifestum est. Et ideo nimis
errant qui suas insanias in veros mathematicos nituntur sanc-
torum auctoritate tueri, et falso abutentes dictis sanctorum
damnare veritatem praesumunt. Unde suas opiniones licet
erroneas statuere moliuntur, quas fingunt ex ignorantia mathe-
maticae verae et falsae. Et cum nullam rationem afferre
possunt eo quod contra omnem rationem et philosophiae
virtutem est quod contra mathematicos veros dicunt, rapiunt
et furantur auctoritates sanctorum, quae nihil faciunt ad pro-
positum, ut manifestum est inquirenti.

Et adhuc considerandum est, quod si consideremus dicta They ao
sanctorum, nos inveniemus manifeste quod non solum non AO deny
reprobant mathematicos veros, sed approbant in futurorum logythrows
cognitione. Quoniam Augustinus dicit libro secundo de Doc- li£ht on
trina Christiana, quod mathematica habet futurorum regulares events.
conjecturas, non suspiciosas et ominosas, sed rectas et certas
tam de futuris quam praesentibus et praeteritis. Et Cassio-
dorus concordat, ut prius dictum est. Et ad Januarium
ostendit multipliciter, quomodo futura possunt cognosci per
coelestia. Et Basilius in Hexaemeron similiter declarat hoc
multis modis ; unde certissimum judicium in aliquibus esse
declarat. Et Ambrosius in Hexaemeron consentit ; et Isidorus
in suo opere de astronomia. Et sancti confirmant quod dicunt
per evangelium, *de coelo rubicundo in sero et mane, et
iterum, *erunt signa in sole et luna, &c. Et in Joele, ‘sol
convertetur in tenebras, &c. Non igitur est mathematica

248 OPERIS MAJORIS PARS QUARTA.

infamis ex futurorum cognitione quam fideliter assignat; licet
a principio sancti minus usi sunt et minus commendaverunt
eam, propter errorem falsae mathematicae, cui nomine et
quadam consideratione coelestium respectu futurorum vera
mathematica familiaris est et conveniens, sicut determinat
Augustinus in libro de Doctrina Christiana.
But sub- Sed postquam in ecclesia fuit evacuata falsitas magicae
theologians Mathematicae, venit in usum catholicorum doctorum con-
have con- sideratio mathematicae verae, et duravit usque ad adventum
true mathe: quorundam theologorum, qui philosophiae potestatem et
maticswith artis magicae fallacias ignoraverunt, et ob hoc eam in
lectionibus praedicationibus et collationibus publicis et pri-
vatis damnantes, primo in maximam philosophiae destruc-
tionem, deinde in laesionem theologicae majestatis, et in
damna ecclesiae et totius reipublicae fidelium et infidelium
conversionis, ut prius pro magna parte ostensum est, et
residuum postea ostendetur; quia ignorata mathematica,
tota philosophiae potestas ignorabitur. Et si veritas philo-
sophiae laedatur, damnum infertur theologiae, cujus est
uti potestate philosophiae, non solum absolute, sed prout
ordinat ecclesiam, dirigit rempublicam fidelium, et juvat ad
infidelium conversionem praedestinatorum et reprobationem
praescitorum. Sed non solum errant in hoc quod futurorum
cognitionem per mathematicam fiendam imprudenter damnant,
sed quia pro parte, quam licet ex sua abhorrent ignorantia,
totum reprobant. Quamvis enim in partibus philosophiae sint
plurima inutilia et minus bene tacta et aliqua erronea, nihilo-
minus tamen tota philosophia a nullo damnatur, nec debet nec
potest. Quapropter cum in mathematicae partibus omnibus
aliis a judiciaria omnia utilia proponantur respectu theologiae
et ecclesiae ac reipublicae et conversionis infidelium aut repro-
bationis et totius philosophiae, et nihil reprobatum determinatur
etiam in illa parte cui judicium ascribitur, multa etiam praeter
artem judicandi praeclara de proprietatibus coelestium rerum
et secundis stellarum et caeteris rebus hujus mundi tanguntur,
manifestum est eos omnino errare, qui pro una parte, quam
falso damnant, totum residuum quod maximas habet utilitates
et in nullo habet calumniam ausi sunt reprobare. Et iterum

JUDICIA ASTRONOMIAE. 249

licet pars judiciaria de humanis rebus esset culpanda, tamen
alia pars de naturalibus et coelestibus calumniam fidei non
importat.

Sed in rebus humanis veri mathematici non praesumunt Astrology
certificare, sed considerant quomodo per coelum alteratur Drediet.
corpus, et alterato corpore excitatur anima nunc ad actus action: it

privatos nunc publicos, salva tamen in omnibus arbitrii liber- dicites a
tate. Quamvis enim anima rationalis non cogitur ad actus motive.
suos, tamen fortiter induci potest et excitari ut gratis velit ea

ad quae virtus coelestis inclinat, sicut nos videmus homines per
societatem consilia timorem et amorem et hujusmodi multum
mutare de proposito, et gratis velle ea quae prius non volebant

licet non cogantur, sicut ille qui spe salutis projicit merces in

mare carissimas. Caeterum nos videmus quod species seu
virtutes rerum inferiorum immutantes sensus nostros, etiam
species visibilium et audibilium quae debiliter immutant cor-

pus, ita fortiter excitant homines ad volendum quae prius non
curabant, quod aliquando nec mortem nec infamiam nec
timorem aestimant dummodo suas compleant voluntates, sicut

sunt illi qui vident et audiunt suos inimicos eis occurrere, et
feruntur omni casu contingente ut se vindicent. Similiter
voluptuosi, opportunitate accepta complendi suas delicias circa

res visas et auditas, quasi bruta animalia moventur contra
judicium rationis, gratis eligentes ea ad quae excitantur.

Sed longe magis possunt virtutes coelorum et species eorum Tempera-
et stellarum fortes imprimere in corpus et organa, quibus ment e by
vehementer alteratis excitabitur homo fortiter ad actus de stellar

. . . . . "n . influence.
quibus non curavit prius, salvo suae libertatis arbitrio ; quoniam
virtutes coelorum fortiores sunt quam istorum inferiorum
visibilium et audibilium et multorum aliorum sensibilium, et
possunt mutare substantiam non solum accidentia, et cor-
rumpere et destruere res omnes inferiores ; quoniam secundum
allationem solis sub obliquo circulo accidunt generatio et
corruptio in rebus, ut Aristoteles dicit. Et non solum haec
allatio solis absolute considerata, sed cum virtutibus aliorum
planetarum et stellarum ; et ideo valida est alteratio corporum
nostrorum per virtutes coelestes, et per consequens animus
- fortiter excitatur ad actus suos licet non cogatur, et secundum

National
Character

moulded by

climate.

250 OPERIS MAJORIS PARS QUARTA.

hoc currit judicium astronomi, et non per infallibilitatem et
necessitatem. Et astronomus in hoc multum juvatur, quod
videt homines in actibus suis sequi multum suas complexiones
quas habent, ut cholericus movetur de facili ad iram, nec
potest refraenare primos motus omnes, et sic de aliis, secundum
quod homines diversificantur in complexionibus. Et ideo
astronomus, cum videt homines sequi suas complexionés, quae
oriuntur a coelesti operatione, sicut et tota generatio, non est
mirum si se extendat ad considerationem actuum humanorum.

Caeterum ipse videt manifeste, quod secundum diversitatem
habitantium sub diversis cocli parallelis variantur mores, sicut
habitantes versus polum, ut Scythae, alios habent mores quam
habitantes versus meridiem, sicut Aethiopes ; et alios ab his
habent illi, qui in quarto climate ; immo secundum diversitatem
cujuslibet climatis et etiam partium climatis variantur mores
habitantium, ut in climate scilicet septimo Picardos, Gallicos, et
Normannos, et Flamingos, et Anglicos, videmus manifeste in
moribus discrepare, cum tamen sint continui ad invicem et
propinqui. Hoc autem non est ex ipsis hominibus a parte
diversitatis animae rationalis, sed propter complexiones cor-
porum innatas a natura coeli, sub cujus parallelis diversis et
stellis situantur, et secundum diversitatem situs eorum respectu
planetarum. Et non solum est haec diversitas secundum
latitudinem regionum ab aequinoctiali circulo versus polum,
sicut nunc tactum est, sed secundum longitudinem, licet
causae sint occultiores. Per experientiam enim videmus,
quod sub eodem parallelo variantur regiones, secundum quod
magis ab occidente vel oriente distant, et non solum ipsae
regiones sed partes regionum. Et non potest in terra nec in
hominibus inveniri causa principalis hujus rei, sed in coelo
requiritur secundum omnes sapientes ; unde, sicut prius dictum
cst, ad omne punctum terrae incidit conus unius pyramidis
virtuosáe a toto coelo. Et coni isti sunt diversae in natura,
et pyramides similiter, quia diversas habent bases propter
diversitates horizontum, quoniam quilibet punctus terrae est
centrum proprii horizontis. Et ideo oportet omnium rerum
diversitatem magnam ex hac causa oriri, etiam quantumcunque
propinqui sunt, ut gemelli in eodem utero; et sic de omnibus,

JUDICIA ASTRONOMIAE. 251

prout videmus quod a duobus punctis terrae proximis oriuntur
herbae diversae secundum speciem. Et hic sumit astronomus
fundamenta sui judicii, et merito, quia diversitas plena rerum
per coelum sic invenitur.

Quapropter potest astronomus peritus non solum in natura- Predictions
libus sed in humanis rebus multa considerare de praesenti et *5 °° £om-

munitics
futuro et praeterito, et ideo saltem super regna et civitates more easy

potest judicare per coelestia et secunda coelestium quae per te ttvidas ts.
virtutes speciales coelorum renovantur, ut sunt cometae et
hujusmodi, quia facilius judicium est super communitate quam
super singulari persona. Nam judicium communitatis est
judicium universale, et astronomus potest bene in judicia
universalia. Et quia ad mores et consuetudines cujuslibet
civitatis famosae tota provincia circumjacens inclinatur, tum
propter refugium ad eam et communicationem negotiorum
vitae, tum propter potentiam civitatum super loca vicina ; (et
similiter est de regno potentiori respectu regnorum circum-
jacentium,) tum propter communicationem, tum propter violen-
tiam ; prudens astrologus potest multa considerare utiliter in
hac parte super moribus et legibus et sectis et guerris et pace
et hujusmodi, quae pertinent ad rempublicam civitatum, pro-
vinciarum, et regnorum, quamvis difficultatem recipiat majorem
in actibus singularium personarum judicandis.

Et si velit considerare diligenter et sine errore horas con- But even
ceptionum et nativitatem singularium personarum, ut sciatur Wt in-

dividuals
dominium coelestis virtutis ad horas illas, et diligenter con- bodily

sideret quando ad eas dispositiones venient coelestia secun- may be
dum singulas partes aetatis cujuslibet, potest de omnibus forecast.
naturalibus, sicut de infirmitatibus et sanitate et hujus-
modi judicare sufficienter, quandocunque debent occidere et
qualiter terminari, secundum quod auctores non solum
astronomiae sed medicinae, ut Hippocrates, Galenus, Hali,
Isaac, et omnes auctores determinant. Sed medici hujus
temporis pauci sciunt astronomiam et ideo nec auctores suos
multi intelligunt nec possunt intelligere, et ideo negligunt
meliorem partem medicinae. Sed de his longus sermo fieri
potest et utilis, cum fuerit opportunum. Et cum secundum
complexiones infirmitates et sanitates varientur voluntates

‘The horo-
scope of
the ruler
throws
light on the
future of
his realm.

252 OPERIS MAJORIS PARS QUARTA.

hominum et desideria et considerationes, licet non cogantur
sed fortiter inducantur, ut manifestum est, tunc prudens
astronomus potest de actibus moralibus singularis personae
prudenter judicare, salva tamen omnibus arbitrii libertate,
et poterit in multis habere judicium certum secundum pos-
sibilitatem materiae quam tractat. Nam quia ista est con-
tingens et non necessaria, non potest dicere quod de necessitate
contingent haec vel illa, potest tamen dicere jn multis quod
contingent, et quod veritas est de futuro, licet non necessaria.
Aliud enim est esse verum, et aliud necessario verificari. Et
hoc est judicium medium inter necessarium et impossibile.
Et in quibus non potest habere hujusmodi judicium, habebit
de facili judicium universale, aut medium inter universale et
particulare; per judicium tamen universale et secundum quod
possibile est de persona publica, ut principe et consiliario
principis in civitate vel regione potest saepius habere judicium
particulare de factis reipublicae; quia, ut dictum est, facilius
est, judicare de communitate quam de singulari persona, et
secundum judicium principis regulantur civitates et regna ;
quod enim principi placet, legis habet vigorem.

Et ideo super negotiis civitatum famosarum et provin-
ciarum et regnorum potest multum astronomus, dummodo
sciat bene dominium coeli in conceptione et nativitate principis,
et bene sciat quod complexio variatur per hoc, et qualiter ad
mores inclinatur juxta proprietatem complexionis. Et tunc
notet quando constellatio veniet quae stimulet complexionem
et fortificet ut stimuletur et excitetur animus ad actus con-
similes ; et similiter quando in contrarium mutatur complexio
per contrarium coeli dispositionem, ut ad contraria excitetur
animus principis. Secundum enim hujusmodi variationes
constellationum et complexionum et voluntatem principum
et praelatorum oriuntur in populo auctoritate superiori inno-
vationes consuetudinum et mutationes legum et morum.
Deinde de facili oriuntur aliquando discordiae et dissensiones
ad quas sequuntur bella, vel aliquando propter legum hones-
tatem et utilitatem oritur concordia civium et aliorum, et fit
pax. Et ideo astronomus peritus potest de facili judicare de
hujusmodi negotiis communibus civitatum et regionum, quia

JUDICIA ASTRONOMIAE. 253

non solum per vias proprias eis habeat unde procedat, sed
per conditiones personarum, quae principantur. Et similiter
per proprietates earum personarum quae principibus et prae-
latis assistunt, et quorum consiliis innituntur, quia principes
mali ducuntur ad bona reipublicae per bonos consiliarios, et
principes boni pervertuntur per malos consiliarios. Si igitur
ex constellatione nativitatis et conceptionis complexio alicujus
principis, vel alterius cui innititur, inveniatur disposita ad
perversitatem morum et discordias et guerras, et astronomus
simul cum hoc videat quod trahunt hujusmodi in consuetu-
dinem et fortius excitantur quando constellatio consimilis
accidit, potest rationabiliter judicare de infortuniis civitatis
et regni quibus praesunt, quando dispositio coeli et eorum
quae per coelestia renovantur, ut cometae et hujusmodi, con-
formiter accidunt. Et optima judicia fieri possunt, secundum
oppositas conditiones principum et eorum quibus per omnia
credunt, quando similiter coelestis dispositio conformis in-
venitur. Et quoniam tales personae in uno regno paucae
sunt, et sunt publicae et notae omnibus, quorum mores relucent
toti regno, multum potest astronomus certificare de eis, et
utiliter judicare de factis publicis per proprietates talium
personarum. Haec igitur sunt quae volui recitare pro infamia
mathematicae tollenda in hujusmodi judiciis, ex quibus patet
omni sapienti quod non sit vera mathematica in hac parte
vituperanda, sed omnino amplectenda et diligenda propter
gloriosas utilitates quae possunt evenire ex judiciis mathe-
maticae verae, quae in nullo veritati contradicit.

Postquam potestas mathematicae respectu scientiarum Astrology
philosophiae et rerum istius mundi et theologiae, et sic strengthens
respectu totius sapientiae ostensa est, prout ipsa sapientia in the
secundum se consideratur absolute, nunc volo ostendere illud stability
idem secundum quod refertur haec sapientia ad ecclesiam Church.
Dei et rempublicam fidelium et conversionem infidelium et
repressionem eorum qui converti non possunt. Et quia in
multis quae nunc numerari non possunt necessaria est ecclesiae,
nunc volo tres casus proponere, qui sunt quasi infiniti miraculi
et utilitatis ineffabilis. Primus consistit in certificatione fidei
quam tenet ecclesia. Magnum enim solatium fidei nostrae

The moral
influence
peculiar
to each
planet.

The heaven
divided into
houses.

254 OPERIS MAJORIS PARS QUARTA.

possumus habere, postquam philosophi qui ducti sunt solo
motu rationis nobis consentiunt, et sectam seu professionem
fidei Christianae confirmant et nobiscum concordant in stabi-
litate hujus sectae ; non quia quaeramus rationem ante fidem,
sed post fidem, ut duplici confirmatione certificati laudemus
Deum de nostra salute quam indubitanter tenemus. Et per
hanc viam mathematicae non solum certificamur de professione
nostra, sed praemunimur contra sectam Antichristi, de qua
simul cum secta Christi fit consideratio in mathematica. Et
hujusmodi nobilissima perscrutatio fit per revolutionem
omnium sectarum! principalium a principio mundi, nec
possunt esse plures, et sunt sectae Hebraeorum, et Chaldae-
orum, et Aegyptiorum, et Agarenarum seu Saracenorum, qui
fuerunt de Agar et Ismaele, secta Christi, ac secta Antichristi.
Nec mirum si locuti sunt philosophi de his, quoniam fuerunt
post patriarchas et prophetas et instructi per filios et libros
eorum, ut prius ostensum est.

Quanto igitur planius et plenius possum ad praesens,
recitabo sententias mathematicorum in quibus auctores con-
cordant. Dicunt igitur Jovem et Venerem esse planetas
benivolos et fortunatos, Saturnum et Martem malivolos et in-
fortunatos. Mercurium dicunt medio modo se habere, quia cum
bonis est bonus, cum malis malus, quia convertibilis naturae
est. De benivolis vero fortunatis dicunt Jovem meliorem
esse, et majorem fortunam ei deberi, minoremque Veneri.
Et ideo cum duae vitae sunt, praesens et futura, et plus valet
futura quam praesens, sicut aeternum quam temporale, dicunt
Venerem significare super fortunas hujus vitae, quantum ad
ludos et gaudia atque laetitiam et hujusmodi, et Jupiter re-
spectum habet ad bona alterius vitae, quae majora sunt. Et
significat super sapientiam et intellectum et solutionem
somniorum .et divinum cultum fidem et legis doctrinam,
religionem et venerationem et Dei timorem et aptationem
morum et multa talia ut astronomi narrant.

Praeterea distinguunt totum coelum in xii partes, quae

! The list of religions given in the fourth part of Bacon's Moralis Philosophia
is somewhat different; viz. Pagani, Tartari, Idololatrae, Saraceni, Judaei,
Christiani.

JUDICIA ASTRONOMIAE. 255

vocantur domus, quae distinguuntur per meridianum cir-
culum et horizontem, et alios quatuor circulos intersecantes
se in eorum sectionibus, ita ut prima domus incipiat ab
horizonte et sub eo sit constituta, deinde succedunt ei
secunda domus et tertia usque ad angulum terrae, qui est
punctus in coelo sub terra oppositus puncto meridei super
terram. Et ab illo puncto sunt aliae tres domus usque
ad lineam occidentis. — Deinde supra horizonta incipit vii
et sequitur viii et ix usque ad punctum meridiei. Deinde
x et xi et xii usque ad horizontem. . Primam igitur
domum dant Saturno, secundam Jovi, et sic ulterius se-
cundum ordinem planetarum, ita quod octava iterum datur
Saturno, et nona Jovi Consideraveruntque omnes con-
corditer quod domus nona est domus religionis et fidei. Et
Ptolemaeus et Albumazar et Altavicus et Messehalac et alii
omnes assignaverunt istis domibus proprietates suas, quia
prima est domus vitae, secunda domus substantiae, et sic de
caeteris, juxta suas proprietates et dispositiones naturales.
Unde nona domus, ut dicunt, est peregrinationum atque
itinerum fidei et deitatis et religionis, ac domus culturae
Dei sapientiae librorum epistolarum et legatorum narrationum
ac rumorum et somniorum. Et ideo merito, ut dicunt, at-
tribuitur Jovi, qui habet respectum ad bona alterius vitae,
quia illis bonis debentur fides et religio et cultura Dei et
consideratio sapientialis, et librorum et epistolarum multitudo,
ut patet ex lege divina; et legatorum, ut prophetarum et
apostolorum et praedicatorum copia narrantium rumores
idoneos de nobilibus conditionibus illius vitae, et revela-
tiones frequentes habentium in somnis et extasi et raptibus
de hac vita.

Dicunt igitur planetas conjungi et complecti sibi invicem, Religious
et hoc est quando fuerunt in eodem signo et praecipue quando aia
in eodem gradu et in xvi minuto illius gradus et infra. in conjunc-
Volunt ergo philosophi Jovem ex sua conjunctione cum "5? "t^
aliis planetis significare super sectam religionum et fidei. Et planets.
quia sunt sex planetae quibus complecti et conjungi potest,
ideo asserunt sex fore debere in mundo sectas principales.

Unde periti auctores praedicti et alii dicunt, si complectatur

Combina-
tion of

256 OPERIS MAJORIS PARS QUARTA.

Jupiter Saturno, significat libros divinos, et significat de sectis
Judaicam, quia est antiquior aliis et prior, sicut Saturnus
pater planetarum et remotior et prior in exitu planetarum et
ordine in esse. Et ipsam omnes confitentur, et ipsa nullam
aliam, sicut Saturno omnes planetae complectuntur et ipse
nulli, propter tarditatem sui motus. Quia quando planeta est
ante eum ad orientem, nunquam ipse Saturnus consequitur
aliquem, sed in tantum invalescit alius planeta, quod con-
sequitur aliquando Saturnum et conjungitur ei. Omnes quidem
sectae appodiant se ad sectam Judaeorum, quia haec fuit
prima et est radix aliarum, a qua omnes aliquod genus testi-
monii et constitutionis sectae habuerunt: unde philosophia
accepit ab illa multa testimonia et multos modos constituendi
sectam, sicut prius patuit. Si vero Jupiter complectatur
Marti, tunc dicunt ipsum significare super legem Chaldaicam,
quae docet adorare ignem, cujus naturae Mars est in naturali
potentia et effectu. Si Soli, significatur lex Aegyptia, quae
ponit coli militiam coeli, cujus princeps est Sol. Si Veneri,
significare dicitur super legem Saracenorum, quae est tota
voluptuosa et venerea, quam licet in scriptis Mahometus
redegit, ipsa tamen per longa tempora in usu vitae habebatur
a suis cultoribus ; unde in libro qui ascribitur Ovidio! de vitae
suae mutatione cum loqueretur de secta venerea, quam homi-
nibus sui temporis legem dixit esse, dicit in metro suo,
*In qua, si libeat, quod cunque licere putatur,
Scripta licet super hoc nondum lex inveniatur ; '

Quam postea per sexcentos annos et amplius scripsit
Mahometus in libro qui dicitur Alcoran. Ovidius enim ante
Christum et in temporibus Christi fuit, et secta Mahometi
incepit per sexcentos annos et amplius post incarnationem
Christi, sicut patet ex differentia annorum Christi et Arabum,
quae est dcxxi annorum, et cxcv dies. Sed anni Arabum
computantur a Mahometo, ut dicit Alfraganus et alii
similiter.

Si vero complectatur Mercurio, tunc est lex Mercurialis.

1 The poem De vetula seu de mutatione vilae suae, attributed to Ovid, is believed
to have been written in the twelfth century by Leo, protonotary of the palace of
Byzantium.

-

JUDICIA ASTRONOMIAE. 257

Mercurius enim habet respectum, ut dicunt, ad Deitatem et Jupiter
oracula prophetarum et credulitatem et orationem, et maxime Mercury
quando conjungitur ei Jupiter; quoniam tunc significat related to
numerum psallendi et numerum librorum divinorum. Et anity.
dicunt, quod lex Mercurialis est difficilior ad credendum quam
aliae, et habet multas difficultates supra humanum intellectum.
Et hoc convenit propter motus Mercurii difficiles, cujus
circuitus est in epicyclo et eccentrico et aequante, in quibus
considerantur sui motus longitudinis et inflexus et reflexus in
motibus latitudinis, per declinationem eccentrici ab orbe
signorum ad septentrionem et meridiem, et epicycli ab
eccentrico in partem septentrionis et meridiei, et sunt mira-
biliores et difficiliores omnibus motibus planetarum, sicut
patet ex dictis Ptolemaei, et planius ex sententiis Albategni,
Thebit, et Archaselis, et probabiliter ex dictis Alfragani. Et
propter hoc significat, ut dicunt, super legem quae habent
difficiles articulos et occultas veritates, cujusmodi est lex
Christiana. Sed quia Mercurius est significator scripturae et
scriptorum, et profunditatis scientiae in libris profundis, atque
facunditatis, sive dulcedinis locutionis et linguae, et rhetoricae
et velocitatis ejus et explanationis sententiarum, significat
quod tam authenticis scripturis et tot profundis scientiis et
tanta potestate eloquentiae defendetur, quod stabit semper in
robore suo, donec ultima lex Lunae perturbet eam ad tempus.
Et dicunt, quod haec lex est prophetae nascituri de virgine,
secundum quod omnes antiqui Indi, Chaldaei, Babylonii,
docuerunt quod in prima facie Virginis ascendit virgo mundis-
sima nutritura puerum in terra Hebraeorum, cui nomen
Jesus Christus, ut dicit Albumazar in majori introductorio
astronomiae. Et in moralibus recitabitur auctoritas ejus inter
alias philosophiae auctoritates de iis quae pertinent ad philoso-
phiam moralem, quia etiam ea quae dicuntur hic praeparat
mathematica ad usum illius philosophiae, ut ibi declarabitur
expressius. Et ortus prophetae de virgine multum convenit
legi Mercuriali, quia Mercurius habet maximam potestatem
in Virgine secundum judicium astronomorum . omnium.
Creatus enim fuit in Virgine, et dignitates, seu potestates seu
testimonia seu virtutes seu fortitudines quinque quae debentur
VOL. I. S *

258 OPERIS MAJORIS PARS QUARTA.

planetis ratione signorum habet Mercurius in Virgine, ut sunt
scilicet domus, exaltatio, triplicitas, terminus, facies.

Double Et domus nunc et prius dicitur aequivoce! ; quoniam istae
meaning of
House in 1 'The two senses of the word Domus will be best illustrated by the accom-

astrology. panying figures taken from Bacon's commentary on the Secretum Secretorum

(Tanner MS. 116). In the lower figure which represents the domus accidentales
or situales described on a previous page, the division into houses gives the state
of the sky at any particular moment. The sign placed in the first house may be

MED'UM
OOEL!

IO*"^ DOMUS

OAPRICORNUS

DOwus 12 QUAE SUNT 12 PARTES
TOTVIVS COEU DIVISI IN EAS; NEC
POSGUNT IN PLANO MELIUS FIGU-
MARI, CUM ALIAS NASCITUR UT
A0 QUAESTIONEM VENIUNT MQU-
RARI HMUIC GIMILES FACIES 81C-
UT CIRCA HORAM QUAMGTIONIS
PLURIMAE GUNT IN 8IGNIS IPSAM
PIGURAM DESCRIBAB BED US! NUNC
Ger ARIES i" ORTU 18)! PONE
SIGNUM ASCEKDENS MORA FIQURA-
TIONS QUOOCUNQUE 1D FUERIT,

DEin Sis! PROXIMO SIGNUM
QUCCEDENS USQUE TOTUM COM-
PLEATUR,

ANGULUS
TEARAE

JUDICIA ASTRONOMIAE. 259

domus vocantur essentiales et naturales, priores vocantur
accidentales et situales; quoniam hae domus sunt xii signa,
quorum divisio naturalis est, quia sectiones zodiaci et coeli
manent in suis locis de circulo coelesti, hoc est de firmamento,
quam divisionem signorum faciunt sex circuli sese inter-
secantes in polis zodiaci, et dividunt totum coelum et mun-
dum in xii partes aequales. Quae partes possunt considerari
in zodiaco solum, et tunc sunt proprie signa, ut Aries et alia,
aut possunt illi circuli imaginarie extendi ad polos, in quibus
se intersecant, et tunc dividunt totum coelum in xii partes
aequales habentes angustiam in extremitatibus circa polos et
latitudinem in medio ad modum fundi naviculae, ita quod illa
latitudo continet extremitates partium zodiaci, quas communi
nomine vocamus signa, unde signum dicitur proprie, ut Aries,
vel Taurus, &c. Et sumitur aliter pro tota coeli parte contenta
inter duos circulos transeuntes, verbi gratia per fines Arietis,
qui circuli concurrunt in polis mundi; et istud signum
dicitur esse signum Arietis, quia ejus latitudo consistit in
extensione Arietis, et sic stellae quae sunt extra corpus
Arietis dicuntur esse in signo Arietis, quamvis sint juxta
polos mundi. Sed aliae domus dicuntur accidentales, quia
divisio earum est accidentalis, et non manent sectiones in
eodem loco coeli, quia non sequuntur motum coeli, et ideo
mutantur earum loca in circulo seu coelo in omni hora. Et
sumuntur hae sectiones, ut dictum est, per circulum meridi-
anum et horizontem cum aliis quatuor. Domus autem quae
dicitur naturalis adhuc est duplex ; quaedam est principalis,
quaedam non principalis, unde dicitur accidentalis respectu
principalis. Principalis autem domus planetae est in qua
creatus fuit, ut Leo est domus Solis, Cancer Lunae, Virgo
Mercurii, Libra Veneris, Aries Martis secundum quosdam,
secundum alios Scorpius, Sagittarius Jovis, Capricornus

any of the twelve, according to the hour at which the horoscope is taken. The
figure here given shows Aries rising, and Libra setting.

In the upper figure, representing the domsus essentiales et naturales, special
signs of the zodiac are allotted to each planet; one to the Sun, one to the
Moon, and two to each of the other five. Each of these five has a masculine
and a feminine sign ; corresponding, I suppose, to the distinction in the text
of principales and sinus principales.

S2

Exaltation
and
Triplicity.

Terminus
and Facies.

260 OPERIS MAJORIS PARS QUARTA.

Saturni. Domus autem minus principales sunt, ut Aquarius
Saturno datur, Pisces Jovi, Scorpius Marti secundum unam
opinionem, secundum aliam Aries, Taurus Veneri, Gemini
Mercurio ; ita quod quilibet quinque planetarum habet duas
domos sed Sol et Luna non nisi singulas. Ita decrevit
antiquitas sapientum.

Exaltationes vero sunt hae. Sol exaltatur in Ariete, Luna
in Tauro, Saturnus in Libra, Jupiter in Cancro, Mars in Capri-
corno, Venus in Piscibus, Mercurius in Virgine. Et sicut
Sol exaltatur in Aricte, sic ejus descensio est in Libra, et sic
de reliquis ; et similiter depressio Mercurii est in Piscibus, et
ideo exaltatio Mercurii est in Virgine, sicut ejus domus, et est
haec exaltatio in xv gradu Virginis. Triplicitas planetae
dicitur, cum sit in signo in quo creatus est, vel in aliquo
ejusdem naturae cum signo in quo creatus est. Unde scien-
dum est quod quatuor sunt triplicitates signorum. Una est
calida et sicca quae continet tria signa calida et sicca cujus-
modi sunt Aries, Leo, Sagittarius. Unde cum est Sol in
aliquo istorum trium dicitur esse in sua triplicitate. Et alia
est triplicitas secunda, ex Tauro, Virgine, et Capricorno, et
haec est frigida et sicca ; et Mercutius, quando est in aliquo
istorum, est in triplicitate sua. Quia licet domini istius
triplicitatis in die sint primo Venus, deinde Luna, et in nocte
primo Luna, postea Venus, et eorum particeps in nocte et die
sit Mars, tamen Mercurius participatur eis in Virgine proprie,
ut dicunt astronomi, et ideo triplicitatem habet in Virgine
sicut exaltationem et domum. Tertia triplicitas est ex
Geminis, Libra, Aquario, quae est calida et humida. Et
quarta est ex Cancro, Scorpione, et Pisce, quae est frigida et
humida.

Famosiores autem termini sunt Aegyptiorum. Jupiter
habet sex primos gradus Arietis, Venus sex sequentes,
Mercurius octo, Mars quinque, Saturnus quinque, Venus
adhuc octo primos Tauri, Mercurius sex sequentes. Et sic
mira diversitate variantur isti termini, ut patet in tabula
terminorum, ita quod Mercurius habeat septem primos gradus
Virginis pro termino, non solum secundum Aegyptios, sed
secundum Ptolemaeum, et hoc est quod nunc quaerimus.

JUDICIA ASTRONOMIAE. 261

Facies autem signorum accipiuntur per divisionem cujuslibet
signi in tres partes aequales; et unaquaeque constat ex decem
gradibus, quae vocantur facies, et alio modo decani; quarum
facierum initium est a primo gradu Arietis, et terminatur in
decimo gradu ejusdem, et dicitur Martis. Secunda usque
in vicesimum, et dicitur facies Solis, quia Sol succedit ei in
ordine circulorum. Tertia est in finem Arietis et dicitur
facies Veneris, et sic de caeteris secundum ordinem, ut patet
in tabula facierum ; ita quod Mercurius habet decem gradus
Virginis ultimos pro facie. Et sic patet, quod Mercurius
habet omnes istas potestates in Virgine. Et vocantur istae
potestates per similitudinem. Unde planeta in domo sua
comparatur regi in domo sua regia et in dominatione sua ; et
cum fuerit in exaltatione sua, est sicut vir in regno suo et
gloria; et cum fuerit in triplicitate sua, est sicut vir in honore
suo et inter auxiliatores atque ministros; et cum fuerit in
termino suo, est sicut vir inter parentes suos et cognatos et
gentem suam; et cum est in facie sua, est sicut vir in
magisterio suo. Et domus dicitur habere quinque fortitu-
dines, exaltatio quatuor, triplicitas tres, terminus duas, facies
unam. Unde domus habet in se fortitudines quinque facierum,
et exaltatio habet fortitudinem quatuor facierum, et sic
ulterius.

Ex his igitur patet quod hae potestates Mercurii essentiales Connexion
et principales sunt omnes in Virgine. Atque addendum o ereury
est, quod unusquisque planeta habet adhuc potestatem stellation
accidentalem quandam in signo sibi debito, quae vocatur ^^^
gaudium. Unde Saturnus, cum intrat Aquarium, gaudere
dicitur, ut Jupiter in Sagittario, Mars in Scorpione, Venus
in Tauro, et Mercurius in Virgine. Et ideo nusquam domi-
natur Mercurius tantum, sicut in Virgine. Nec aliquis
planeta habet tot in ea dominia, propter quod appropriatur
Virgini Mercurius. Et ideo ex hac causa dicunt legem
Mercurialem debere esse sectam prophetae nascituri de
virgine: et ideo haec secta Mercurialis ponitur ab eis esse lex
Christiana. Si vero complectatur Lunae, dicunt domini
astronomiae, quod erit lex Lunae et ultima, quia circulus
Lunae est ultimus, et haec erit lex corruptionis et foeda quae

These
things
point to
supremacy
of Christian
Faith.

262 OPERIS MAJORIS PARS QUARTA.

violabit omnes alias leges et suspendet eas, etiam Mercurialem
ad tempus. Luna enim, ut dicunt, significat super nigro-
mantiam et mendacium, et ideo lex Lunae erit nigromantica
et magica et mendosa. Et propter corruptionem Lunaris
motus et figurationum Lunarium significat super corruptionem
istius legis, quae in se erit corrupta et alias corrumpens.
Non tamen multum durabit, ut dicunt, quia Luna velociter
mutatur a figuratione et luce sua et motu propter brevitatem
sui circuli. Et hoc, ut dicunt, statuetur ab aliquo magno et
potente qui praevalebit aliis, et aestimant astronomi fideles
tam moderni quam antiqui quod haec est lex Antichristi,
quia ille ultimo in fine mundi adveniet, et inducet legem
corruptionis, et infatuabit mundum per artem magicam et
mendacia sua.

Sic igitur astronomi discutiunt sectas et praecipue Albu-
mazar! in libro conjunctionum, et maxime primo et secundo
libro, ut inveniantur sex sectae principales in quibus homines
occupantur in hoc mundo. Et per hoc habetur quod secta
Christi sit una de principalibus, Et si comparemus eam ad
alias, manifestum est per nobiles conditiones legislatoris et
ipsius sectae quod nulla alia digna est, sed sunt hominum
figmenta. Et hoc de ultima lege statim patet, quia non
est ibi veritas. Et in lege Venerea, quae est Saracenorum,
delectatio peccati abundat secundum tenorem ejus praedictum.
Sed philosophia excludit peccatum a lege. Similiter lex
Aegyptiorum nulla est nec Chaldaeorum, quia docent colere
creaturam, et hoc negat philosophia. Nam soli Deo cultus
debetur, sicut exponetur in moralibus. Secta vero Judaeorum
minus elongatur a veritate. Sed lator non fuit filius virginis,

! This astrological writer is frequently cited by Bacon. He is entered in the
Museum Catalogue as Jafar ibn Muhammad (Al Balkhi). His principal works
appear to be (a) the Liber Conjunctionum, otherwise called Albumasar de
magnis conjunctionibus, annorum revolutionibus, ac eorum profectionibus, octo
continens tractatus; and (b) Introductorium in Astronomiam Albumasans Aba-
lacht, octo continens libros partiales. Both were printed at Vienna, 1489. The
latter treatise deals with objectors to astrology, and is specially severe on the
more ignorant medical practitioners (plebaei medicinae professores) who neglect
the science, as contrasted with the skilled and experienced physicians who
acknowledge its value. See Zsnfroduct. £n Astron. lib. i. cap. 5, entitled ‘De
Utilitate Astrologiae.’

JUDICIA ASTRONOMIAE. 263

sicut in lege Christiana ; atque non habet confirmationem per

tot scripturas authenticas, nec habet tam nobiles articulos
secundum quod prius expositum est secundum philosophos. Et

ideo oportet quod lex Christi obtineat principatum. Sed in

morali philosophia hoc ex propriis erit planum. Nam non

solum sic in universali investigant leges, sed determinant
tempora inceptionum earum et finem aliquarum. Et hoc Three kinds
investigant per conjunctiones planetarum, et per revolutiones junction of
motuum eorum. Albumazar igitur in libro conjunctionum et Jupiter and
caeteri astronomi determinant tres esse Saturni et Jovis con-
junctiones, magnam scilicet, majorem, et maximam. Magna

est, qua conjungitur in omnibus viginti annis in quocunque

signo hoc sit. Jupiter enim perficit suum cursum in duodecim

annis, et Saturnus quasi in triginta annis, et ideo fit ut post

viginti annos junguntur in nono signo ab eo, in quo prius

juncti fuerant ; et post alios viginti in quinto a primo; et post

tertios viginti iterum in illo primo. Et haec est conjunctio

magna, quae fit in hac triplicitate duodecies, vel aliquando
terdecies. Primum enim signum, quintum, et nonum faciunt
triplicitatem. Et haec conjunctio dicitur significare pluries

super sublimationem regum et potentum, et super gravitatem
annonae, et super ortus prophetarum. Et postquam totiens

in ista triplicitate conjuncti fuerint, ut ad aliam mutentur,

tunc vocatur conjunctio major. Et hoc fit in omnibus ducentis
quadraginta annis vel circiter, et significat super sectam et
mutationem ejus in quibusdam regionibus. Etquando mutata

fuerit conjunctio ab ista triplicitate in aliam, ut a fine Cancri

ad initium Arietis, tunc dicitur maxima, per revolutionem

Saturni triginta duabus vicibus, et fit omnibus nongentis
sexaginta annis, et significat super mutationes imperiorum et
regnorum, et super impressiones ignitas in aere, et super dilu-

vium, et super terrae motum et gravitatem annonae. Et una One of the
major vel fere maxima fuit xxiv anno Augusti Caesaris, quam en") at
dixerunt sapientes astronomi significare super legem Mercuri- Christian
alemfuturam. Et in libro, qui dicitur de mutatione vitae Ovidii, "

qui inscribitur de Vetula, propter quam mutatio fuerat facta,

refertur Ovidius Naso locutus fuisse de hac conjunctione, et

ex ejus dispositione prorupisse in admirationem sectae

264 OPERIS MAJORIS PARS QUARTA.

Mercurialis producendae in mundum per prophetam nasci-
turum de virgine absque maris commixtione, quam futuram
esse praedixit post illam conjunctionem per annos sex, ita
quod secundum ipsum nasceretur xxx anno Octaviani
Augusti. Nam xii anni fluxerunt a morte Julii usque ad
Actium bellum, in quo plene obtinuit imperium Octavianus
Augustus. Nam ante magis laboravit ut acquireret regnum,
quam possedit. Et tunc Christus fuit natus xxx anno
Octaviani. Si vero computentur illi xii anni de regno ejus,
tunc Christus fuit natus xlii anno Augusti, secundum quod
alii computant Sed in idem redit. Gessit enim Augustus
quinque bella civilia magna infra illos xii annos, ut narrant
historiae, et maxime Orosius in libro de Ormesta! Mundi.
Ultimum vero fuit ad Actium, in quo Antonium et Cleopatram
devicit et quievit imperium in pace. Loquens igitur Ovidius
de conjunctione majore et fere maxima dicit in metro suo
hoc modo,

‘Una quidem talis fatali tempore nuper
Caesaris Augusti fuit anno bis duodeno

A regni novitate sui, quae significavit

Post annum sextum nasci debere prophetam,
Absque maris coitu de virgine, cujus habetur
Typus, uti plus Mercurii vis multiplicatur.
Cujus erit concors complexio prima futurae
Sectae nam nusquam de signis sic dominatur
Mercurius sicut in signo Virginis."

Et prima facies Virginis ascendebat in oriente, quando
conjunctio illa facta fuit. Et fuit conjunctio illa prope
caput Arietis. Si enim revolvamus motus Saturni et Jovis
ad tempus illud, inveniemus eos fuisse conjunctos per
medios cursos suos ante nativitatem Christi per sex annos,
quinque dies, et tres horas; et erat medius cursus utriusque
in Ariete decem gradus, lvi minuta, lii secunda. Medius vero

! The title, Ormesta Mundi, was often applied to the encyclopaedic work of
Orosius. Ducange throws out the suggestion that Ormesta is a misreading for

Orchestra, scene or spectacle. But this seems hardly a satisfactory explanation
of the word.

JUDICIA ASTRONOMIAE. 265

motus octavae sphaerae erat ex signis circuli parvi decem
gradus, quinque minuta, li secunda, xxvii tertia, et erat
minuenda a locis omnium planetarum ; unde remanserunt de
Ariete ii gradus, xiv minuta, xlii secunda. Cum ergo
differentia inter duas conjunctiones per cursus medios addat
viii signa, ii gradus, xxv minuta, xvii secunda, sequitur
quod praecedens conjunctio fuerat in Cancro xxix gradibus,
li minutis, xxv secundis, et ita mutata fuit triplicitas a
signo aquatico ad igneum. Si vero haec conjunctio fuisset
propinquior capiti Arietis, fuisset maxima, et tunc erant anni
Graecorum perfecti trecenti quinque et novem menses, et fere
xviii dies, quod potest probari per tabulas annorum.

Per revolutiones vero motuum planetarum considerant illud Influence of
idem. Nam Albumazar octava differentia libri secundi de E s
conjunctionibus dicit, quod mora sectae et regni et permutatio on political
accidunt praecipue secundum quantitatem decem revolutionum religious
Saturniarum, praecipue si Saturno conveniat mutatio ad signa “D=™8*
mobilia, quae sunt Cancer, Libra, Capricornus, Aries,
dummodo Jupiter fuerit cadens ab eo. Sed si Jupiter fuerit
cum eo, aut aspiciat eum, minuet multum de malo propter
ejus bonitatem. Quando enim fuerunt completae decem
revolutiones Saturni in diebus Darii, fuit apparitio Alexandri
magni, et destructio regni Persarum. Et circiter post decem
alias revolutiones completas apparuit Jesus filius Mariae, super
quem sunt orationes cum permutatione sectae. Et quando
completae sunt decem aliae apparuit Meni !, et venit cum lege
quae est inter Paganos et Nazarenos. Et post decem alias
venit Mahometus, et fortasse illud est ante complementum
decem revolutionum, ut in revolutione nona, et forsan post, ut
in undecima. Et illud est secundum quantitatem ejus, quod
exigunt conjunctiones praemissae, quae sunt fortiores istis
revolutionibus. Et similiter mutatur citius vel tardius secta
secundum proprietates planetarum dominantium regnis
diversis, ut Saturnus Indiae dominatur, Jupiter Babyloniae,

Mars Thraciae, Sol Romanis et imperio eorum, Mercurius
Aegypto, Luna Asiae.

! Meni, commonly written Manes, is the originator of the Manichaean heresy,
which arose in Mesopotamia towards the end of the third century.

266 OPERIS MAJORIS PARS QUARTA.

Destruc- Et de destructione legis Mahometi pulchre et certitudina-
Mahom- liter loquuntur. Nam secundum quod Albumazar dicit viii
medanism. capitulo secundi libri, non potest lex Mahometi durare ultra
sexcentos nonaginta tres annos. Sed tantum valet durare et
durabit nisi propter aliquam causam coincidentem abbrevietur
tempus secundum quod prius tactum est, quod abbreviatio
potest fieri major et minor ex causis diversis. Et nunc est
annus Arabum sexcentesimus sexagesimus quintus ! a tempore
Mahometi, et ideo cito destruetur per gratiam Dei, quod
debet esse magnum solatium Christianis. Propter quod
laudandus est Deus, qui philosophis dedit lumen sapientiae,
per quod lex veritatis confirmatur et roboratur, et per quod
percipimus inimicos fidei destrui debere. Et huic sententiae
concordat Apocalypsis xiii capitulo. Nam dicit quod
numerus bestiae est 663, qui numerus est minor praedicto per
xxx annos. Sed scriptura in multis locis subticet aliquid
de numero completo, nam hic est mos scripturae, ut dicit
Beda. Et hic forsan voluit Deus, quod non exprimeretur
totaliter, sed aliquantulum occultaretur, sicut caetera quae in
Apocalypsi scribuntur. Unde ante tempus ultimum quod
isti sectae determinatur, secundum ejus causam principalem,
prout determinat Albumazar, forsan continget quod Saraceni
destruentur aut per Tartaros aut Christianos. Et jam major
pars Saracenorum destructa est per Tartaros, et caput regni
quod fuit Baldac, et Caliph qui fuit sicut papa eorum. Jam
haec facta sunt xii annis elapsis ?.
Planetary Et quamvis loquantur de sectis, et sectae dependent ex
changesnot ti ertate rationis, tamen non imponunt aliquam necessitatem
merely ibertate rationis, O P q
figns one libero arbitrio, dicentes planetas esse signa innuentia nobis ea
co-opera- quae Deus disposit ab aeterno fieri sive per naturam, sive per
ieee, voluntatem humanam, sive per rationem propriam secundum
though — beneplacitum suae voluntatis. Ita dicitur in libro de cursibus

not com-

pulsory. 1 665 Arabic years of 354 days make very nearly 644 of our years, which

added to 622 the date of the Hejira brings the date to 1267, the year in which
Bacon was writing.

3 The capture of Baghdad, called by Bacon and others Baldac, by Halagu,
grandson of Chinghis Khan, was in the 656th year of the Hejira, which counting
Arabic years, would bring the date to 1258 of our era, But Halagu's expedition
had begun three years before. .

JUDICIA ASTRONOMIAE. 267

planetarum. Et praeterea dicunt quod voluntas non cogitur,
sed tamen corpus alteratur per virtutes coelorum, et tunc anima
corpori unita excitatur fortiter et inducitur efficaciter, licet in
nullo cogatur, ut velit gratis sequi inclinationes corporis ad
actus privatos vel publicos, et ad bonos sicut ad malos, ut sic
opiniones et sectae et mutationes consuetudinum inducantur
per aliquem famosum in populo et potentem, secundum quod
praevisum fuit et praecognitum a Deo; ita quod planetae sic
non solum sint signa, sed aliquid faciant in excitando.

Et cum posuerunt Dominum Jesum Christum esse Deum
et hominem, ut Ethicus astronomus manifeste dicit in Cosmo-
graphia, et Alchimus similiter, necnon et in illo libro qui
inscribitur, Ovidius de vetula, Deum incarnari in Christo
colligitur, attribuentes ei quod soli homini denegatur, volunt
quod dispositio coelestis potuit esse in signum conceptionis
Virginis, et nativitatis illius Hominis, in quantum homo, sicut
stella praestitit signum in ejus nativitate, secundum quod
dicitur in libro cursuum planetarum, quod planetae omnes et
caeterae stellae aliter Deo homini facto, aliter puro homini,
aliter creatori, aliter creaturis famulantur. Voluit ergo Deus
res suas sic ordinare, ut quaedam quae futura praeviderit vel
praedestinaverit rationabilibus per planetas ostenderentur,
ideo scilicet ut mens humana Dei mirifica recognoscens in
amorem sui conditoris succensa excresceret. Et ideo volunt
quod innuere et significare possunt coelestia hoc opus deificum
conceptionis et nativitatis, quatenus creatura attestetur suo
creatori in carne venienti. Sicut contra naturam sol obscura-
tus fuit in passione; propter quod philosophi haec videntes
dixerunt, quod aut aliquid Deus naturae patiebatur, aut tota
mundi machina dissolveretur. Et proculdubio volunt quod
impossibile sit Deum subjici creaturae, nec quod istud opus
divinum in quantum fuit a virtute infinita et supra naturam,
aliquo modo fuerit subjectum dispositioni coelesti: sed solum
quod illud fuerat in signum. In quantum tamen Virgo mun-
dissima fuit vera mater et naturalis Domini Jesu Christi, et
operata fuerit ex virtute naturali in praeparando materiam
et in fovendo post conceptionem et in hujusmodi, posuerunt
virtutem coeli cooperatam fuisse virtuti naturali Virginis

Astrolo
may help
us to fore-
tell the
time when
Antichrist
shall come.

268 OPERIS MAJORIS PARS QUARTA.

gloriosae, et excitasse eam in quantum naturaliter operabatur,
quia homo generat hominem et sol. Si enim aliquid naturale
fuerit in illa conceptione per materiae praeparationem et
fomentum in utero et hujusmodi, in quantum fuerat naturalis
et vera mater, non aestimant inconveniens ponere coelestem
dispositionem esse plus quam signum, consideratis pure natu-
ralibus. Sed quicquid dicunt in hac parte, hoc ad regulam
fidei reducendum est, ut a catholica veritate non discordet.
Et licet omnia et ad plenum non sufficiant ostendere secreta
istius sectae, tamen an sit haec secta, et qualis sit in universali,
pulchre attestantur, ut satis admirantes sapientiam eis datam
facile excusemus eorum ignorantiam, quia defecerunt a plena
certificatione ritus Christiani, cum in eo non fuerant instructi.
Et laudare debemus, quod nobiscum concordant et confirmant
nostram professionem. Sed in tertia parte moralis philosophiae
de hac confirmatione abundantior fiet sermo.

Et quoniam post legem Mahometi non credimus quod
aliqua secta veniet nisi lex Antichristi, et astronomi similiter
concordant in hoc, quod erit aliquis potens qui legem foedam
et magicam constituet post Mahometum, quae lex suspendet
omnes alias, multum esset utile ecclesiae Dei considerare de
tempore istius legis, an cito veniet post destructionem legis
Mahometi, an multum longe. Et Ethicus philosophus in sua
Cosmographia dicit expresse, quod gens quae fuit clausa infra
portas Caspias irruet in mundum et obviabit Antichristo et
eum vocabit Deum Deorum. Et proculdubio Tartari fuerunt
infra portas illas et exiverunt. Jam enim fractae sunt portae,
sicut certi sumus. Nam fratres minores!, quos dominus rex
Franciae Ludovicus qui nunc regnat misit, transiverunt cum
Tartaris per medium portarum ultra longe inter montes, ubi
fuerunt inclusi. Et notum est non solum omnibus nationibus
orientis quod Tartari exiverunt a locis eis, sed et eis qui bene
sciunt mundi dispositionem, et noverunt partes habitabiles et
regionum diversitates per astronomiam, et per auctores alios
ut Plinium et Martianum et caeteros qui mundi regiones
describunt, et per historias. Nolo hic ponere os meum in

! Much will be said in the course of the work of this important mission, of
which William Rubruquis was the leader.

JUDICIA ASTRONOMIAE. 269

coelum, sed scio quod si ecclesia vellet revolvere textum
sacrum et prophetias sacras, atque prophetias Sibyllae, et
Merlini et Aquilae, ct Sestonis, Joachim et multorum aliorum,
insuper historias et libros philosophorum, atque juberet con-
siderari vias astronomiae, inveniretur sufficiens suspicio vel
magis certitudo de tempore Antichristi .

Sed haec hactenus. Nunc vero inferam secundum? quod Reforma-
tion of the

! The subject of Astrology is again discussed at the end of the geographical Julian
section in what may almost be regarded as a distinct treatise. Calendar.

It has often been remarked that Roger Bacon was supported by Albertus
Magnus, by Aquinas, and indeed, all the best thinkers of his time in his convic-
tion of the truth of astrology. To a believer in a limited and spherical universe
with a terrestrial centre, nothing could seem more valid as a working hypothesis
for explaining physical changes on the earth's surface than that alterations of
the directions in which the planets were seen should be followed by corre-
sponding alterations of terrestrial objects. The combinations of planetary bodies
as seen in conjunction, in opposition, or in intermediate positions, offered a wide
field of speculation, which became practically boundless when to the appa-
rent relation of these bodies to one another were added their apparent relations
(also ever varying) with the fixed stars. Human and terrestrial events com-
plicated as they might be, were paralleled by equal complication in the play of
celestial forces. It may be said on the whole that so far from belief in astrology
being a reproach to Bacon and his contemporaries, to have disbelieved in it
would have been in the thirteenth century a sign of intellectual weakness. It
conformed to the first law of Comte's pitlosophia prima as being the best hypo-
thesis of which the ascertained phenomena admitted.

When the universe was unlocked by the Copernican theory, it might have
been supposed that astrology would speedily disappear. Yet it was not so.
Francis Bacon, writing three centuries and a half after Roger Bacon, had not
abandoned belief in it, and Campanella’s work (.4sfrologicorusm hbri sex) pub-
lished in 1629, is a treatise that Roger Bacon might himself have written.
‘Sunt causae ipsae stellae,’ says Campanella (lib. ii. x), nedum signa, ut optime
probat S. Thomas; corporearum mutationum per se, voluntariarum per accidens,
. .. Omne judicium astrologicum aut est de mutationibus aeris et maris et telluris;
unde de penuria et abundantia rerum nobis utilium et noxiarum ratiocinamur ;
aut de monarchia et rerum publicarum initiis et mutationibus, et de gentium et
legum et morum translationibus et civitatum et provinciarum ; aut de cujusque
hominis ortu vita morte et eventibus, aut tandem de bonis malisque electionibus

rerum agendarum.

* In Opus Tertium, chap. 68, p. 274, there is an almost exact repetition of
what follows in the next sixteen pages. [In O. these are altogether omitted.
The Cottonian MS. (Jul. supplies them.) It is probable that the scribe
copied the MS. of Opus Tertium; since in the passages of that work here
referred to, Bacon explains that what had been said in the copy of Opus Majus
sent to the Pope on the subject of the Calendar, was not in all respects correct,
so that, he goes on to say, ‘hic iterum feci transcribi et correxi.

That
calendar
makes the
solar year

too long by

rity of a
day.

270 OPERIS MAJORIS PARS QUARTA.

non solum expedit ecclesiae, sed quod maxime decet eam, et
quod sine grandi periculo et confusione vitari non potest ;
quamvis tamen longis temporibus jam accidit multiplex
abusus. Et quoniam totus hic error procedit ex pura igno-
rantia et negligentia considerationis, tanto est vilior coram
Deo et hominibus sanctis, et apud omnes, non solum sapientes
astronomos. Sed et computistae vulgati sciunt multiplicem
errorem, et scribunt super hoc sicut et astronomi, quorum
utrorumque scripta per Dei ecclesiam vulgata sunt, in quibus
errores hi notantur, et de remediis datur consilium. Sed
nullus propter concilium generale ausus est facere remedium.
Quod autem intendo hic est de correctione calendarii quo
utitur ecclesia. Julius quidem Caesar in astronomia edoctus
complevit ordinem calendarii secundum quod potuit tempore
suo; et sicut historiae narrant contra Achorium astronomum
et Eudoxum ejus doctorem disputavit in Aegypto de quantitate
anni solaris, super quam fundatum est calendarium nostrum.
Unde, sicut Lucanus refert, ipse dixit,
‘Non meus Eudoxi vincetur fastibus annus.’

Sed non pervenit Julius ad veram anni quantitatem, quam
ponit esse in calendario nostro ccclxv dies et quartam diei in-
tegram ; quae quarta colligitur per iv annos, ut in anno bisextili
computetur unus dies plus in quarto anno, quam in aliis annis
communibus. Manifestum autem est per omnes computistas
antiquos et novos, sed et certificatum est per vias astronomiae,
quod quantitas anni solaris non est tanta, immo minor. Et istud
minus aestimatur a sapientibus esse quasi cxxx™ pars unius
diei!. Unde tamen in cxxx annis superflue computatur unus
dies, qui si auferretur, esset calendarium correctum quoad hoc
peccatum. Et ideo cum omnia quae sunt in calendario fun-

! That the length of the year was wrongly given in the Julian Calendar must
have been known to the small group of Arabian men of science who studied
Ptolemy's Almagest. But that the amount of the error was not matter of
common knowledge half a century after the Opus Majus was written, is shown
by the passage in Dante (Paradiso, xxvii. 142-3), where the error is spoken of
as being the hundredth part of a day. The difference between zy}, and yt}, is
considerable to those who know Dante's minute and precise way of dealing
with such questions. The mean length of the equinoctial year is 3654, 5^, 489,
51*. 6.

CORRECTIO CALENDARII. 27I

dentur super quantitatem anni solaris, necesse est ea vacillare,
postquam est erroneum fundamentum.

Deinde accidit alius error major, scilicet de fixione aequi- It takes no

. eae . account of

noctiorum et solstitiorum!. Nam hic error non solum ex changes in
quantitate anni exoritur, sed habet in se graves errores. the time of
Ponuntur autem aequinoctia et solstitia in diebus fixis, ac si and of —
semper fuissent ibi et debeant esse in aeternum. Sed certum *obtices.
est astronomis quod non figuntur, immo ascendunt in calen-
dario, sicut per tabulas et instrumenta probatur sine dubita-
tione. Et in principio ecclesiae ponebatur solstitium hyemale
viii calendas Januarii in die nativitatis Domini, et aequinoc-
tium vernale viii calendas Aprilis in festo annuntiationis
Virginis gloriosae, et solstitium aestivale viii calendas Julii,
scilicet in die nativitatis beati Johannis Baptistae, et aequinoc-
tium autumnale viii calendas Octobris. Et istius opinionis
fuit Hippocrates medicus? ; cui Christiani facile concordabant,
propter hoc quod beatus Joannes dixit, Illum oportet crescere,
me vero minui. Unde expositores aliqui sacrae scripturae
"posuerunt Dominum natum quando dies crescit, et hoc est in
solstitio hyemali ; et Johannem Baptistam nasci quando dies
incipiunt minui, ut in solstitio aestivali. Et Isidorus fuit istius
opinionis Hippocraticae, ut patet ex viii libro Etymologiarum,
et sanctus Anatolius, qui in principio ecclesiae de hujusmodi
disputavit. Sed postea mutaverunt haec viri ecclesiastici, et
statuerunt aequinoctium vernale esse xii calendas Aprilis, sicut
dicit Beda in libro temporum, quod usque nunc tenetur. Et
hoc manifestum est omnibus qui aliquid sciunt de computo,
et qui considerant usum ecclesiae. Nam sicut in lege veteri
post aequinoctium vernale quando luna fuerat xiv celebrabatur
Pascha, sic ecclesia ordinavit quod terminus Paschae sit ibi, et
in dominica sequente celebraretur Pascha ; quia oportet quod

! It should be noted that the time of the solsti#a in the middle of the thirteenth
century coincided almost exactly with that of the sun's apogee and perigee
(aux et oppositum augis’. In our own time the former occur about nine days
before the latter. The perigee and apogee have a progressive motion on the
ecliptic of 11". 8 annually. The retrograde motion annually of the equator on
the ecliptic (precession of the equinoxes) is 50”. 1.

1 Hippocrates of Chios the geometer, not Hippocrates of Cos the physician,
is presumably meant. They were contemporaries,

These occur

earlier than
in the
official
tables at
the rate of
one day in
125 years.

272 OPERIS MAJORIS PARS QUARTA.

in die dominica fiat festum istud apud Christianos, et ideo
non possumus celebrare Pascha xiv luna, sed in dominica
sequente. Et posuerunt quod primum Pascha sit xi calen-
das Aprilis ut nullo modo sit ante, propter hoc quod
aequinoctium dixerunt figi in xii calendas ubi luna potest
aliquando esse xiv. Nam sicut dicit Beda in computo suo,
ecclesia non utitur xiv luna quae praecedit aequinoctium, sed
quae est in aequinoctio, vel post ipsum; et ipsum aequinoc-
tium, ut dicit, est xii calendas Aprilis, et ibi est primus
terminus Paschae, sicut omnes computistae sciunt ; quod si sit
in die sabbati, tunc in crastino potest esse Pascha quia dies
dominicus est. Et ideo propter rationem aequinoctii fixam in
xii calendas Aprilis, dicit ecclesia quod infimum Pascha est
in xi calendas Aprilis.

Sed quamvis usus ecclesiae tenuit in principio aequi-
noctium esse viii calendas et postea mutavit, et teneat nunc
aequinoctium fixum xii calendas Aprilis, tamen certum
est quod aequinoctium istud non est in locis illis, sed
jam ascendit in calendario longe ab his locis, et similiter
solstitia et reliquum aequinoctium. Nam hoc anno fuit
solstitium hyemale idibus Decembris per duodecim dies ante
nativitatem Domini, et aequinoctium vernale iii idus Martii,
et solstitium aestivale est xvii calendas Julii, et aequi-
noctium autumnale xvi calendas Octobris. Et hoc potest
non solum astronomus certificare, sed quilibet laicus ad
oculum perspicere per casum radii solaris, nunc altius, nunc
inferius ad parietem vel aliud, secundum quod quilibet potest
notare. Et mutabuntur ab his locis in temporibus succeden-
tibus, quia post annos circiter xciv, scilicet anno Domino
mccclxi, erit solstitium hyemale pridie idus Decembris et
aequinoctium vernale iv idus Martii, et solstitium aestivale
xviii calendas Julii, et aequinoctium autumnale xvii calen-
das Octobris, scilicet quodlibet eorum per unum diem ante-
quam sit modo. Nam post annos circiter cxxv ascendit
per unum diem. Et hoc accidit ex errore quantitatis
anni, quia sol circiter tantum tempus deficit de quantitate
anni, quo utitur calendarium, per unum diem. Et hoc est
quod plus concordat cum annis quos computamus ab In-

CORRECTIO CALENDARII, 273

carnatione. Nam Ptolemaeus anno cxl ab Incarnatione
invenit aequinoctium vernale xi calendas Aprilis et solsti-
tium hyemale xi calendas Januarii, ut patet ex Almagesti.
Sed ab hoc loco in calendario usque ad idus Decembris,
ubi nunc est solstitium, sunt ix dies quibus ascendit hoc
solstitium. Sed ab anno probationis Ptolemaei sunt nunc
de annis Domini mcxxvii eo quod nunc sit annus Domini
mcclxvii, a quibus si demantur cxl, qui fluxerunt ab
Incarnatione usque ad probationem Ptolemaei, remanebunt
mcxxvii anni. Sed in isto tempore nunc dicto cxxv anni
reperiuntur novies et duo anni ultra. Quapropter hoc
tempus, scilicet cxxv anni, satis convenit cum numero
annorum Christi, ut semper unus dies in tanto tempore
minuatur de quantitate anni, et denotet mutationem solstitit
et aequinoctii.

Protestor tamen quod in tanta difficultate non loquor There are
praecise, sed multum propinque veritati certificandae, usque Pots
quo currat finalis probatio super anni quantitate et mutatione farther in-
solstitiorum. Per jam dicta tamen secundum probationem Ye5UEstion.
Ptolemaei non potuit in viii calendas esse solstitium hyemale
in tempore nativitatis Domini, sed oportuit quod in decimo
calendas fuerit; eo quod in clx annis a tempore nativitatis
usque ad probationem Ptolemaei non potuit mutari solsti-
tium per tres dies, nec per duos, sed per unum et parum
de alio. Et ideo x calendas Januarii potuit esse secundum
hoc quod Ptolemaeus invenit xi calendas. Et cum per
eandem probationem Ptolemaei potuit aequinoctium primo
anno nativitatis fuisse xi calendas Aprilis, non potuit esse
viii sicut primo crediderunt in ecclesia primitiva, et longe
magis non potuit esse xii calendas Aprilis, sicut nunc
creditur secnndum usum ecclesiae. Quia cum semper ascen-
dit aequinoctium, et in tempore Ptolemaei fuit xi calendas
Aprilis, tunc ante illud tempus fuit retro hunc locum magis
versus Aprilem ; et ideo x calendas secundum probationem
Ptolemaei. Secundum haec igitur neque sunt aequinoctia
et solstitia fixa, nec sunt fixa illis diebus quibus usus fuit
in ecclesia. Nec fuit Hippocrates longe a veritate, quoniam
ipse fuit ante Christum plus quam ccc annis, et ideo potuit

VOL. I. T

Hence
ensue
grievous

274 OPERIS MAJORIS PARS QUARTA.

esse aequinoctium temporibus suis viii calendas vel prope,
scilicet vii.

Sed tertium inconveniens est longe majus. Nam, ut prius
tactum est, veritas est, quod sine errore debet Pascha celebrari

errors as to die dominica post xiv lunam quae invenitur vel in aequi-

the time of

keeping
Easter.

noctio, vel post aequinoctium vernale, propter conformitatem
legis Christianae ad legem antiquam propter Paschae
solemnitatem quae primo fuit in lege veteri, et praecessit
sicut figura novi Paschae. Cum igitur verum est quod
aequinoctium sit iii idus Martii, et possibile est quod ibi sit
luna xiv, scilicet in xiv anno cycli decemnovennalis, ut prima
computetur pridie calendas Martii super C literam, oportet
quod die dominica proxima post illam diem sit Pascha
secundum veritatem. Sed non potest ab. hac xiv luna dies
dominica elongari plus quam usque ad xiii calendas Aprilis,
ut patet in calendario. Sed hoc est ante xi calendas
Aprilis ubi primum Pascha celebrat ecclesia. ^ Quare in
ilo anno xiv cycli celebrabitur Pascha gloriosum tempore
non suo. Et idem accidit in tertio anno cycli, ut patet per
aureum numerum in calendis Martii. Nam xii calendas
Aprilis vel citra erit Pascha. Et quoniam potest contingere
dies dominica in his annis pridie idus Martii, et idibus, et
sic ultra, usque ad xii calendas Aprilis, ideo multipliciter
debet fieri Pascha in illis diebus, quod observari non potest
si primum Pascha sit xi calendas Aprilis. Et quoniam
aequinoctium verum ascendit plus et plus, ita quod circiter
mcccclxxxi annum erit v idus Martii, et sic ascendendo
ulterius versus principium Martii secundum computationem
calendarii, et ultra Martium continue propter errorem de
falsitate anni, necesse est quod Pascha fieret circa principium
Martii vel in Februario, et sic semper antecedendo secundum
antecessionem aequinoctii. Sed hoc est inconveniens maxi-
mum; quia sic non solum Pascha; sed Quadragesima et
omnia festa mobilia recederent horribiliter a statu suo, et
confunderetur totus ordo ecclesiastici officii. Praeterea cum
secundum veritatem Pascha potest celebrari ante xi calendas
Aprilis secundum aequinoctiorum veritatem, et hoc per
multos dies et quot volumus secundum quod aequinoctium

CORRECTIO CALENDARII. 275

antecedit, oportet quod verum Quadragesimae, principium
similiter ascendat antequam incipiatur secundum usum
ecclesiae, et ita in vera Quadragesima carnes per multos dies
comedentur; et in tantum potest aequinoctium antecedere,
quod tota Quadragesima vera erit in tempore quo Christiani
comedent carnes, quod est absurdissimum. Et sic festum
Paschale quo mundus salvatur, et festum Pentecostes quo
gratia Dei diffusa est in ecclesiam, et caetera festa mobilia
violantur: et per consequens alia festa immobilia, quia illa
cedunt Paschati et festis aliis sui generis, ut notum est
evidenter. Et cum haec sunt horribilia ex se, sunt magis
stulta et derisione digna ; quia propter ignorantiam et negli-
gentiam diabolus procuravit quod sic accideret ecclesiae Dei.
Nam non oporteret aliud, nisi quod certificarentur anni "
quantitas et aequinoctium. Et si peritissimis astronomis non
denegatur certificatio quantitatis anni, tamen facilius est
certificare aequinoctium, quia per centum et circiter viginti
annos non mutatur nisi per unam diem secundum opinionem
magis probatam nunc diebus. Et daretur ars de hoc, et
etiam inveniretur aequinoctium per secula futura usque in
finem mundi et ultra, quod facile est, et fierent tabulae et
canones de hoc, et scriberentur per totam ecclesiam Dei, et
ponerentur cum calendario, et tunc non accideret impedi-
mentum in hac parte. Et similiter aliud aequinoctium
inveniri posset, et solstitia de facili, et omnis error in his
evacuaretur ad laudem et honorem Dei, et tollerentur infamia
et scandalum, quae nunc multiplicantur apud omnes compu-
tistas et astronomos et sapientes propter errores qui in hac
parte vulgari ab ecclesia permittuntur.

Sed majus inconveniens accidit ex primatione designata per The error
aureum numerum in calendario. Nam quilibet potest videre cage
ad oculum, si aspiciat coelum, quod luna est prima secundum moon as
veritatem per tres dies vel quatuor antequam signetur in ends ne
calendario, et in omnibus Ixxvi annis recedit primatio a loco increases
suo in calendario per xvi minuta unius diei et xl secunda, of nearly

et hoc est plus! quarta unius diei, et prope tertiam unius diei, ae youn

! I have corrected this passage from Opus Tertium, cap. 70. Minutum unius
dies means the sixtieth part of a day, i. e. twenty-four minutes, It does not
T 2

276 OPERIS MAJORIS PARS QUARTA.

quia xvi minuta et xl secundae sunt sex horae et xl minuta
unius horae. Et in omnibus ccciv annis recedit a loco prima-
tionis in calendario per unum diem et vi minuta unius diei,
et xl secunda. Et post 4,256 annos dicetur luna secundum
calendarium prima, quando est plena lumine. Et post 7,904
annos erit error unius lunationis integrae, excepto modico,
scilicet exceptis xxxviii minutis, et xxx secundis. Et hic error
potest devenire ad centum lunationes, et tunc iterum redibit
error primus, ut sequantur sequentes per ordinem, et sic in
infinitum hi errores revolvuntur. Et quod haec omnia sint
vera non est dubium peritis astronomis. Etiam quilibet
computista novit, quod fallit primatio per tres dies vel quatuor
his temporibus, et quilibet rusticus potest in coelo hunc
errorem contemplari.
The lunar Quantumcunque vero brevius possum, aperiam grossam
we doesnot declarationem errorum praedictorum. Nostrum vero calen-
mismo A darium ponit cyclum decemnovennalem esse aequalem xix
to nineteen annis solaribus cum quarta integra sumptis, secundum quod
solar years. calendarium utitur hujusmodi anno solari, ut prius habitum
est. Et hic cyclus continet lunationes omnes, quae con-
tingunt in xix annis lunaribus Et computantur ccxxxv
quia quolibet lunari anno, qui dicitur communis, habemus
xii lunationes, et illis addimus vii lunationes in toto cyclo
decemnovennali ad restaurationem defectuum, qui accidunt
xii lunationibus respectu xii mensium solarium in anno
solari, quia annus lunaris consistens ex xii lunationibus non
habet nisi cccliv dies integros, et solaris habet xi plures,
nam habet ccclxv. Et ideo annus lunaris citius finitur
quam solaris per xi dies; et tunc colliguntur isti xi dies
superflui usque ad tertium annum, et fit una lunatio seu
mensis lunaris. Et sic in tertio anno cycli apponitur unus
mensis lunaris, et vocatur embolismus et annus embolismalis,
id est, superexcrescens, quia habet xiii lunationes, et sic
ultra per totum cyclum semper colliguntur isti menses
embolismales, ut fiant anni embolismales, quatenus cyclus

seem quite clear why Bacon chose the numbers 4,256 and 7.904, except that
they were multiples of 76. The error in the first period would be 154, 12",
57™, 36*, and in the second, 28!', 19", 327.

a

CORRECTIO CALENDARII. 271

lunationum decemnovennalis aequetur xix annis solaribus.
Sed istud est impossibile. Nam secundum Ptolemaeum in
Almagesti et omnes astronomos mensis lunaris non est
proprie a visione novae lunae, quia hoc tempus est inaequale ;
quia aliquando in mane ejusdem diei est novacula veteris
lunae, et in vespere novacula novae lunae, et aliquando est
spatium duorum dierum inter eas, et aliquando tres dies
intercipiuntur, ut planum est sensui, et causae ab astronomis
assignantur; sed menses debent aequari. Item nec a con-
junctione solis et lunae secundum eorum cursum verum, quia
hoc tempus est inaequale; et ideo considerabitur penes
conjunctionem solis et lunae secundum utriusque eorum
cursum medium et aequalem, quia hoc tempus est aequale et
uniforme. Et secundum quod probat Ptolemaeus in Alma-
gesti, hoc tempus est xxix dies, et xxxi minuta unius diei,
et | secunda, et viii tertia, et ix quarta, et xx quinta. Et
huic concordat Arzachel, qui fundavit tabulas suas super
quantitatem anni lunaris, qui annus lunaris continet cccliv
dies et quintam et sextam unius diei, id est, xxii minuta.
Et secundum hoc erit tempus aequalis lunationis xxix dies,
et xxxi minuta et ] secunda, quae multiplicata per xii
faciunt cccliv dies et xxii minuta. Sed Arzachel omisit
tertia Ptolemaei et quarta et quinta, quia in maximo tempore
parum quantitatis adjiciunt.
Posito ergo quod tempus aequalis lunationis sit xxix dies The.

. oye os Arabian
et xxxi minuta et 1 secunda, accidit quod minimum tempus gycle of
reducens integras lunationes ad idem temporis principium est thirty years
xxx anni Arabum, qui continent ccclx lunationes integras ; lunar
et continet dies 10,631 praecise. Quoniam cum una lunatio preferable.
sit xxix dies, et xxxi minuta, et ] secunda, xii lunationes
quae faciunt unum annum Arabum et annum unum lunarem,
continebunt cccliv dies et xxii minuta unius diei Sed
cccliv multiplicata per triginta faciunt 10,620, et xxii multi-
plicata per triginta faciunt xi dies integros, qui prioribus
additi faciunt 10,631, reducentes primo lunationes aequales ad
consimile temporis initium. Cum igitur xxx anni Arabum
sint tempus minimum quod reducit integras lunationes ad
consimile temporis initium, non est possibile ut aliud tempus

Successive
periods of
nineteen
solar years
are not of
the same
length
owing to
leap-years.

278 OPERIS MAJORIS PARS QUARTA.

hoc idem faciat, nisi sit ei aequale vel multiplex. Sed xix!
anni calendarii nostri non aequantur xxx annis Arabum, nec
sunt eis multiplices, quia xxx anni Arabum continent xxix
annos solares et unum mensem et octo dies. Ergo relin-
quitur quod xix anni solares non possunt aequari vero
cyclo primationum, nec per consequens xix anni cycli decem-
novennalis. Et ideo cyclus decemnovennalis non est verus
cyclus primationum.

Praeterea istud potest magis in particulari manifestari,
ut appareant inconvenientia prius nominata. Nam singuli
xix anni solares non sunt aequales ad invicem, eo quod in
primo cyclo sunt tantum quatuor bisextiles anni, et in tribus
aliis sunt quinque, quia quartus annus in primo cyclo bisextilis
est, et viii et xii et xvi, eo quod quartus annus semper sit
bisextilis. Et ideo in secundo cyclo primus est bisextilis et sic
ulterius, ita quod in illo sunt quinque, ut patet consideranti,
et similiter in aliis duobus; et tunc iterum redit cyclus qui
habet quatuor bisextiles, et subsequuntur tres qui habent
quinque, et sic semper currit ordo cyclorum. Primus autem
cyclus annorum solarium xix praecise habet dies 6,939, et in
illis assignantur ccxxxv lunationes. Sed si multiplicaverimus
tempus aequalis lunationis, hoc est xxix dies, et xxxi minuta,
et 1 secunda, in ccxxxv resultabunt 6,939 dies et xl minuta et
] secunda, quae sunt plus quam duae tertiae unius diei.
Quapropter completis xix annis habentibus tantum iv dies
bissextiles, nondum completae sunt ccxxxv lunationes, sed
desunt eis xl minuta et | secunda unius diei. Quilibet vero
xix anni habentes quinque dies bisextiles habent dies 6,940.
Unde cum ccxxxv lunationes aequales habeant 6,939 dies,
et xl minuta, et 1 secunda, tunc xix anni habentes quinque
annos bisextiles superant ccxxxv lunationes spatio xix
minutorum, et x secundorum, quod est fere tertia unius diei.
Quod patet si de uno die, quo superfluunt nunc dicti xix anni
super ccxxxv lunationes, subtrahantur xl minuta, et ] se-
cunda, quibus illae lunationes superfluebant super xix annos
habentes tantum quatuor dies bisextiles. Et ita patet, quod
non quilibet xix anni solares aequantur sibi invicem. Sed

! xxix in J.

CORRECTIO CALENDARII. 279

quater xix anni redeunt ad idem temporis principium, qui
faciunt Ixxvi annos, et semper aequantur aliis lxxvi annis.
Si ergo aggregentur ter xix minuta et decem secunda, quae
quilibet xix anni habentes quinque bisextos addunt super
ccxxxv lunationes, provenient nobis lvii minuta et xxx
secunda, quibus isti ter xix anni habentes quinque bisextos
simul sumpti excedunt suas lunationes. Sed xix anni habentes
tantum dies quatuor bisextiles sunt minores suis lunationibus
in xl minutis et ] secundis. Si igitur subtrahantur haec xl
minuta et ] secunda a praedictis lvii minutis et xxx secundis,
relinquentur xvi minuta et xl secunda, quibus quater xix
anni solares, qui faciunt lxxvi annos, excedunt suas luna-
tiones.

Et hic est primus error notabilis, quem a principio notavi,
ex quo sequitur secundus. Nam si accipiamus quater Ixxvi
annos, qui faciunt ccciv annos, superabunt suas lunationes
in quater! xvi minutis et xl secundis. Sed haec sumpta
quater faciunt unum diem et sex minuta, et xl secunda.
Relinquitur ergo error secundus, quod ccciv anni superant
suas lunationes in uno die et vi minutis unius diei et xl
secundis. Et ideo accidit quod post ccciv annos dicamus
secundum calendarium lunam primam, ipsa existente majoris
aetatis quantitate unius diei et vi minutorum et xl secun-
dorum. Et si haec accidunt, manifestum est inquirenti, quod
multiplicato tempore multiplicabuntur inconvenientia. Et
ideo post 4,256 annos dicetur luna prima secundum computa-
tionem calendarii, quando ipsa erit plena lumine. Et ulterius,
quod una lunatio integra superabundabit; et tandem quod
centum lunationes in maximo tempore superfluent, sicut patet
per radices jam datas. Nec est necesse facere computationes
majores pro praesenti persuasione, quia promptae sunt demon-
strationes ad hoc, cum fuerit opportunum. Manifestissimus
igitur est error primationum secundum calendarium, et non
unus sed multiplex, nec parvus sed quasi infinitus.

Et cum ita sit error cycli decemnovennalis in singulis annis, Error in
sequitur quod similiter erit error in cyclis epactarum. Nam ‘he epacts.
xi dies excrescentes in anno solari super annum lunarem

! J. has quantitate.

280 OPERIS MAJORIS PARS QUARTA.

dicuntur epacta sequentis anni solaris, quasi efzaucía, hoc est,
superaugmentata ; et per illos xi dies majoratur aetas lunae in
primo die sequentis anni, et per eosdem dies majoratur aetas
lunae in principio cu;uslibet mensis futuri anni super aetatem
suam in principio cujuslibet mensis prioris anni. Et quia
hujusmodi errores contingunt, necesse est ut aetas lunae vera
quaeratur aliter quam per hujusmodi cyclos.
Superiority Et remedium horum omnium est, quod possumus cognoscerc
d obth ad primationem lunae secundum veritatem astronomicam, si
of Hebrew numeremus tempora secundum annos et menses Arabum;
' . quia primus dies cujuslibet mensis anni Arabum est dies con-
junctionis solis et lunae secundum eorum utriusque cursum
medium. Unde si diem hunc volumus dicere primum diem
aetatis lunae, tunc cognitis initiis mensium cognoscuntur
initia primationum. Quod si velimus inchoare primationes
nostras prima die visionis lunae vel secunda vel tertia, in-
cipiemus primationes nostras a secundo die vel tertio cujuslibet
mensis Arabum, et procedemus uniformiter in computatione
lunationum et non proveniet nobis error. Et quia scientia
annorum Arabum, et initia mensium eorum, dabit nobis veram
cognitionem primationum, ideo non oportet nisi recurrere ad
tabulas et canones annorum et mensium Arabum. Et hoc
dico secundum doctrinam quae vulgata est apud astronomos
Latinos et Árabes. Si tamen velimus alia via procedere, pos-
sumus eadem certitudine sed majori auctoritate probare quae
volumus, scilicet per tabulas Graecorum, et maxime Hebrae-
orum. Nam a principio Hebraei fuerunt peritissimi in
sapientia astronomiae; et omnes nationes habuerunt hanc
scientiam sicut caeteras ab eis, sicut probavi in superioribus.
Et ideo si quis consideret tabulas Hebraeorum ad occasum
solis Jerusalem, inveniet plenam in hujusmodi veritatem.
In the Sed quamvis errores quos enumeravi sint horribiles secun-
present dum se, tamen non est comparatio ad eos qui ex jam dictis

year, 1267, ol

Lent begins sequuntur. Nam totus ordo ecclesiasticarum solemnitatum

and ends . . . . .

a weck too confunditur per hujusmodi primationes erroneas secundum

late. calendarium, sicut per aequinoctiorum falsam fixionem. Et
ne differam in alios annos ad evidentiam istius erroris, pono

casum in hoc anno. Nam non solum media conjunctio solis

CORRECTIO CALENDARII. 281

et lunae hoc anno fuit vi calendas Aprilis, super B literam,
sed prima accensio lunae et visio primae lunae. Ergo luna
fuit xiv quinto idus Aprilis, super A literam, et xiv luna est
terminus Paschae, ac dominica sequens est dies Paschae.
Quare in B litera sequente, scilicet in crastino, videlicet iv
idus Aprilis debet esse dies Paschae secundum veritatem. Sed
modo transfertur usque ad octo dies ultra propter primationem
sumptam juxta aureum numerum. Nam aureus numerus
istius anni est xiv, qui ponitur iii calendas Aprilis super E
literam, et ibi dicitur esse primatio secundum calendarium.
Et ideo secundum hoc xiv luna, quae est terminus Paschae
est pridie idus Aprilis, et in dominica sequente assignatur
Pascha, scilicet xv calendas Maii, et sic per viii dies ultra
veritatem. Quapropter solemnitas paschalis qua mundus sal-
vatur non celebrabitur tempore suo, sed jejunatur hoc anno
per totam septimanam Paschae veram. Nam jejunium exten-
ditur per viii dies plus quam deberet. Et tunc sequitur aliud
inconveniens, quod per octo dies tardius incipiebatur jejunium
Quadragesimae ; ergo Christiani comedebant carnes in vera
Quadragesima per octo dies, quod est absurdum. Et iterum
tunc nec Rogationes nec Ascensio, nec Pentecostes, celebrantur
hoc anno suis temporibus. Et sicut hoc anno 1267 accidit,
ita accidet anno sequenti. Nam secundum aureum numerum
erit Pascha iv idus Aprilis, scilicet 1268 anno Domini. Sed
esse debet tertio nonas Aprilis per octo dies ante, quia luna
prima est per tres dies antequam assignatur per aureum
numerum. Et ideo quarto calendas Aprilis, vel saltem
tertio, erit decima quarta luna quae est terminus Paschae;
quapropter in prima dominica sequente erit dies secundum
veritatem. Et sicut hoc anno accidit, ita et saepius per
antecessionem aequinoctii et primationis potest contingere
quod Pascha non solum per octo dies, sed per multo plures
celebretur antequam debeat, et caetera festa, sicut prius ex-
positum est de aequinoctio. Nam per longitudinem temporis
accidet lunaris diei primatio quando erit plena, et quando
erit in quacunque distantia a sole, ut prius habitum est in
erroribus primationum. Et ideo maximum inconveniens et
intolerabile hic sequetur.

The
remedy is
of easy
applica-
tion.

Objection
that the
Council of
Nice, and
afterwards
Pope Leo,
have de-
cided the
matter.

At that
time the
error had
not become
serious.

282 OPERIS MAJORIS PARS QUARTA.

Cum igitur omnes astronomi et computistae possunt videre
hos errores, et omnis homo qui vult inclinare cervicem suam
ad veritatis inquisitionem potest hos intueri, necessarium esset
et debitum ac Deo beneplacitum et hominibus sapientibus
desideratum ut remedium poneretur. Et remedium facile
esset ; nam inveniretur verum aequinoctium per tabulas astro-
nomiae et per instrumenta, et verificaretur primatio per easdem
considerationes, ut evacuarentur omnes modi errorum prae-
dictorum, et xiv luna ab aequinoctio sumeretur, sive esset in die
aequinoctii sive post eum, et ibi fieret terminus Paschae ut in
die dominica sequente fieret dies paschalis. Et ideo non esset
sequendus aureus numerus, ut aliquid fixum super calendas.
Et possent fieri tabulae de his primationibus et aequinoctiis,
et secundum illas posset ordinari calendarium in anno et in
mensibus secundum consimile artificium quo Hebraei utuntur.

Sed contra haec possit objici de synodo Nicaena, quae
statuit primationes paschales inveniri juxta cyclum decem-
novennalem. Et beatus papa Leo, discussione facta de hujus-
modi contentione, tandem definivit adhaerere sententiae synodi
Nicaenae. Atque Beda in libro temporum capitulo xliii nititur
quantum potest roborare hunc cyclum et primationes per
decursum hujus cycli accidentes. Nam auctoritatem Nicaenae
synodi et Leonis papae introducit et miraculum interponit.
Nam cum multi voluerunt quodam tempore Pascha debere
celebrari viii calendas Aprilis, et alii x calendas Maias
secundum quod ordo cycli decemnovennalis exigebat, elisa
est haec contentio per quoddam baptisterium, in quo nocte
Paschae singulis annis replebatur fons sacer aqua per se, et
baptizatis hominibus sicut venerat recedebat ; quod accidit
decimo calendas Maias secundum quod cycli ratio exigebat,
et non octavo calendas Aprilis.

Sed haec si bene intelligantur non contradicunt veritati.
Nam cum Eusebius Caesariensis episcopus primo ordinaverat
hunc cyclum, ipse parum fuit ante synodum Nicaenam, ita
quod cum ipse ordinavit veraciter hunc cyclum secundum
quod cursus lunae tunc fuit, non potuit esse mutatio aliqua
sensibilis in tempore quo celebrata fuit illa synodus sacro-
sancta. Et ideo sancti patres statuerunt hunc cyclum obser-

CORRECTIO CALENDARII. 283

vari, quia non habuit tunc errorem, nec diu postea habuit
falsitatem notabilem. Unde cum papa Leo! fuerit post
synodum Nicaenam quasi cxx annis, sub Martiano principe,
manifestum est non posse primationem ad plus recessisse
a loco suo in calendario a tempore Eusebii nisi per unum
diem. Et cum ipse papa discussit hunc errorem, saltem dedit
occasionem posterioribus considerandi veritatem in hac parte.
Caeterum novus error fuit et non multum notabilis, et synodus
Nicaena magnae auctoritatis fuit, propter quod non expedivit
tunc temporis definitioni hujus synodi contraire.

Etiam non invenit astronomos in ccclesia sufficientes ad Scientific
hoc, quia a principio fuit astronomia odiosa Christianis, knowledge
propter causas superius annotatas, scilicet in parte prima hujus not suffi-
tractatus. Nec adhuc inventi sunt usque nunc qui darent vet sme
remedia in hac parte. Nam bene fuerunt multi qui sciverunt settlement
probare hos errores per vias astronomiae, et quantum erratur ; necessary.
nec mirum, cum visus nobis multos ostendat ; et in universali

dixerunt quae essent remedia, scilicet quod certificaretur

quantitas anni, quod aequinoctia et solstitia invenirentur
veraciter, quod primationes similiter; et tangunt modos
universales ad haec. Sed nullus adhuc expressit nobis veram
quantitatem anni, cum plena demonstratione, in qua non sit
dubitatio. Similiter nec de aliis. Et ideo non fuit mirum si
non fuerunt haec certificata temporibus ecclesiae primitivae,
quando mathematica reputabatur inter artes suspectas et
inutiles Dei ecclesiae, sicut multae aliae nobiles scientiae

! Pope Leo was in doubt as to the day on which Easter should be celebrated
in 455 A.D. According to the calculation of Theophilus of Alexandria, it
should be the 8th before the Calends of May, that is on April 24. This seemed
too late: for the view hitherto maintained was that Easter day should not be
earlier than March 22, nor later than April 2r. The Pope wrote on the
subject to the emperor Martian who referred his letter to Proterius of Alex-
andria. Proterius confirmed the view of Theophilus, and the Pope to avoid
schism in the matter accepted his authority, and wrote to the bishops of the
Western church in accordance with it. To avoid similar difficulties in future,
he urged Victorius, a Gaul of Aquitaine, to construct a new paschal canon.
Victorius multiplying the lunar cycle of nineteen years into the solar cycle of
twenty-eight, produced a cycle of 532 years, beginning with the consulate of
the Gemini which he took for the date of the Passion, and terminating in
559 A.D. This canon was usually followed by the Latin church afterwards.
(See Fleury, Hist. Ecclesiast. lib. xxviii. ch. 51.)

284 OPERIS MAJORIS PARS QUARTA.

propter quinque rationes in prima parte signatas. Synodus
igitur Nicaena decrevit cyclum observari dum haberet veri-
tatem et quia illis temporibus non fefellit. Caeterum decrevit
hoc teneri, ut vitaretur contentio juxta caput cujuslibet, donec
accideret in ecclesia Dei potestas mathematicae, qua certifi-
cari possunt omnia de quibus est contentio. Minus enim
malum est sine comparatione unum inconveniens ad tempus
tolerari propter impossibilitatem remedii, quam quod quilibet
opinionem suam promulget aeque falsam sicut est illa quae ab
omnibus communiter sustinetur. Et sic loquitur Beda. Nam
dicit, ‘cum lunam sic secundum cycli rationem signabant,
aliud majus periculum per hoc declinaverunt.’ Et quod Beda
adduxit miraculum, concedendum est quod illis temporibus
non fuit error in cyclo, ut manifestum est, sed postea crevit et
apparuit sensibiliter.

Quod etiam adducit exemplum de lapide selenite, cujus
splendor crescit cum luna primi mensis et decrescit, per
quae cognoverunt antiquitus primationes paschales, istud
non est pro cyclo, nisi dum habuit veritatem, sed magis
contrarium : quia ille lapis ostendit nobis verum aequi-
noctium, et decimam quartam lunam paschalem in eo
vel post ipsum sumendam pro termino Paschae; quod non
potest hic cyclus his temporibus facere, nec unquam faciet,
nec fecit diu ecclesiae. Caeterum Beda fuit circa tempora
exordii cycli. Nam ipse refert in computo suo se tunc
attigisse annum Domini septingentesimum primum. Et ab
Incarnatione usque ad tempora Constantini, sub quo fuit
synodus Nicaena, fuerunt cccxxxii anni secundum Bedam.
Et ab hoc tempore usque ad Martianum principem fuerunt
centum viginti anni, sub quo Leo papa fuit, qui sunt in universo
ccccli. Ex quo patet, quod Beda non fuit per ccc annos
postea, sed nec a synodo nisi per circiter ccclxix annos, et
ideo non potuit lunatio multum recedere a loco suo. Nam
ad plus per unum diem integrum et per aliquid de secundo,
eo quod in ccc annis et iv fit mutatio unius diei. Et ideo
propter causas prius tactas bene potuit cyclus observari in
tempore Bedae, sicut in tempore Leonis papae. Sed tamen
scrupulus dubitationis jam exortus fuit a tempore Leonis, et

CORRECTIO CALENDARII. 285

augmentabatur haec dubitatio in tempore beati papae Hilarii,
qui praecepit Victorio novum cyclum componere, in quo quia
non fuit certitudo, sicut nec in decemnovennali, adhaeserunt
posteriores consuetudini antiquae et statuto concilii Nicaeni.

Patet igitur ex his, quod salva omni auctoritate Nicaenae At present

synodi, potest cyclus hic immutari ; quia tunc error non fuit,
et sustinebatur ut vitaretur majus periculum ad tempus, donec

the im-

perfections
of the

Calendar

ecclesia posset habere astronomicam potestatem, per quam pring dis-

solam potest remedium adhiberi. Nam primitiva ecclesia non
habuit usum astronomiae. Et ideo postea usque nunc fuit
omissa correctio hujus rei propter longam consuetudinem, et
propter hoc quod usus astronomiae non fuit in usu praelatorum
nec multitudinis studentium, nec adhuc est ; licet aliqui sunt
satis prompti et periti in hac parte. Debet autem nunc temporis
remedium apponi propter istos errores manifestos et palpabiles,
atque propter scandalum multiplex in ecclesia. Nam omnes
literati in computo et astronomi sciunt haec, et derident
ignorantiam praelatorum qui haec sustinent. Atque philosophi
infideles, Arabes, Hebraei, et Graeci, qui habitant inter Chris-
tianos ut in Hispania, et Aegypto, et in partibus orientis, et
in multis aliis mundi regionibus abhorrent stultitiam quam
conspiciunt in ordinatione temporum quibus utuntur Christiani
in suis solemnitatibus. Et jam Christiani habet peritiam
astronomiae, per quam potest fieri certificatio. Potest igitur
Vestra Reverentia jubere, et invenietis homines qui praeclara
remedia apponent in hac parte; et non solum in praedictis, sed
in totius calendarii defectibus. "Nam tredecim sunt radicales,
et habent ramos quasi infinitos. Si igitur istud opus gloriosum
fieret temporibus Vestrae Sanctitatis, tunc una de majoribus
rebus et melioribus et pulchrioribus consummaretur quae
unquam in ecclesia Dei fuerunt attentatae!.

! Paul of Middelburg, bishop of Fossombrone, in his work, Paulina de recta
Paschae celebratione (A. D. 1513) discusses the question of the Calendar with great
fullness. Speaking of the confusion resulting from the error as to the length of
the year and from the imperfection of the lunar cycle, he says, 'Quod animad-
vertentes mayjores nostri exhortati sunt aliquando Romanos pontifices ut errori
huic enormi succurrerent.’ That he should not have mentioned Bacon's name
in this connexion is the more strange that he does mention him in another
part of his work, when he treats at some length of his conjecture as to the date

credit on
the Church.

The value
of mathe-
matical
science in
the govern-
ment of the
world.

285 OPERIS MAJORIS PARS QUARTA.

Postquam ! declaratum est quomodo mathematica potenter
requiritur ad philosophiam et theologiam et Dei ecclesiam,
nunc manifestandum est qualiter est necessaria rei publicae
fidelium dirigendae. Et duobus modis principalibus valet.
Uno scilicet modo propter cognitionem futurorum, praesentium,
et praeteritorum ; alio modo in operibus utilibus. Cum vero
humanum genus sit expositum infinitis periculis de futuro,
summe necessarium est, ut habeat vias cognoscendi futura.
Et cum Deus dedit homini majora, scilicet animam et corpus,
et promittit vitam aeternam, non debuit denegare minora.
Nam et sceleratis sol oritur et piratis patent maria; qua-
propter longe magis Deus debet bonis utilem cognitionem
rerum, et praecipue multitudini, propter hoc quod in ea bonum
publicum invenitur. Et quia semper aliqui boni et Deo
placentes in mundo inveniuntur, ideo Deus mundo dedit
multiplicem futurorum cognitionem, nec potest stare sine ea,
ut docet Avicenna in primo de Anima, et decimo Metaphysicae.
Prius vero tactae sunt radices de cognitione futurorum in illa
distinctione in qua de excusatione mathematicae disputavi, ct
ostensum est quod possibile est sufficiens judicium in omnibus,
quod est scilicet medium inter necessarium et impossibile, et
inter universale et particulare. Nam per haec mens humana
illustratur, ut possit prudenter in omnibus dissere et utilitates
sibi et aliis providere. Postea vero descendi ut res postulabat
ad judicia specialia in humanis, scilicet in distinctione de
sectis, Et si in rebus humanis et praecipue in hujusmodi fiat
verum et utile judicium, multo magis in rebus naturalibus
potest hoc fieri, tam in particulari quam in propria disciplina.

Et licet, ubi actum est de excusatione mathematicae, atque
superius de comparatione virtutum coelestium ad haec inferiora,
of the Passion. But the ssajores whom he speaks of here are Peter d'Ailly
and Nicolas of Cusa. The first of these had, as will be seen presently, copied
into his Imago Mundi an extract from Bacon's Geographical treatise: and with
regard to the lunar cycle, he advocated Bacon's view that the Arab cycle of
thirty lunar years should be adopted. It is abundantly clear that the impulse
to this reform was given by Bacon. By no previous writer had any attempt
been made to apply astronomical science to the rectification of the Calendar.

! Bacon now passes to the subject of Geography. A survey of the planet

was needed in order to estimate the dangers to the Church from foreign foes;
and generally for the exercise of the Pope's functions as universal bishop.

GEOGRAPHIA. 287

sit tactum de cognitione locorum mundi et rerum generabilium Effect of.
in eis per coelestia, tamen nunc uberius hoc exponam trans- Syncs
eundo ad medicinam propter corpus humanum, cujus cognitio on in.
magis est homini necessaria quam alicujus rei alterius in hoc and

. mundo. Et non solum manifesto quomodo res in diversis organic
locis mundi cognoscuntur, sed quomodo in eisdem per tem-
porum diversa curricula causantur. Effectus vero non cog-
noscitur nisi per suam causam, ut certum est apud omnes; sed
coelestia sunt causae inferiorum, unde oportet quod sciant haec
generabilia per ingenerabilia quae sunt coelestia. Quod vero
coelestia non tantum sint causae universales, sed causae rerum
inferiorum propriae et particulares, probatur per Aristotelem,

qui dicit secundo de Generatione, quod elementa deterius agunt
quam organa et instrumenta artificialia respectu artificis. Sed

tota actio artificialis principaliter attribuitur artifici, ut aedifi-
catori, non ejus organo, ut securi. Ergo manifestum est quod:
coelo attribuitur operatio principalis omnium inferiorum, cum

non sint agentia nisi coelum et elementa quae sunt ejus instru-
menta. Praeterea hoc patet inductive. Nam in omnibus
inanimatis coelum est causa particularis sine contradictione ;
quia inanimata non generant aliquod, nec producunt individua

suae speciei quia lapis non generat lapidem, sicut homo
hominem et asinus asinum. Manifestum est igitur quod virtus
coeli incorporata in materiam elementorum producit omnia
inanimata, et animata per putrefactionem similiter: nam circa
eorum generationem non sunt nisi coelum et elementa. Prae-
terea dicit Averroes septimo Metaphysicae quod idem facit
virtus solis in materia putrefacta quod virtus patrum in
seminibus, quare necesse est coelum esse causam particularem
usque ad generationem rerum ex propagatione. Sed quod
similiter sit ibi probo. Nam in Vegetabilibus Aristoteles dicit
primo de plantis, quod sol est pater plantarum et terra mater ;

et in Animalibus vult illud idem ; quia de homine, de quo minus
videtur, dicit secundo Physicorum, homo generat hominem ex
materia et sol, et constat quod pater non continuat nec terminat
generationem, sed incipit tantum per decisionem seminis ;
quapropter oportet quod continuans et perficiens generationem

sit sol seu virtus coeli. Et non solum est coelum causa in

General
principles
of geo-
graphy.

Celestial
and
terrestrial
equator
and equi-
noctia
colure.

288 OPERIS MAJORIS PARS QUARTA.

recte generatis, sed in peccatis naturae et monstris. Nam
Avicenna decimo octavo libro de Animalibus dicit; Si embryo
non potest recipere humanitatem, recipiet animalitatem sicut
in rebus monstruosis: ut quando filius hominis habuit caput
arietis, et agnus habuit caput tauri: quoniam virtus in eo
induxit formam secundum figuras coelestes, quae accidunt
unicuique. Et si ulterius descendamus, possumus causas
rerum inferiorum magis prope investigare per coelestia. Primo
vero articulus hic est, quod quilibet punctus terrae est conus
unius pyramidis virtuosae coeli.

Ut hoc autem certius planiusque videatur quod intendimus,
necesse est considerare quae sit diversitas regionum mundi, et
quomodo eadem regio in diversis temporibus variatur, et
quomodo res diversae ejusdem regionis diversas recipiunt
passiones in eodem tempore. Sed haec sciri non possunt, nisi
quantitatem et figuram habitabilis terrae et climata ejus
distinguamus, Quatenus vero ad haec deveniamus, oportet
nos supponere mundum esse sphaericae figurae, sicut superius
est demonstratum. Et imaginabimur tres lineas a mundi
terminis ductas intersecantes se in centro mundi ad angulos
rectos, ut una sit a dextro in sinistrum in coelo, et hoc est
quod ab oriente in occidens per centrum mundi ducatur; alia
a sursum in deorsum, id est a meridie in septentrionem, et hoc
est a polo antarctico ad polum arcticum, et tertia ab ante et
retro, id est a puncto medii coeli supra nos usque ad punctum
oppositum in coelo sub terra. Et per quandam transump-
tionem vocabuli vocatur angulus terrae. Sic docet nos
Aristoteles imaginari sex diversas positiones in coelo in
secundo Coeli et Mundi.

Si igitur imaginabimur unum circulum transeuntem per
oriens, et medium coeli, et occidens, et angulum terrae, hic
dividit coelum in duas partes aequales, in medio ejus re-
linquens unam medietatem respectu unius poli, et aliam
respectu alterius, et vocatur aequinoctialis, et quia habitantes
sub eo habent perpetuum aequinoctium, et quia omnibus
habitatoribus terrae est aequinoctium quando sol venit ad
illum circulum et describit eam in die naturali: et hoc est
in principio veris et in principio autumni, quando sol

GEOGRAPHIA. 289

ingreditur capita Arietis et Librae. Si vero imaginemur
alium circulum magnum, qui transeat per polos mundi et
per fines orientis et occidentis, intersecantem priorem
circulum ad angulos rectos, qui vocatur colurus transiens
per aequinoctia, tunc coelum sic dividetur per quatuor quartas,
quarum duae erunt supra terram in situ nostro, et aliae
duae sub terra. Et erit una quarta septentrionalis supra
nos, scilicet quae continebitur inter medietatem aequinoc-
tialis circuli et duas quartas coluri dicti, terminatas ad polum
arcticum ex una parte, et ex alia ad puncta orientis et occi-
dentis apud aequinoctialem, ut patet in figura, et haec est
quarta pars quae est supra. Consimili autem modo oportet
nos imaginari terram sphaericam esse, et illae tres lineae
praedictae transibunt per centrum terrae intersecantes se in eo
ad angulos rectos; nam. sunt perpendiculares super eam, et
quia in earum intersectione est centrum coeli et totius mundi,
necesse est quod idem punctus sit centrum mundi et terrae;
quia intersectio ista non est nisi in puncto uno, per quintam primi
libri Theodosii de Sphaeris. Nam si linea recta descendat a
coelo perpendiculariter ad superficiem contingentem sphaeram
terrae, in ea erit centrum terrae, per illam quintam, quae
dicit, Si sphaeram plana superficies contingat, a puncto vero
contactus recta linea ad contingentem superficiem perpendicu-
lariter ducatur, in eadem centrum sphaerae esse necesse est:
sed illa eadem linea erit perpendicularis ad superficiem con-
tingentem sphaeram coeli, ergo in illa erit centrum coeli, et
haec linea est una trium dictarum. Similiter et utraque
aliarum per eandem rationem transibit per centrum coeli et
centrum terrae: sed quaelibet istarum non intersecat aliam
nisi in puncto uno, ergo in eodem erit centrum terrae cum
centro coeli, et propter hoc terra jacet in medio mundi. Et
ideo si imaginemur circulos duos in terra respondentes circulis
in coelo praetactis, unum sub aequinoctiali circulo trans-
euntem per oriens et occidens, et punctum in terra sub puncto
medii coeli; et alium, per occidens et oriens et puncta in
terra respondentia polis ; tunc per hos circulos dividetur terra
in quatuor quartas, quarum duae erunt in superficie terrae in
situ nostro; et alia ex altera parte terrae. Et una erit
VOL. I. U

What pro-
portion of
the earth's
surface is

habitable.

290 OPERIS MAJORIS PARS QUARTA.

septentrionalis, scilicet a medio terrae sub aequinoctiali usque
ad punctum terrae sub polo arctico contenta infra lineas quae
ab oriente et occidente concurrunt in polum sive punctum
terrae polo suppositum. Et haec est quarta quam quaerimus,
in qua est habitatio nota, et est sub quarta coeli prius notata.

Habitatio ! vero dupliciter consideratur ; uno modo respectu
coeli, scilicet, quantum propter solem potest habitari, et
quantum non. Et de hoc dictum est prius in universali, et
tangetur posterius. Alio modo consideratur quantitas habi-
tabilis respectu aquae, scilicet, quantum aqua impediat. Et
hoc est modo considerandum. Ptolemaeus vero in libro de
Dispositione Sphaerae vult quod fere sexta pars terrae est
habitabilis propter aquam, et totum residuum est coopertum
aqua. Etideo in Almagesti secundo libro ponit quod habi-
tatio nota non est nisi in quarta terrae, scilicet in qua
habitamus ; cujus longitudo est ab oriente in occidens, et est
medietas aequinoctialis; et ejus latitudo est ab aequinoctiali
in polum, et est quarta coluri. Sed Aristoteles vult in fine
secundi Coeli et Mundi quod plus habitetur quam quarta. Et
Averroes hoc confirmat. Dicit Aristoteles? quod mare parvum
est inter finem Hispaniae a parte occidentis et inter princi-
pium Indiae a parte orientis. Et Seneca libro quinto Natura-
lium dicit quod mare hoc est navigabile in paucissimis diebus, si
ventus sit conveniens. Et Plinius ? docet in Naturalibus quod

! This paragraph, including half of that which follows, has a remarkable
history. It is inserted without acknowledgement of its source in the Jmago
Mundi of Cardinal d'Ailly (Petrus Alliacus), who died 1425, and whose work
was printed at Louvain, 1480. It forms the greater part of the eighth chapter,
entitled, * De quantitate terrae habitabilis.’ From this work it was quoted by
Columbus in a letter written in October 1498 to Ferdinand and Isabella
from Hispaniola. See Jmago Mundi, fol. 13,b; and Humboldt, Examen
Critique, vol. i. pp. 61-70 and pp. 96-108: also Cosmos, vol. ii. p. 621 (Bohn's
ed.). Humboldt remarks that the Imago Mundi * exercised a greater influence
on the discovery of America than did the correspondence with the learned
Florentine Toscanelli.'

7 Arist. De Coelo, ii, 14, $ 15 80 rots iwoAapBdvovras avvásrew roy sepi rds
"HpaxAelovs arfjAas TÓwov TQ wept Tr)» 'I»Dujv, xal ToUrov roy Tpówov «lvai rip
0áAaTrav piay, pt) Alay bwoXauBárer dmora Boxety. Cf. Seneca, Nat. Quaest. i,
Prolog., ‘Quantum enim est quod ab ultimis litoribus Hispaniae usque ad Indos
jacet! Paucissimorum dierum spatium, si navem suus ferat ventus, implebit.'

* Pliny, Nat. Hist. ii. 63.

GEOGRAPHIA. 291

navigatum est a sinu Arabico usque ad Gades: unde refert
quendam fugisse a rege suo prae timore et intravit sinum
maris Rubri qui vocatur Arabicus, qui circiter spatium navi-
gationis annualis distat a mari Indico secundum Hieronymum
in epistola, ut inferius exponetur. Et ideo latitudo terrae per
quam decurrit mare Rubrum est magna valde ; ex quo patet
principium Indiae in oriente multum a nobis distare et ab
Hispania, postquam tantum distat a principio Arabiae versus
Indiam. A fine Hispaniae sub terra tam parvum mare est
quod non potest cooperire tres quartas terrae.

Et hoc per auctoritatem alterius considerationis probatur. More than
Nam Esdras! dicit quarto libro, quod sex partes terrae sunt att of the
habitatae et septima est cooperta aquis. Et ne aliquis cate te
impediat hanc auctoritatem, dicens quod liber ille est apo-
cryphus et ignotae auctoritatis, dicendum est quod sancti
habuerunt illum librum in usu et confirmant veritates sacras
per illum librum. Et pluries in officio divino «utuntur
auctoritatibus illius libri. Et ideo, sive Esdras sive alius
hunc fecerit, supponendus est pro auctoritate. Et propter hoc
dico quod licet habitatio nota Ptolemaeo et ejus sequacibus
sit coarctata infra quartam unam, plus tamen est habitabile.

Et Aristoteles potuit plus nosse, quia auctoritate Alexandri
misit duo millia hominum ad investigandum res hujus mundi,
sicut Plinius dicit octavo Naturalium. Et ipsemet Alexander
perambulavit usque ad finem orientis, et sicut patet ex
historia Alexandri et ex epistolis quas Aristoteli conscripsit,
semper mandavit ei de omnibus mirabilibus et insolitis quae
inveniebat in oriente. Et ideo potuit Aristoteles plus certi-
ficare quam Ptolemaeus. Et Seneca similiter; quia Nero
imperator discipulus ejus similiter misit ut exploraret dubia
hujus mundi, sicut Seneca narrat in Naturalibus. Et ideo
secundum haec quantitas habitabilis magna est et quod aqua
cooperitur modicum debet esse. Versus enim polos mundi
oportet quod aqua abundet, quia loca illa frigida sunt propter

1 What Bacon calls the fourth book of Esdras answers to the second book in
the Apocrypha, See ch. 6, v. 42, ‘Upon the third day thou didst command
that the waters should be gathered together in the seventh part of the earth:
six parts didst thou dry up.’

U 2

292 OPERIS MAJORIS PARS QUARTA.

elongationem a sole, sed frigus multiplicat humores; et ideo
a polo in polum decurrit aqua in corpus maris et extenditur
inter finem Hispaniae et inter principium Indiae non magnae
latitudinis, et vocatur Oceanus ; ut principium Indiae possit
esse multum ultra medietatem aequinoctialis cicculi sub terra
accedens valde ad finem Hispaniae. Sed ne verum hic pro
falso damnetur, oportet nos scire quod Hispania in hoc loco
accipitur non pro citeriori sed pro ulteriori, de quo auctores
certi loquuntur, ut Plinius! in Naturalibus et Merlinus in pro-
phetia sua, et Orosius in libro de Ormesta Mundi, et Isidorus
decimo quarto libro Etymologicorum. |. Quoniam docet quod
inter Hispaniam quae nunc vocatur et Africam nunc dictam
non fuit aqua decurrens, sed terra continua ab antiquis tem-
poribus, sed postea oceanus irruit in profunda terrae et con-
junxit se mari Tyrrheno, quod decurrit per littus Arragoniae
provinciae et Italiae. Citerior igitur Hispania a Pirenaeis
montibus usque ad Carthaginem porrigitur: sed ulterior
transit Gaditanum fretum usque in provincias Africae. Unde
extenditur ultra Gades Herculis et attingit montem Atlantem.
Haec necessario recitavi secundum auctores dictos, ne Aris-
toteles et suus commentator per ignorantiam ulterioris
Hispaniae deriderentur, cum dicunt ad probationem parvi-
tatis maris inter Hispaniam et Indiam quod elephantes sunt
tantum in illis duobus locis. Verum enim est quod circa
montem Atlantem abundant elephantes, ut Plinius dicit, sicut
et Aristoteles, et similiter in India, et ideo in ulteriori
Hispania est frequentia elephantorum ; sed Aristoteles dicit
quod elephantes in illis locis esse non possunt nisi essent
similis complexionis, et si essent multum distantes non haberent
similem complexionem, et ideo nec elephantes essent in illis
locis tantum. Quapropter concludit haec loca esse propin-
quiora, et ideo oportet quod mare sit parvum inter ea.

Non igitur mare cooperiet tres quartas terrae, ut aestimatur.
Nam sit medietas terrae superior a 4 c d, in cujus una quarta,
scilicet a0 c, est habitatio nobis nota. Jam patet quod multum

! Pliny speaks of the tradition that Spain was originally continuous with the
opposite African coast (lib. iii, pro&mium), But he never speaks of any part of
Africa as Hispania ulterior.

GEOGRAPHIA. 293

de quarta illa sub nostra erit habitatione, propter hoc quod
principium orientis et occidentis sunt prope, quia mare parvum
ea separat ex altera parte terrae. ' Et

ideo habitatio inter orientem etocciden- b

tem non erit medietas aequinoctialis cir-

culi, nec medietas rotunditatis terrae, nec

‘ duodecim horae, ut aestimant, sed longe “ c

=

plus medietate rotunditatis terrae et plus
quam revolutio medietatis coeli.’ Quan-
tum autem hoc sit, non est temporibus
nostris mensuratum, nec invenimus in
libris antiquorum ut oportet certificatum ; nec mirum, quoniam
plus medietatis quartae in qua sumus est nobis ignotum ; nec
sunt civitates a philosophis comprehensae, ut patebit ex
sequentibus. Similiter si loquamur de aliis duabus quartis, et
consideremus vias naturales secundum quod philosophia
naturalis decurrit, non erunt illae coopertae aquis, ut vulgus
mathematicorum aestimat. Nam cum poli et regiones versus
eos sint ejusdem remotionis a sole et planetis secundum com-
parationem polorum ad vias planetarum in medio mundi inter
duo tropica ; necesse est quod secundum haec aequales dis-
positiones sint in quarta nostra, et in quarta ultra aequinoctialem
versus alterum polum ; et similiter in quarta sub pedibus nostris
usque ad aequinoctialem ; et in quarta ultra aequinoctialem
erit consimiliscomplexio secundum tenorem praedictorum. Et
ideo si quarta nostra non est cooperta aquis saltem usque ad
latitudinem et distantiam ab aequinoctiali per 66 gradus, ut in
fine insularum Scotiae et in regno Norguegiae, manifestum est
quod similis causa naturalis erit in alia quarta ultra aequinoc-
tialem in superiori parte terrae sicut in illa in qua sumus, quia
elongatio a via solis inducit frigus, et frigus multiplicat
humorem, et ideo circa polos erit congregatio naturalis
aquarum, et in regionibus quae sunt prope. Et ideo in
altera quarta ultra aequinoctialem secundum hoc debet esse
multum habitabile ; saltem usque ad regiones quarum latitu-
dines sunt usque ad 66 gradus, sicut hic.

FIG. 22.

Caeterum potest argui secundum mathematicos major The ec-

habitatio ex defectu aquae ibi quam in quarta nostra,

orbit is
likely to
produce
more dry
Jand in the
southern
hemi-
sphere.

Descrip-
tion of the
known
world.

294 OPERIS MAJORIS PARS QUARTA.

quoniam in parte illa est oppositum augis solis, et sol
descendit ad terram ibi multum. Unde oportet quod com-
burat quartam illam in aliqua parte sui, et residuas usque ad
polum magis calefaciat quam partes nostrae quartae in qua
habitamus. Et similiter contingit persuadere de reliqua
quarta sub illa. Et iterum sumitur argumentum ad hoc per
Aristotelem in primo Coeli et Mundi et per Averroem, quod
reliqua medietas terrae ultra aequinoctialem circulum est
locus sursum in mundo et nobilior et ideo maxime competit
habitationi. Et propter hoc ex ordinatione naturae erit
quod impedimenta habitationis magis excludantur, saltem in
magna parte illiug medietatis, scilicet longius ab opposito
augis solis, si eccentricum ponimus, et ubique si non ponatur
eccentricus, et hoc propter stellas nobiliores in illa parte, ut
vult Averroes primo Coeli et Mundi. Et Ptolemaeus dicit in :
libro de Dispositione Sphaerae quod natura exigit ut sint duo
genera Aethiopum, scilicet sub duobus tropicis. Ex quo
arguunt aliqui quod habitatio est ultra aequinoctialem sicut
citra: et secundum haec non erit figura habitabilis quartae
sphaerae nec semicirculus descriptus in plano, nec aqua
circuet in circuitu mundi per polos et oriens et occidens co-
operiens tres quartas ejus, ut creditur: sed magis erit figura

PritNCIPIU INDIAE

Si 1YNOIQUIN
sng

nvauog smog

PRIMOIPIUM HISPAN.AE

FIG, 23.

aquae hujus vel consimilis, ita quod hoc mare vocetur Oceanus,
habens plurimum de aqua circa polos, cujus longitudo ex-
tenditur a polo in polum inter principium Indiae et finem
Hispaniae, quae est mathematicis nota.

Et quoniam non est mathematicis nota habitatio nisi in
quarta in qua sumus, et etiam non tota quae comprehenditur
intra medietatem aequinoctialis et medietatem coluri trans-

-0T 0T meme = IC — Geo FER —MMMMMÁÁEÉDMÓ EPI apud DR NQENDR aoo-

GEOGRAPHIA. 295

euntis per polos et extremitates medietatis aequinoctialis ! The seven
zones of
Ptolemy

sub hac figura, ideo in executione sententiae mathematicorum

oportet relinqui quod incertum est, et fieri sermonem de eo and Al-

quod philosophis magnis innotescit. Ptolemaeus? inter
omnes ab incarnatione Domini maxime certificavit in hac
parte, et in secundo Almagesti quartam istam, in qua sumus,
distinguit. Et ejus et Alfragani et aliorum divisio magis nota
est per septem climata famosa. Clima vero apud eos est
spatium terrae in quo dies prolixior excedit per dimidiam
horam diem prolixiorem alterius partis terrae, vel exceditur
ab eodem. Certum tamen est quod magis naturalis et verior
distinctio esset penes quartam horae, secundum quod
Ptolemaeus primo dividit: sed quia istae partes sunt parvae,
ideo considerant philosophi majores et conjunxerunt duas
illarum in uno climate. Et quoniam haec climata et civitates
famosae in eis non possunt evidenter percipi sermone, oportet

! The words, ‘et medietatem celuri . . . medietatis aequinectialis" are
printed twice over in Jebb's edition.

* In the first printed edition of Ptolemy's Cosmographia, dedicated to Pope
Sixtus IV, in 1478, there are twenty-seven maps: one of the World, ten of
Europe, four of Africa, twelve of Asia. These correspond exactly to the
description given in the eighth book of the Cosmographia. In all of them
parallels of latitude and meridians are given, as in modern Atlases. In his map
of the World, embracing as it did, on his system, 180 degrees of longitude and
8o degrees of latitude, a very elaborate and scientific attempt is made to project
those curved lines accurately on a plane surface. It appears probable that
these maps are the work of Agathodaemon of Alexandria a contemporary of
Ptolemy. (Bunbury, vol. ii. p. 578.]

The parallels of latitude are twenty-five in number: four of South latitude,
twenty-one of North. They are arranged according to the length of the day at
the Summer solstice, by intervals of one quarter of an hour. Beginning with
16° 25 S. where the longest day is thirteen hours, proceeding north to the
Equator where it is twelve; thence northwards to lat. 45°. From this point
the parallels are drawn at half-hourly intervals to lat. 58°, where the longest day
is eighteen hours. The next parallel is drawn at 61^, the day being nineteen
hours; the last at 63°, where it is twenty hours. This, says Ptolemy, is the
latitude of Thule. .

In Ptolemy's Atlas longitude is calculated in degrees and half degrees, taking
as the starting-point the meridian of the Fortunate islands (Ferro in the Canary
islands), which he wrongly estimated as being only 2? 30’ west of the Sacred
Promontory (Cape St. Vincent). Further, owing to his acceptance of Posidonius'
estimate of the Earth's magnitude, 180,000 stadia, his degrees of longitude as
measured on the Equator, were only 500 stadia (i.e. fifty geographical miles
instead of sixty).

fraganus.

296 OPERIS MAJORIS PARS QUARTA.

quod figura sensui ministretur!. Primo igitur figuram hujus
quartae cum climatibus suis ponam, et signabo civitates
famosas in locis suis per distantiam earum ab aequinoctiali,
quae vocatur latitudo civitatis vel regionis ; et per distantiam
ab occidente vel oriente, quae longitudo regionis vocatur. Et
in divisionibus climatum atque in latitudinibus et longitu-
dinibus civitatum utar auctoritate et experientia sapientum.
Sed in signatione civitatis in loco suo per longitudinem et
.datitudinem suam inventas ab auctoribus, superaddam arti-
" ficium, quo locus civitatis habeatur per distantiam ejus
. a meridie et septentrione et oriente et occidente. Et hoc
artificium consistit in concursu lineae rectae aequidistantis
aequinoctiali signatae in plano: secundum formam lineae
rectae ductae a numero graduum latitudinis regionis signato
in quarta coluri ducta ab aequinoctiali ad polum mundi in
concursum, inquam, cum arcu circuli magni qui transit per
polos mundi et per numerum longitudinis civitatis signatum
in aequinoctiali circulo. Hic autem modus melior est et
facilior, et sufficit considerationi locorum mundi in hujusmodi
figuratione sensibili.
Equatorial — Ostendam etiam cum latitudine cujuslibet climatis quot
sch of miliaria quodlibet contineat in se, et quot gradus in coelo
the zones, cuilibet respondeant, et quot horas habet dies prolixior.
Elevatio autem poli supra horizonta in quolibet climate est
latitudo ejus ab aequinoctiali, et distantia zenith capitis ab
aequinoctiali, idem cum latitudine et cum elevatione poli: et
pono numerum milliariorum totius spatii septem climatum.
Sed licet non notata sunt a philosophis nisi septem climata,
nihilominus tamen signant alia spatia terrae et ante climata *
et post. Nam Ptolemaeus dicit in libro de Dispositione
Sphaerae, quod perambulatum est auxilio regum Aegypti
usque ad aequinoctialem circulum. A paucis tamen et raro
pertransitum est hoc spatium ante climata propter distantiam
ejus, sed magis propter negligentiam principum qui philosophos
deberent juvare in hac parte. Signo ergo spatia tria ante
! It is evident from this and other passages that Bacon prepared a map of
the world to illustrate this part of the Opus Majus. No trace of it, however,

has been hitherto discovered.
* Ante climata, i. e. beyond 16° 25’, South latitude.

GEOGRAPHIA. 297

climata nota, quae plus de terra habent quam unum clima, et
pono numerum milliariorum latitudinis istius spatii inter
aequinoctialem et primum clima, et quot milliaria sunt ab
aequinoctiali usque ad finem septimi climatis; deinde divido
spatium quod est ultra climata. Et Ptolemaeus in secundo
Almagesti distinguit istud spatium per excessum quartae
unius horae adjectum super longitudinem diei in praecedenti
regione usquequo veniat ad latitudinem regionis quae est 1xi
gradus. Et postea per medietatem unius horae usque ad
latitudinem Ixiv graduum ; et ab illo loco dividit spatia per
unam horam usque ad latitudinem lxvi graduum ; ubi est
nox continua in solstitio hyemali, nisi quod medietas solis
fertur subito sub horizonte et est dies continuus in solstitio
aestivali, et hoc est ultra Scotiam longe. Et deinde semper
apparet sol in aquilone versus polum.

Sed tunc ulterius dividitur spatium notabiliter per quanti-
tatem diei unius mensis, vel duorum, vel trium, vel quatuor,
vel quinque, vel sex. Nam habitantes sub polo habent
dimidium annum diem, hoc est, solem supra horizonta per sex
menses et sub horizonte per alios sex ; sed tamen crepusculum
vespertinum durat per septem septimanas et unum diem,
scilicet, a sexto decimo die Septembris inclusive, in quo sol
ingreditur nunc temporis signum Librae usque ad sextum
diem Novembris exclusive. Etin tanto spatio est claritas solis
super terram, sicut apud nos in aestate accidit post occasum
solis : quia in illo die sexto est declinatio solis sub horizonte per
octodecim gradus et sex minuta ; et crepusculum durat usque
ad finem octodecim graduum et non plus. Et ab eodem die
sexto Novembris inclusive usque ad 21 diem Januarii inclusive
est nox obscura per decem septimanas et per quinque dies.
Nam in illo 21 die est sol sub horizonte octodecim gradibus et
sex minutis; et ideo non potest incipere crepusculum matu-
tinum in illo, sed oportet quod sol prius transeat illa sex minuta.
Sed ab illo die, scilicet 21 Januarii exclusive incipit aurora, et
durat usque ad ingressum solis in signum Arietis, et hoc est 13
die Martii nunc temporis, unde durat per septem septimanas
et unum diem. Et per residuum temporis dum sol vadit a
primo gradu Arietis usque ad primum gradum Librae est sol

Polar
regions.

Different
senses in
which East
and West
are taken.

298 OPERIS MAJORIS PARS QUARTA.

semper super horizonta eorum; et hoc est per dimidium
annum: quia horizon eorum est aequinoctialis circulus. Et
ideo sex signa septentrionalia sunt semper super horizonta, ut
apparet in sphaera ad sensum. Et ideo dum sol est in illis
signis habent diem manifestum. Et nihilominus duo crepus-
cula in quibus apparet claritas solis super horizonta simul
sumpta continent tres menses et quindenam et duos dies, et
ideo respectu crepusculorum et diei habitatores illius loci sub
polo parum habent de nocte per annum.

Haec omnia scripsi sequendo principaliter Ptolemaeum et
Alfraganum !, et tabulam de longitudinibus et latitudinibus
civitatum. Nam in latitudinibus climatum et spatiorum ante
climata et post secutus sum sententiam Ptolemaei in Alma-
gesti. Expansionem autem climatum per sua milliaria et
spatiorum ante climata et post, atque quae civitates et regiones
continentur in illis climatibus et spatiis, descripsi secundum
Alfraganum principaliter, nisi quod ipse non tangit praecise
computationes quas pono per examinationem majorem, atque
sequendo alios auctores aliquod immuto aliquando et addo,
secundum quod oportet propter certitudinem * majorem: ut
tetigi de civitate Syene.

Quod si objiciatur, quod in canonibus astronomiae et in
tabulis aliis invenitur aliter in longitudinibus et latitudinibus
civitatum, ut evidenter patet de Toleto, ad cujus meridiem
factae sunt tabulae? Toletanae ; dicendum est quod aliter et

! Ahmad Ibn Muhammad Ibn Kathir, commonly known as Alfreganus or
Alfraganus, lived early in the ninth century. His works on astronomy, geography,
and chronology were translated in the twelfth century by Joannes Hispalensis.
This version was very inaccurate, and a more correct one was made afterwards by
the Jew Jacobus Anatolius. The mathematician, Regiomontanus, gave lectures
on Alfraganus at Padua in the fifteenth century. His works were printed at
Nurimberg in 1537, together with a very interesting lecture on the history of
Mathematics by Regiomontanus. Another edition was published, apparently
from the corrected version, at Frankfurt, in 1590. The seven zones described
by Alfraganus, extend from the equator to lat. 45?. The parallels are arranged
according to the length of the day at the Summer solstice: the length in each
exceeding that of the parallel to the south of it by half an hour. See the two
editions referred to: also Cantor, vol. ii. p. 238, and Jourdain, p. 115

2 Alfonso X of Castile appointed a committee of astronomers to construct new
astronomical tables, In this work the Rabbi Isaac Ebn Sid Hazan played an

important part. ‘ Their principal defect was the introduction of an inequality
in the motion of the fixed stars in longitude by which this motion appeared

GEOGRAPHIA. 299

aliter accipiunt oriens et occidens. Nam oriens et occidens The _
de quibus hic loquimur sunt ultima terrae habitabilis. Sed }ipronsine
uno modo accipiuntur oriens et occidens sub aequinoctiali
circulo in medio terrae; ita quod principium Indiae sub
aequinoctiali est oriens habitabilis ; et finis Hispaniae ulterioris,
si extenderetur usque ad aequinoctialem circulum, esset
occidens; sed non tantum extenditur, immo est magnum
spatium terrae a meridiana parte Hispaniae ulterioris usque
ad aequinoctialem. Finis igitur istius spatii a parte occidentis
est occidens habitabilis. Sed cum terra a parte occidentali
habeat magnam latitudinem, scilicet ab aequinoctiali usque
ad montem Atlantem et Gades Herculis, et citra per totum
circuitum Hispaniae totius et Hiberniae, possunt diversi
diversimodo accipere occidens ; unde aliqui accipiunt a Gadi-
bus, aliqui a monte Atlantis, aliqui a fine habitabilis sub aequi-
noctiali. Sed cum accipitur sub aequinoctiali, certius accipitur,
quia illud uno modo est et melius, quia hoc est in medio
mundi inter duos polos, et ideo est verum occidens; et eodem
modo est de oriente. Tabula vero latitudinum et longi-
tudinum non accipit longitudines ab occidente sub aequi-
noctiali, ut certum est. Nam sic longitudo Toleti est viginti
novem graduum ab occidente, et secundum tabulam non est
nisi undecim. Et auctor illius tabulae sumpsit occidens ei
notum et certum et respectu situs suae regionis. Consideran-
dum vero hic est quod oriens et occidens in divisione terrae
non possunt sumi nec debent nisi penes ultima terrae, ubi
mare quod vocatur Oceanus deficit, qui extensus est inter
Indiam et Hispaniam ulteriorem et regiones alias occiden-
tales et orientales, quae sequuntur Indiam et Hispaniam.
Unde non debent accipi penes oriens et occidens secundum
fines alicujus orientis, secundum quod nos dicimus aliquando
oriens et occidens penes ortum et occasum solis, Nam

to be sometimes accelerated and sometimes retarded. It was known as the
trepidation of the fixed stars, or the motion of the eighth sphere. This
imaginary inequality continued to disfigure the best tables till the time of
Copernicus, See Library of Useful Knowledge, History of Astronomy, p. 38.

Previous tables had been constructed at Toledo in the eleventh century by
Arzachel. It does not appear quite certain whether it is to those that reference
is made, or to those of Alfonso.

Determina-
tion of
longitude
and
latitude.

Bacon’s
map.

More
accurate
determina-
tion of

300 OPERIS MAJORIS PARS QUARTA.

infiniti sunt horizontes tam obliqui quam recti. Et ideo oriens
et occidens in divisione terrae non sumuntur penes horizonta;
tunc enim quod esset oriens unius horizontis esset occidens
alterius horizontis, et medium ejus.

Et notandum quod verum occidens et oriens sub aequi-
noctiali circulo est, ut dictum est: et hoc est ad ultimum
habitabile ulterioris Hispaniae pro occidente et ad ultimum
Indiae ulterioris pro oriente. Si igitur volumus sumere dis-
tantiam civitatis ab occidente nunc dicto ducemus unam
lineam ab hoc occidente aequidistantem civitati, et “linea
intercepta inter civitatem et dictam aequidistantem dengtabit
longitudinem ejus ab occidente. Et similiter ducatur una
linea ab Arym! civitate in medio mundi usque ad polum
arcticum, et ab ea ducatur linea recta usque civitatem, quae
notabit distantiam civitatis a medio mundi. Sed aliquando
accipitur distantia ab occidente respectu finis habitabilis in
directo illius civitatis: et quia hoc variatur infinitis modis
apud diversos habitantes, variatur sumptio longitudinum.
Sed melior acceptio est ab occidente sub aequinoctiali, quia
hoc est uno modo. Et quia aliarum civitatum a Toleto
longitudines et latitudines non inveniuntur congregatae nisi
in hac tabula, ideo secutus sum eam in hac parte. Quam-
quam major certitudo requiratur, quia nondum apud Latinos
certificatae sunt longitudines et latitudines civitatum et
regionum ; nec unquam certificabuntur nisi per apostolicam
auctoritatem vel imperialem, aut per auxilium alicujus regis
magni praebentis philosophantibus adjutorium. Secundum
igitur praedicta praesentem affero descriptionem in albiori
parte pellis?, ubi civitates notantur per circulos rubros; nam
in alia parte pellis alia descriptio poterit assignari propter
evidentiam majorem locorum mundi. Et hanc secundam
descriptionem addo propter summam utilitatem locorum.

Quoniam igitur locorum mundi cognitionis maxima utilitas
est, ideo aliam descriptionem oportet afferri. Nam res
mundi sciri non possunt nisi per notitiam locorum in quibus

! O. has ab arcu civitatis, which is clearly wrong. See note on p. 310.
3 Another reference to the lost map included in the writings sent by Bacon
to the Pope.

—

--— ^» Hp ~— eee

GEOGRAPHIA. 301

continentur. Locus enim est principium generationis rerum, latitudes
ut dicit Porphyrius; quia secundum diversitatem locorum longitudes
est diversitas rerum ; et non solum naturalium, sed moralium necessary
et scientialium, ut videmus in hominibus quod secundum {ledge
diversitatem regionum habent mores diversos et occupant 9 man and
se in artibus et scientiis diversis. Quia igitur philosophia
intromittit se rebus mundi, multum ei deest adhuc apud
Latinos, postquam non habet certificationem locorum mundi.

Sed haec certificatio stat in cognitione longitudinis et lati-

tudinis cujuslibet loci; tunc enim sciremus sub quibus stellis

est quilibet locus, et quantum a via solis et planetarum, et
quorum planetarum et signorum loca recipiant dominium,

quae omnia faciunt diversas complexiones locorum: quae si
scirentur, possit homo scire complexiones omnium rerum

mundi et naturas et proprietates quas a virtute loci contra-

hunt.

Et hoc requirit non solum philosophia, sed sapientia Dei (2) For
cujus series tota decurrit per loca mundi. Unde sensus inim
literalis stat in cognitione locorum mundi, ut per convenientes ment of the
adaptationes et similitudines sumptas ex rebus eliciantur
sensus spirituales. Nam haec est propria expositio scripturae,
ut superius manifestavi in exemplo. Et haec cognitio locorum
mundi valde necessaria est reipublicae fidelium et conversioni
infidelium et ad obviandum infidelibus et Antichristo, et aliis.

Nam propter diversas utilitates reipublicae et propter praedi-
cationem fidei mittuntur homines ad loca mundi diversa, in
quibus occupationibus valde necessarium est proficiscentibus
ut scirent complexiones locorum extraneorum, quatenus
scirent eligere loca temperata per quae transirent, Nam
valentissimi homines aliquando ignorantes naturam locorum
mundi seipsos Christianorumque negotia peremerunt, eo quod
loca nimis calida in temporibus calidis aut nimis frigida in
frigidis transierunt. Receperunt etiam pericula infinita, eo
quod nesciverunt quando intraverunt regiones fidelium, quando
schismaticorum, quando Saracenorum, quando Tartarorum,
quando tyrannorum, quando hominum pacificorum, quando
barbarorum, quando hominum rationabilium. Deinde qui
loca mundi ignorat, nescit non solum quo vadit, sed quo

(3) For
knowledge
of the ten
tribes and
of Anti-
christ.

302 OPERIS MAJORIS PARS QUARTA.

tendat; et ideo sive pro conversione infidelium proficiscatur,
aut pro aliis ecclesiae negotiis, necesse est ut sciat ritus et
conditiones omnium nationum, quatenus proposito certo
locum proprium petat; ne, si velit Paganos adire, cadat
in idololatras, vel si illos intendat, scismaticos invadat, vel
pro scismaticis obedientes Romanae ecclesiae eligat, aut in-
differentes utrique parti, cujusmodi sunt populi qui vocantur
Aas; quatenus etiam Nestorianos desiderans Nicholaitas
declinet ; et sic multis gentibus sectarum diversarum ne unam
pro alia eligat oberrando. Quamplurimi enim a negotiis
Christianorum maximis sunt frustrati eo quod regionum
distinctiones nesciverunt.

Deinde non modica necessitas sciendi loca mundi oritur ex
hoc, quod oportet ecclesiam optime scire situm et conditiones
decem tribuum Judaeorum, qui exibunt in diebus futuris.
Nam Orosius in libro de Ormesta Mundi ad Augustinum libro
tertio dicit; Ochus, qui est Artaxerxes, plurimos Judaeorum
in transmigrationem egit, atque in Hyrcania ad Caspium mare
habitare praecepit; quos usque in hodiernum diem amplis-
simis generis sui incrementis consistere atque exinde quando-
que erupturos opinio est. Et magister in historiis addit, quod
Alexander magnus conclusos ibi invenit, et ob malitiam eorum
arctius eos constrinxit, quos tamen egressuros circa finem
mundi testatur, et magnam stragem hominum esse facturos.
Et in Cosmographia sua Ethicus astronomus! dicit gentes
varias debere exire circa dies Antichristi, et eum vocabunt
Deum Deorum, prius mundi regiones vastaturi. Et Hiero-
nymus hoc confirmat in libro quem transtulit de sapientiis
hujus philosophi.

! Under this title two geographical writers of the early middle ages are
often confounded. One is Julius Honorius, sometimes spoken of as Julius
Aethicus. The work of the other is known as Cosmographia Aethia bina,
written in barbarous Latin, and fabulously said to have been translated from
the Greek by St. Jerome. To the first is perhaps due (or on the other hand his
work may be a modification of) the summary of geography prefixed to the
history of Orosius. The second, purporting to be written by a mysterious
traveller who visited all parts of the known, and many of the unknown, world,
is a treatise wholly without value, except on the ground of its popularity as
a text-book of geography in the middle ages, (Cf. Bunbury, vol. ii. pp. 692-3,
and pp. 703 -5-)

GEOGRAPHIA. 303

Et Alexander magnus cum eis pugnavit, sed superare non Attempts
"potuit, sicut iste Ethicus testatur et refert Hieronymus, QA dte
ideo ingemuit et ait, ‘Gentes rationabiles et sapientes vasta- control in-

. oe . . . cursions of
vimus, attrivimus populum inclytum et sublimem ac sinceram dangerous
gentem. Quid utilitatis aut necessitatis fuit? cum omnes tribes.
inferorum daemones et adversariorum phalangas hic relinqui-
mus in humana specie latitantes. Item ne quando audiant
vel percipiant terram mellifluam et uberrimam mundi gloriam ;
ne forte irruant in universam superficiem terrae, et quasi
panem cuncta decerpant atque deglutiant. O terra, mater dra-
conum, nutrix scorpionum, fovea serpentum, lacus daemonum,
facilius fuerat in te infernum esse quam tales gentes par-
turire. Vae terrae fructiferae et mellifluae, quando ingruent tot
serpentes et bestiae ineam. Vae habitatoribus orbis, cum istae
coeperint triumphare : contra quos nisi ad tempus posuisset
Alexander remedia, nulla gens aut populus oppressionem
illorum ferre potuisset. ut scribit Hieronymus. Quando igitur
hae nationes inclusae in locis certis mundi exibunt in desola-
tionem regionum et obviabunt Antichristo, multum deberent
Christiani et maxime ecclesia Romana considerare situm
locorum, ut posset percipere hujusmodi gentium feritatem et
per eos percipere tempus Antichristi, et originem ; nam debent
obedire ei: ergo si illi ex una parte mundi veniant, ipse ex
contraria procedet, quando autem claustra Alexandri rupta
sunt. Nam aliqua fuerunt ante Isidorum quassata, quoniam
scribit de eis. Atque frater Willielmus!, quem dominus rex
Franciae misit ad Tartaros anno Domini 1253, quando fuit
ultra mare, scripsit regi nunc dicto quod transibat cum
Tartaris per medium portarum quas Alexander construxit.
Quando enim non potuit vincere has gentes, tunc ut scribit
Ethicus et confirmat Hieronymus, Alexander immolavit
hostias Deo et deprecatus est tota nocte et die Dei miseri-
cordiam et consilium, et divina potentia affuit terrae motus
magnus, et convenerunt montes adversus montes, et approxi-

! More will be said on this subject in a subsequent note. For an account of
Alexander's gates, and the nations enclosed by them, see Aethiopian version of
the pseudo-Callisthenes, edited by Mr. Wallis Budge, pp. 230-238 (1896). See
also Marco Polo, i. 4 (vol. i. pp. 49-50, Yule's ed.).

304. OPERIS MAJORIS PARS QUARTA.

maverunt per stadium unum usque ad spatium unius quadrigae,
et ipse tunc erexit portas mirae magnitudinis et linivit eas
bitumine incognito, quod nec igne nec ferro nec aqua nec
aliqua re dissolvi potest, nisi solo terrae motu violento.
Quoniam igitur infinita est utilitas cognitionis locorum
hujus mundi pro philosophia et theologia et ecclesia Dei, volo
Perd from adhuc alium sermonem de hujusmodi locis componere et
Pliny and divisiones regionum evidentiores assignare ; et sequar Plinium
wlters, abundantius, quem omnes sancti et sapientes sequuti sunt.
Ubi autem aliquod certum per alios auctores invenero tam
per sanctos, ut Hieronymum, Orosium, Isidorum, quam per
alios auctores, non negligam quae necessaria sunt assignare.
Sed regionum nobis notarum divisiones particulares non
oportet annotare, similiter nec loca singula in aliis regionibus,
sed magis notabilia et famosiora in scriptura et philosophia ;
de quibus gentes tyrannicae venient et venerunt, quae mundum
referuntur de praeterito vastasse aut aliquando vastaturae.
Et assignabo ritus et sectas gentium, ut qui sunt Pagani, qui
idololatrae, qui Tartari, et sic de aliis, ut certior apprehensio
locorum pateat perlegenti. Haec autem via, qua procedam,
non est per certificationem astronomiae, scilicet per veras
longitudines et latitudines! locorum respectu coeli; quía
nondum habent eam Latini, sed est sumpta ex auctoribus qui
mundi regiones describunt secundum quod quilibet potest
loca natalis soli describere, et per alios de locis extraneis
edoceri.
partly from Non nunquam tamen plura reperiuntur scripta, quae ex

reports of
travellers.

Special hi
geographi-
cal ie

1 In Ptolemy’s Atlas, lines of longitude and latitude are drawn, so as to give
an appearance of precision to his maps, which in reality they do not possess.
His conception of what a map ought to be was derived from Hipparchus, and is
thoroughly scientific. Having made these maps, he drew up a list of places with
the precise latitude and longitude (to the twelfth part of a degree) assigned to
each. But these positions are in the immense majority of cases purely hypo-
thetical, and are determined by the best estimate he could get from travellers’
reports.

Considering the immense reputation of Ptolemy during the middle ages, it is
extremely remarkable that Bacon should have seen so clearly the fallacious
character of this side of Ptolemy’s work, and should show himself so clearly
aware of the necessity for accurate determination of the latitude and longitude
of each place by astronomical observation. Cf. p. goo.

GEOGRAPHIA. 305

rumore magis quam per experientiam habuerunt auctores.
Nam et Plinius minus bene dixit mare Caspium oriri ex mari
Oceano, et Ptolemaeus in Almagesti de plano erravit de situ
Britanniae majoris et minoris, sicut manifestum est cuilibet, et
sic isti de aliis multis, et caeteri auctores similiter. Propter
quod recurram ad eos qui loca hujus mundi pro magna parte
peragrati sunt. Et maxime in regionibus aquilonaribus
sequar fratrem praedictum, quem Dominus Rex Franciae
Lodovicus misit ad Tartaros anno Domini 1253, qui perlus-
travit regiones orientis et aquilonis et loca in medio mundi
his annexa, et scripsit haec praedicta illustri regi; quem
librum diligenter vidi, et cum ejus auctore contuli, et similiter
cum multis aliis, qui loca orientis et meridiana rimati sunt.
Sicut tantam priorem descriptionem feci, magis propter exem-
plar et excitationem Gloriae Vestrae, ut compleatur suo
tempore per sapientes hujus mundi, quam propter certifica-
tionem, sic et hanc divisionem noto ut Vestra Sapientia
recognoscat quod major labor hic requiritur, quam praesens
persuasio debeat continere. Scriptura 'enim perfecta quam
requiritis habet utramque descriptionem perficere.

Expediendo quidem naturalium et experimentatorum in- Triabited
super sanctorum sententias circa partes habitabiles non oportet "£5,
nos coarctari in his quae mathematici apud Latinos certifi- the
carunt; nam pauca sunt haec; sed latius progredientes nator.
auctoritate et experientia multiplici roborati dicimus quod
non solum septem climata habitantur, sed quarta terrae, et
plus longe quam quarta, hominum continet nationes. Nam
invenimus apud Plinium et alios, quod quaedam loca sunt in
nostro habitabili, quae ascia dicuntur, id est sine umbra, ab
a quod est sine, et scia quod est umbra, et haec multis modis
variantur. Nam in aliquibus locis res non habent umbram
aquilonarem nec meridianam in solstitio aestivali. Nam
quando sol fertur supra capita eorum in meridie, non est
aliqua umbra neque ad septentrionem vel ad meridiem, neque
ad orientem vel occidentem, et hoc est in insula Nili quae
dicitur Syene, quae est in suprema parte Aegypti in confinio
illius et Aethiopiae, sicut patet ex Plinio in libro secundo et
quinto; et Lucanus dicit * umbram nullo flectente Syene’; id

VOL. I. X

The habit-

able region
may extend

306 OPERIS MAJORIS PARS QUARTA.

est, in meridie solstitii aestivalis, et hoc est versus finem se-
cundi climatis, de qua in Ezechiele pluries sermo fit. Alialoca
dicuntur ascia, quia bis in anno umbram non habent. Nam
quaedam in aestate nostra projiciunt umbram in austrum,
solem ad aquilonem habentes. Et in hyeme nostra, faciunt
umbram ad aquilonem, quoniam sol est in austro, secundum
Plinium secundo libro: et haec alternatio umbrae fit per senos
menses, sicut Plinius dicit sexto libro, capitulo decimo nono.
Quod impossibile est fieri, nisi sub aequinoctiali, quoniam
licet ei qui habitant inter tropicum Cancri et aequinoctialem
habeant varietatem multiplicem de umbris projiciendis nunc
ad aquilonem nunc ad meridiem, tamen non possunt habere
hanc varietatem per menses sex, sed plus projicient umbram
in aquilonem quam in meridiem ; quia solem plus habent ad
meridiem quam aquilonem ; sed illi qui sub aequinoctiali
circulo sunt, habent aequaliter solem ad septentrionem et
meridiem, scilicet per senos menses utrumque. Et haec gens
in India Orestes dicuntur et Monedes et Simari, apud quos
est mons Malcus nothine, in quo umbrae sic per senos menses
variantur, ut dicit Plinius secundo et sexto libro. Sed, quod
plus est, invenimus per eum habitationem fieri sub tropico
Capricorni ultra. Nam regio Pathalis in India dicitur habens
portum, ut dicit, celeberrimum, ubi umbrae solum in meridie
cadunt; ergo habitatores ejus habent semper solem ad Aqui-
lonem. Et idem refert sexto libro de insula Taprobane in
India, de qua homines, cum Romam venerunt Claudii princi-
patu, mirati sunt quod umbrae eorum cadebant in Aquilonem
et quod sol a meridie oriebatur; et ideo apud eos umbrae cadunt
semper in meridiem, et sol semper oritur eis aquilonaris !.

Et ideo verum est quod Ptolemaeus dicit libro de dispositione
sphaerae, quod natura exigit ut sint duo genera Aethiopum

beyond the sub duobus Tropicis. Quod si sol habeat eccentricum, tunc

tropic of
Capricorn.

licet quantum ad naturalem coeli dispositionem erit locus
inhabitabilis in superficie terrae propter calorem, quando sol

! Pliny, Hist. Natur. lib. vi. cap. a2 ‘Sed maxime mirum iis erat umbras suas
in nostrum caelum cadere, non in suum : solemque a laeva oriri et in dexteram
occidere potius quam e diverse.’ As Ceylon is in north latitude these men must
have come from far more distant and southerly regions.

GEOGRAPHIA. 307

venit ad Sagittarium et Capricornum propter appropinqua-
tionem ejus ad terram, et propter confusionem aequidistantium,
et propter casum radiorum ad angulos rectos ; et inhabitabilis
propter frigus, quando est in Geminis et in Cancro, quia sol
tunc nimis recedit ab eis, et cadunt radii ejus ad angulos
obliquos; tamen propter alias dispositiones locorum acci-
dentales, tum propter altitudinem montium prohibentium
calorem solis, tum propter alias causas, possunt aliqua loca ibi
esse habitabilia et maxime in locis subterraneis, quando sol
est circa oppositum Augis. Et alibi potest esse talis planities
inter eos et solem, et a posteriori talis montium laevitas et
figuratio ad modum speculorum concavorum et comburentium,
quod loca possunt esse habitabilia quando sol est in Auge
non obstanti frigore, sicut prius dictum est de locis circa polos
mundi!. Quod si ponamus solis concentricum cum epicyclo,
sicut possibile est, ut dicit Ptolemaeus in Almagesti, tunc de
facili potest salvari habitatio illius loci, quia tunc sol non
tantum accedit ad terram ut omnino comburat eam sub
tropico hyemali, nec tantum recedit ab ea ut eam frigore
destituat. Quod si nec epicyclum nec eccentricum ponamus
ut naturales aestimant, tunc nullum inconveniens sequitur de
habitatione. Et ideo quamcunque opinionem in hac parte
sequamur potest Plinius salvari. Et necesse est, quia ex-
perientia certa docuit eum saltem per eos qui de Taprobane
insula venerunt in Romanam civitatem, et per eos qui ad
insulam perducti sunt. Sed quamvis locus ultra tropicum
Capricorni sit optimae habitationis, quia est superior pars in
mundo et nobilior per Aristotelem * et Averroem primo Coeli
et Mundi, tamen non invenimus apud aliquem auctorem terram
illam describi, nec homines illorum locorum vocari, nec quod
ad nos venerunt, nec nostri ad eos. Et ideo opinio aliquorum
est quod ibi sit paradisus, cum sit locus nobilissimus in hoc
mundo secundum Aristotelem et Averroem secundo Coeli et
Mundi. Sed non solum philosophi, sed sancti, ut Ambrosius

! See p. 134.

* De Coelo, ii. a, § 8 r&v 82 wbrew Ó piv bwip $pás $awóptvos T) xara pépos
lorír, 6 3’ piv ddnros rd dye. We see here the origin of the view as to the
position of the terrestrial Paradise described in the Purgatory of Dante.

X 2

Pliny and
otheis have
shown how
far it
reaches
northward.

Fast and
west, it is
far larger
than is
commonly
thought.

308 OPERIS MAJORIS PARS QUARTA.

in Hexaemeron et Basilius in hac umbrarum diversitate con-
cordant. Nam quarto libro dicit Ambrosius, * sunt qui per duos
totius anni dies sine umbra sunt in partibus meridianis, eo
quod solem habentes super verticem suum undique per cir-
cuitum illuminantur ; unde ascii dicuntur, id est, sine umbra; et
amphiscii, id est, circum umbrati; et hi sunt sub aequinoctiali
et circiter ab utroque latere, qui quando sol non est super
eorum capita projiciunt aliquando umbram in aquilonem
aliquando in meridiem, secundum quod sol nunc est ad aqui-
lonem, nunc ad meridiem eorum ' ; et addit ‘quod sunt in hoc
quem nos incoluimus orbe terrarum circa meridiem positi, qui
in australem plagam videntur umbram transmittere. Quod
signanter dicit de umbris meridianis, potest intelligi de his qui
solas habent umbras meridianas, scilicet sub tropico Capricorni
et ultra; quia semper sol est eis ab aquilone, nisi quando
semel est super capita eorum in tropico Capricorni.

Quantum vero habitetur versus aquilonem Plinius ostendit
quarto libro per experientiam et auctores varios. Nam usque
ad locum illum habitatur ubi extremi cardines mundi sunt; et
ubi est dies per sex menses et nox per tantum. Et Martianus
in sua mundi descriptione concordat; unde volunt quod sit ibi
gens beatissima, quae non moritur nisi satietate vitae, ad
quam cum venerit praecipitat se alto saxo in mare; et
vocantur hyperborei de Europa et Arumphei in Asia. Haec
igitur dicta sunt secundum latitudinem regionum quae est ab
aequinoctiali citra vel ultra, ut videamus quod habitatio
excedit quartam secundum latitudinem regionum.

Quod similiter potest patere secundum longitudinem, quae
consideratur ab oriente in occidens. Nam, ut Plinius sexto libro
naturalium scribit, sola India est pars tertia! habitabilis. Nam
gentes habet centum et decem et octo. Et Hieronymus dicit
ad Rusticum monachum, * Navigantes rubrum mare multis
difficultatibus ac periculis ad urbem maximam perveniunt.

1 Pliny, Hist. Natur. lib. vi. cap. 17, 18. He states this on the authority of
writers who accompanied Alexander. * Alexandri Magni comites ... scripserunt
. . .Indiam tertiam partem esse terrarum omnium, multitudinem populorum in-
numeram, probabili sane ratione. Pliny had said (lib. iii. cap. 1), somewhat
inconsistently, that Europe was perhaps half the habitable world.

GEOGRAPHIA. 309

Felix cursus, si post sex menses supradictae urbis portum
teneant, a quo se incipit aperire oceanus, per quem vix anno
perpetuo ad Indiam pervenitur. Ergo a portu rubri maris
versus nos exigitur navigatio usque Indiam per annum et
dimidium. Et Hieronymus dicit libro locorum, quod classis
Solomonis per triennium ab India deportabat commercia, ut

anno et dimidio navigarent usque ibi, et tanto tempore
redirent. Sed immensa est distantia rubri maris usque ad finem
ulterioris Hispaniae circa montem Atlantem. — Manifestum — '
est igitur quod a fine occidentis usque ad finem Indiae supra‘ f^:
terram erit longe plus quam medietas terrae; ut cadamus' :
necessario in opinionem Esdrae et Aristotelis et Averrois,

quae superius tacta est de magnitudine habitationis inter
oriens et occidens, quae quartam terrae secundum longitudinem
excedit. Cum vero dicat Plinius, Europam esse majorem

Asia, non includit ibi Indiam sub ea propter Indiae magni-
tudinem ; cum sit tertia pars habitabilis secundum eum, ut
dictum est.

His consideratis in summa circa magnitudinem habitationis, Special de-
nunc partes aliquas magis famosas in scriptura et in philosophia 55.55 °"*
notare dignum est ; et quas utile est sciri a Christianis propter India and
infidelium conversionem, et propter negotia diversa cum diver- Ceylon.
sitate gentium tractanda, ac propter utilitates ecclesiae contra
furorem Antichristi et eorum qui tempora ejus praevenire
creduntur, ut mundum primo vastent donec tribulatio maxima
veniat per Antichristum. Et hic non solum necessaria est
depictio locorum et figuratio, séd narratio eorum quae depingi
debent; neutrum enim sufficit. Sequar vero auctores et
. experimentatores ea diligentia qua valeo quantum modo
sufficit, usquequo perfecta locorum doctrina requiratur. Et
incipiam a meridianis et orientalibus partibus, praecipue propter
scripturam, quae loca illa magis frequentat. Dico igitur
secundum praedicta, quod frons Indiae meridianus pellitur ad
tropicum Capricorni propter regionem Pathalis! et terrarum

! The port of Patale is noted by Pliny (ii. 73) as a place where the sun was
in the north at noon, and the shadows were thrown southwards. It may be
noted here that Bacon's general method in this description is to pass from East
to West in the equatorial region, then to return from West to East in a higher

Arym ; or
Syene.

310 OPERIS MAJORIS PARS QUARTA.

vicinarum, quas alluit brachium maris magnum descendens
a mare oceano, quod est inter Indiam et Hispaniam ulteriorem
seu Africam, de quo superius dictum est secundum Aristo-
telem. Quod enim mare tangat meridiana Indiae hoc expresse
dicit Plinius, et per Hieronymum patet,et Alfraganus similiter
hoc testatur. Et illud mare decurrit per regiones Indiae
meridianas, et annua navigatione protrahitur donec concurrat
mare rubrum, sicut planum est per Hieronymum et Plinium
et caeteros; et in illo mari ad Eurum respectu Indiae est
insula Taprobane distans per mare Nadosii septem dierum
navigatione in qua non videntur septentriones et vergiliae.
Auro et argento et gemmis pretiosis abundant, majoresque
opes eorum sunt quam Romanae. Sed apud Romanos major
usus opulentiae, ut recitat Plinius. Et eligitur apud eos rex
senex et clemens, liberos non habens ; quod si postea habeat
filios, non fit regnum haereditarium. Regi dantur rectores
triginta, quorum utatur consilio in regimine populi; qui si
delinquat criminaliter, morti judicatur, ita tamen quod nullus
manum ei imponat: sed alimenta et omnia ei denegantur,
etiam nullus cum eo loquitur, unde per se deficit. Vita
hominis apud eos centum annorum modica est!.

Meridianum vero latus Indiae descendit a tropico Capri-
corni, et secat aequinoctialem circulum apud montem Malcum
et regiones ei conterminas et transit per Syenem, quae nunc
Arym? vocatur. Nam in libro cursuum planetarum dicitur
quod duplex est Syene; una sub solstitio, de qua superius,
alia sub aequinoctiali circulo, de qua nunc est sermo, distans
per nonaginta gradus ab occidente, sed magis ab oriente
elongatur propter hoc, quod longitudo habitabilis major est
quam medietas coeli vel terrae, et hoc versus orientem. Et
ideo Arym non distat ab oriente per nonaginta gradus tantum.
Sed mathematici ponunt eam in medio habitationis sub aequi-

latitude ; then from East to West in a still more northerly parallel. He does
not, however, always abide strictly by this plan.

! See Pliny, vi. 22.

* Arym was supposed to be situated on the equator, midway between West
and East. Apparently some of the tables of longitude used by Arabian geo-
graphers took it as a point of departure. It was of course quite distinct from
Syene on the Nile, which in Ptolemy's map was not more than 6o? E.

GEOGRAPHIA. gi

noctiali distans aequaliter ab occidente et oriente, septentrione
et meridie. Nec est contradictio, quia mathematici loquuntur
de habitatione eis nota secundum veras comprehensiones
longitudinum et latitudinum regionum : et hoc non est tantum
quantum notum est per experientiam itineris et navigationis
apud Plinium et alios naturales. Secundum vero quod prae-
tendunt auctores et maxime Plinius, mare Indicum decurrens
per latus Indiae a tropico Capricorni secans aequinoctialem
transit per latus meridianum Indiae; deinde immensum
spatium terrae absorbens flectit se versus occidens per meri-
diem, donec recipiat fauces maris rubri et ostia ejus, decurrens
versus aequinoctialem ultra meridiana Aethiopiae in mare
occidentis !.

Et inter fauces maris rubri et mare Aethiopum incipit Aethi- Aethiopia.
opia. Et ubi latitudo regionis est circiter sedecim gradus,
et longitudo diei prolixior fere tredecim horis secundum
Ptolemaeum in Almagesti, et Plinius satis concordat sexto libro
et secundo, est Saba, insula Nilo inclusa, civitas regalis Aethi-
opiae, de qua in Isaia ‘labor Aegypti, negotiatio Aethiopiae et Meroe.
Sabaim,’ super quod decimo tertio libro dicit Hieronymus, quod rell.
est gens Sabaea quae est trans Aethiopiam. Et haec est Meroe,
quae est in ultimo Aethiopiae et in fine habitabilis notae,
secundum quod prius dictum est, et in Ezechiele xxvii, quam
Josephus primo antiquitatum a Cambyse rege Meroen cog-
nominatam ex sororis vocabulo refert, et hoc Hieronymus
testatur libro locorum. Quae civitas distat a mari Aethiopico
circiter septingenta milliaria secundum Plinium sexto libro.
Et est haec civitas in primo climate, a qua nominatur clima
Diameroes. Regnavit ibi Candax foemina, unde nomen Can-
dacis multis jam annis ad reginam transit, ut dicit Plinius,
et infert, cum potirentur rerum Aethiopes, insula ea magnae
claritatis fuit. Tradunt armatorum 250 millia dare solitum,
artificum 400 millia alere? Actus autem apostolorum me-
moriam faciunt de eunucho Candacis reginae Aethiopum,

! It will be noticed that Bacon does not adopt the Ptolemaic view that the

Indian ocean was an enclosed sea.
* These numbers are wrongly given in the MSS. They are given here as in

Pliny, vi. 29.

312 OPERIS MAJORIS PARS QUARTA.

quem Philippus baptizavit: unde Candax est nomen digni-
tatis, sicut Caesar, Ptolemaeus, Pharao, Antiochus, Abimelech.
Nam Abimelech in Philistiim, Antiochi in Syria, Ptolemaei in
Aegypto post mortem Alexandri, Pharaones ibidem tempore
antiquo, sicut Caesares et Augusti in Romano imperio, ut
dicit Hieronymus nono libro super Ezechielem. Sed ubi
latitudo regionis est quasi consimilis super ripam rubri maris
ad orientem, est Ptolemais civitas a Ptolemaeo Philadelpho
condita ad primos venatus elephantorum, ubi quasi per
quadraginta quinque dies ante solstitium et post non sunt
umbrae in meridie, sicut dicit Plinius, et in illis nonaginta
diebus, aut circiter, cadit umbra in meridiem, quia sol est ad
aquilonem, et post hos dies cadit umbra per residuum anni in
aquilonem. Et hic habitant sub circuitione medietatis Tauri
et medietatis Leonis. Unde sol transit bis in anno per capita
eorum in illis medietatibus signorum.

Central Deinde ulterius in eadem latitudine sed versus occidens

Ethiopia. inter Ptolemaidem et Meroen per 4,820 stadia distans a Ptole-
maide, ut Plinius dicit et Beda libro temporum contestatur,
est Berenice urbs Troglodytarum Aethiopum, in qua sol
similiter bis in anno pertransit, et umbrae consimiles sunt sicut
in Ptolemaide. Oportet enim quod Troglodytarum regio de-
clinet in parte versus occidens, ut exponetur inferius. Et ideo
non erit in orientali Aethiopia, sed magis in medio. De istis
vero Troglodytis meminit Scriptura secundo Paralipomenon
duodecimo capitulo, qui venerunt cum Selac rege Aegypti
in adjutorium. Hi, ut Plinius narrat libro quinto specus ex-
cavant, haec illis domus, victus serpentum carnes, stridorque
non vox, sermonis commercio carent. Et in sexto libro dicit,
‘gens Troglodytaruin mirae velocitatis a venatu dicta velo-
ciores equis, Unde Isidorus libro nono, ‘Troglodytae gens
Aethiopum ideo nuncupati, quod tanta celeritate pollent ut
feras cursu pedum assequantur.’ Post hos ad orientem sunt
Aethiopes de Nubia et ultimo illi qui vocantur Indi propter
approximationem ad Indiam, a quibus incipit Plinius de-
scribere gentem Aethiopum. Nam secundum Isidorum nono
libro, Aethiopum tres sunt populi principales; Hesperi,
Garamantes, et Indi. Hesperi sunt occidentales, Garamantes

GEOGRAPHIA. 313

in medio, Indi in oriente. Cum Garamantibus Troglodytas
involvit, qui conjuncti sunt. Meroe vero quae est domina
gentium inter Nubienses et Indos et Garamantes secundum
Alfraganum collocatur. Garamantes a Garama oppido, quod
est caput regni eorum nominati, matrimoniorum exsortes
passim cum foeminis degunt. Hesperi vero circa Hispaniam
commorantur. Nam Hispania dicitur Hespera: unde illi
qui supra ulteriorem Hispaniam inhabitant Hesperi dicuntur,
Multi tamen alii sunt Aethiopes his tribus populis diversis
locis copulati, etiam a natura hominis debita multum de-
pravati, quorum nomina et regiones et mores assignare non
est praesentis persuasionis. Quae omnia ex libris Plinii
et aliorum satis patent, et in scriptura principali debent
annotari.

Aethiopia vero terminatur inferius ad mare rubrum a
parte orientis, ad Africam ex parte occidentis, ad Aegyptum
in medio inter haec extrema ; in quo medio est civitas Syene,
de qua Ezechiel xxix et xxx capitulis expresse loquitur,
dicens, * quod a terra Syene usque ad terminos Aethiopiae non
transibit pes hominis! Syene vero est terminus Aethiopiae
inferior et pars suprema Aegypti, sicut dicit Hieronymus
super Ezechielem nono libro. Meroe vero est terminus superior
notae habitationis secundum Plinium secundo libro. Nam
a meridie ponit Meroen principium habitationis notae. Et
dicit Plinius sexto libro quod a Syene ex utroque latere
orientis et occidentis, scilicet Arabiae et Africae, non remansit
oppidum nec castrum nec villa usque Meroen. Nam omnia
deleta sunt bellis continuis, ut Scriptura sacra verificetur. A
Syene vero usque ad Meroen, secundum Plinium secundo
libro, sunt quinque millia stadiorum. In sexto vero libro
ponit 972 millia passuum. Latitudo autem hujus Syenes
dicta est. Nam sub tropico Cancri collocatur, et ab ea clima
secundum denominatur clima Diasyenes.

Syenc.
nd
parallel.

Non possunt vero sequentia expediri, nisi hic aperitur Egypt.

descriptio Aegypti et Africae et Nili decursus. Caput vero
Aegypti est Syene, ut dictum est. Sed Aegyptus est duplex,
scilicet superior et inferior; quae vero inferior vocatur, con-
cluditur infra Nilum ad modum insulae triangularis, sicut

Alexandria,
Third
parallel.

314 OPERIS MAJORIS PARS QUARTA.

litera Graeca quae delta dicitur: et ideo Aegyptus vocata est
Delta antiquitus. Et haec habet ab oriente terram Philisti-
norum, a septentrione mare Mediterraneum, ab occidente
Africam, a meridie superiorem Aegyptum. Et a parte
Palaestinae est ostium Nili quod vocatur Pelusium, ubi cadit
unum latus trianguli, scilicet unum brachium Nili in mare.
De hoc Pelusio habetur Ezechielis xxx, ubi dicitur, * effundam
indignationem meam super Pelusium robur Aegypti'; et
Hieronymus libro nono ait, ‘quod robur Aegypti dicitur eo
quod habeat portum tutissimum, et negotiationes maris ibi
maxime exerceantur. Aliud quidem ostium vocatur Canopium,
ubi aliud brachium trianguli cadit in mare versus Africam,
inter quae ostia Nili est basis trianguli super littus maris con-
tinens cx milliaria, ut dicit Plinius quintolibro. Et a concursu
brachiorum Nili in vertice trianguli usque ad Canopium ostium
sunt cxlvi, et ad Pelusium ostium cclvi milliaria. Superior
vero Aegyptus est contermina Aethiopiae, ut dicit Plinius, et
Thebais vocatur, et incipit a Syene, quae est civitas Thebaidis,
ut dicit Hieronymus libro Locorum. Et habet a meridie
Aethiopiam, et ab oriente partem Arabiae, ut inferius magis
clarescet ; ab occidente superiorem partem Africae. Et haec
est regio Thebaidis, in qua est Thebae civitas. Thebas autem
Aegyptias, ut dicit Isidorus quinto decimo libro, Cadmus
aedificavit: quae inter Aegyptias urbes numero portarum
nobiliores habentur, ad quas commercia undique Arabes
subvehunt. Deinde Cadmus in Graeciam profectus Thebas
Graecorum condidit in Achaia, quae nunc dicitur terra
principis A moreae.

Aegyptus vero inferior habet in parte Africae super mare
Alexandriam, nobilem urbem ab Alexandro magno conditam,
quae ab illo tempore caput Aegypti constituta est. Et
Alexandria est in tertio climate, quod ab ea nominatur clima
Dialexandrios, et distat a Syene secundum Plinium secundo
Naturalium quinque millia stadiorum. Et ab hac civitate versus
orientem super littus maris per circiter centum leucas, ut
experientia itineris docet, est Memphis civitas, quondam arx
Aegypti et caput, quae nunc Damiata vocatur. A qua per
unam dietam est Tampnis, ubi Pharao habitavit et Moises

GEOGR APHIA. 315

fecit miracula, secundum quod dicit Hieronymus nono libro
super Isaiam. Etin extremis finibus Aegypti, ut Hieronymus
dicit in epistola de mansionibus, est Ramesse urbs versus
orientem, quam aedificaverunt filii Israelis. Olim autem, ut
dicit Hieronymus in libro Locorum, universa provincia sic
vocabatur, in qua habitavit Jacob cum liberis suis; et haec
est terra Gessen, ut Genesis liber testatur, et Hieronymus
dicit libro praedicto quod in ea habitavit Jacob cum filiis
prope Memphim. Et non multum a Tampne est Heliopolis
civitas solis, Arabiae conterminum, ut dicit Plinius, et magnae
claritatis oppidum, in qua, ut dicit Hieronymus libro praefato,
fuit Phutifar sacerdos, cujus filiam accepit Joseph, sicut in
Genesis legimus xli capitulo. Tana vero est civitas Aegypti,
ut dicit Hieronymus in libro Locorum, in qua habitaverunt
Judaei qui ob metum Babyloniorum cum Jeremia fugerunt,
et non solum in ea, sed in Memphi et in terra Phatures et
Magdalo, sicut habetur in Jeremia xliv capitulo. Phatures,
ut dicit. Hieronymus in libro Locorum, est regio Aegypti
in qua profugi habitavere Judaei. Sed Socoth et Ethan
et Phiaroth et Magdalon, de quibus xiii et xiv Exodi
legitur, non sunt in Aegvpto sed prope extra, ut patet ex
epistola Hieronymi de mansionibus, et hoc versus orientem
ad mare rubrum; ad quae loca profecti sunt filii Israelis
de Aegypto, antequam transirent mare rubrum, sicut Exodus
declarat.

Descriptione Aegypti facta quantum hic est necesse, nunc Africa.
ad Africam accedendum est. Et licet Plinius et multi multa
hic scribunt, sententia tamen Sallustii in Jugurthino certior est
et planior, quam principaliter exponam ; quoniam Hieronymus
dicit libro Locorum et Hegesippus in Historia Hierosolymitana
quod Sallustius est auctor certissimus. Et insistam attentius
circa hanc provinciam, quia licet sit prope nos, tamen minus
nota est quam Europa et Asia; atque sacra scriptura et dicta
sanctorum et historiae multa requirunt de hac regione. Africa
quidem dicitur ab uno posteriorum Abrahae, ut dicit Hierony-
mus super Genesim, qui vocatur Affer: qui dicitur duxisse
exercitum adversus Libyam, et ibi victis hostibus consedisse,
ejusque posteros Afros et terram Africam nuncupasse, quae

Getulians
and Lib-
yans.

316 OPERIS MAJORIS PARS QUARTA.

tamen prius Libya et ante omnia Phuticensis regio a filiis
Cham nuncupata fuit, ut inferius exponetur.

Africam autem, ut dicit Sallustius, in initio habuere Getuli
et Libyes. Getuli vero, ut Isidorus aliquando et Hugucio,
a Getis. seu Gotis ab aquilone venerunt per mare. Sed
Hieronymus super Genesim auctor est quod ab Evila, filio
Chus, filio Cham, filio Noe venerunt: nec est verisimile quod
advenae primo inhabitarunt terram debitam uni nationi, unde
Africa debebatur filiis Cham, sicut Aegyptus et Aethiopia.
Libyes vero fuerunt filii Labaim, filii Mesraym, filii Chus,
filii Cham, ut Hieronymus dicit super Genesim. A quo
Labaim Libya appellata est, quamvis secundum Hieronymum
super Genesim et super ultimum capitulum Isaiae, Libya
prius dicebatur Phuth vel Phutensis regio, a filio Cham qui
Phuth dicebatur. Est enim adhuc fluvius in Libya, qui Phuth
dicitur, omnisque regio Phutensis dicta est. Getuli vero magis
versus Aegyptum et Libyes versus occidentem habitabant,
utrique oberrantes latius propter regionum amplitudinem. Et
aliquando tota Africa dicebatur Libya, ab una sua parte domi-
nante nominata, et Libyes vocati sunt populi terrae, de quibus
secundo Paralipomenon xii et xvi, et Naum tertio, et alibi
pluries invenitur ; sed, ut ait Sallustius, postquam in Hispania
Hercules interiit, exercitus ejus compositus ex variis gentibus
dilapsus est. Ex eo numero Medi et Persae et Armeni
navibus in Africam transvecti proximos mari nostro locos
occupavere ; sed Persae! intra oceanum magis et plus approxi-
mabant Aegypto et Italiae quam caeteri prope mare habitantes
sub Getulis. Nam Getuli ad solem magis approximabant,
et Aethiopiae vicini. Hi paulatim copulaverunt se Getulis
per connubia. Et infert, quia saepe temptantes agros alia
deinde loca petiverant, semetipsos Numidas appellavere ; id
est, sine oppido vagos et errantes, sicut dicit Isidorus libro
nono. Medi vero et Armeni supra littus maris nostri a Numidis
usque ad Gades inhabitabant sub Libyis, qui supra eos ad
meridiem versus Aethiopes coarctati sunt. Sed Medorum
paulatim Libyes nomen corrupere, barbara lingua Mauros pro
Medis appellantes.

! J. has per se.

GEOGRAPHIA. 317

Et hi omnes ab oceano et Gadibus usque ad provinciam Carthage.
Carthaginensium habitabant. Nam secundum Sallustium
postea Phoenices imperii cupidine moti a Tyro et Sidone
venientes loca Africae invaserunt, et Numidas ac Getulos et
caeteros Africanos coarctaverunt, et Carthaginem sive pro-
vinciam firmaverunt, in qua sunt Punicae, id est, Phoeniceae
civitates nobiles, scilicet Hippo, civitas beati Augustini, Utica
Catonis magni, Carthago quae tanquam Roma altera [fuit]. :
Cujus imperium extendebatur versus Aegyptum usque ad aras
Philenorum, quam posuerunt lxxii interpretes in Ezechiele,
ubi Hebraeum habet Tharsus, sicut dicit Hieronymus libro
Locorum, et non solum ibi, sed xxiii Isaiae et pluries alibi. Et
xxvii Ezechielis habetur de Carthaginensibus.

Deinde sequitur regio Tripolitana eorum qui Byzantium Tripolis.
incolunt, quam Tyrii et Sidonenses occupabant, unde vocatur
Africa vel Libya Phoenices, quia Phoenices ibi habitabant
scilicet Tyrii et Sidonenses. Terra haec est fertilitatis eximiae,
nam centesimam frugem reddit, ut dicit Plinius. Ibique est
illa Leptis magna inter duas syrtes, minorem a parte Cartha-
ginensium et majorem a parte Aegypti: quae, Sallustio
referente, sunt loca vadosa et arenosa, quae cum excitantur
ventis et fluctibus maris eructant pulverem infinitum et arenas
copiosas, unde syrtes dicuntur a trahendo seu a tractu
arenarum et pulverum. Syrma enim Graece est tractus
Latine, et syro idem est quod traho: unde habitantes loca
terrae proxima perturbant et confundunt.

Deinde sequitur provincia Pentapolitana regio, quae Cyre- Cyrene.
nensis dicitur in scriptura, ubi sunt quinque civitates magnae,
quarum caput Cyrene dicitur, de qua in evangelio Lucae, et in
Marco, ac Matthaeo habetur. Cum Dominus ducebatur ad
passionem apprehenderunt Simonem quendam Cyrenensem,
&c. Et in Actibus Apostolorum, Surrexerunt de synagoga quae
appellabatur Libertinorum et Cyrenensium, &c.,et quartoregum
26 dicitur, quod rex Assyriorum transtulit Damascenos in
Cyrenen; et Amos quinto et nono habetur de ea. Quum vero
arae Philenorum in multis scripturis sanctorum et historiarum
reperiuntur et multotiens corrupte leguntur, ut dicantur arae
Philistinorum, propter hoc ad vitandum errorem non est

Aethiopian
tribes south
of Egypt

and Abica.

The Nile;
its prob-
able source.

318 OPERIS MAJORIS PARS QUARTA.

inutile considerare quod Sallustius dicit in hac parte. Cum
enim Cyrenenses et Carthaginenses multa bella commiserant,
nec fuerunt fines certi inter eorum imperia, ob bonum pacis
decreverunt ut legati eodem die et eadem hora ab utraque
civitate mitterentur, et ubi sibi obviarent invicem, ibi fines
regnorum deberent constitui. Sed legati Cyrenenses casu
impediti non potuerunt in tantum procedere sicut vellent ;
finxerunt igitur quod Carthaginenses citius recesserunt a loco
suo quam debebant, et dixerunt eis quod vivi obruerentur in
loco quem attigerant, si eum pro termino regni habere vellent ;
vel quod eis permitterent transire quo vellent ; aut ipsi mortem
ibi eligerent. Legati vero Carthaginensium consenserunt, et
principales fuerunt duo fratres, qui Philenes vel Phileni dice-
bantur, qui pro republica sua voluntarie vivi obruti sunt:
in quorum memoriam Carthaginenses aras erexerunt quae
vocantur arae Philenorum usque in hunc diem. Sub Cyrenen-
sium vero provincia totum usque ad Aegyptum secundum
multos auctores computatur : sed Plinius parvulam provinciam
per se constituit, quae vocatur ab eo Libya Mareotis. Et sic
terminatur extensio totius Africae a Gadibus in Aegyptum
cum distinctione suarum provinciarum.

Supra vero Aegyptum et Africam ad meridiem extenditur
Aethiopia ab oriente in occidens usque ad mare Aethiopicum,
et principales regiones eorum sunt, ut dixi, Indi, Sabaei, qui
sunt Meroenses, Nubienses, Troglodytae, Garamantes, Hes-
perides. Pars autem Troglodytarum flectit se versus occi-
dentem super syrtes majores et partes vicinas, a quibus distare
videtur secundum Plinium libro quinto per xviii dietas. Et
ideo licet major pars gentis Troglodytarum vergat ad mare
rubrum, tamen aliqua se inclinat in partem occidentalem super
Africae regiones. Et ultra eos versus occidens est regio Gara-
mantum in directo syrtium minorum et Carthaginensium:
orientalis tamen parsGaramantum vergit in directum Cyrenaicae
regionis secundum Plinium libro sexto, ut tandem Hesperides
occidentales Atlanticas partes attingant.

Quoniam vero Nilus Aegyptum et Aethiopiam alluit et
earum provincias multipliciter distinguit, et Scriptura multi-
plicem facit mentionem de eo, et in philosophia et in historiis

GEOGRAPHIA. 319

vulgatus est, satis conveniens est aliquid notabile recitari de
eo. Oritur autem de paradiso, ut scriptura refert, sed ubi
erumpat nostrum habitabile, aestimatur diversimode a diversis.
Verisimile tamen est quod in littore incipientis maris rubri in -
Aethiopia oritur, secundum quod affirmat Orosius in libro de
Ormesta Mundi ad beatum Augustinum, et Seneca tertio
Naturalium! satis concordat. Nam refert Neronem impera-
torem misisse duos centuriones ad explorandum Nili ortum,
et cum venirent ad primum regem Aethiopum fuerunt per
eum instructi et adjuti, ut reges caeteri Aethiopiae darent eis
conductum. Et tandem venerunt ad paludes vadosas et her-
bosas, quarum magnitudo ignorabatur ab incolis: de qua
etiam certificanda desperabant. Nam neque navigio propter
aquae parvitatem potuerunt homines explorare; nec humus
limosa potuit pondus hominis sustinere. Credebant igitur
incolae ibi esse caput Nili: Et ideo quod Plinius dicit Nilum
oriri in finibus occidentis juxta montem Atlantem non procul
a mari, non est credendum. Duplex enim testimonium fortius
est hic quam singulari, et experientia Neronis principis mul-
tum operatur.

Deinde fluvius Africanus tendit in regionem, quae Libya A river in
Aegyptia dicitur, ad immensum lacum?, quo finitur, sicut dicit flows into
Orosius. Et ad hoc est quod paradisus est in oriente. Et * vast lake
ideo verisimilius est quod Nilus erumpat in oriente quam in the Nile

. ] . . . . : may be
occidente ; nec est unus et idem fluvius Africae et Nilus, licet 07 ected,

! This reference is to Nat. Quaest. vi. 8. The marshes are in all probability
those found by modern explorers on the White Nile above its junction with the
Sobat in g^ N. Ptolemy describes this river as formed 2? south of the equator,
by the junction of two rivers flowing from two lakes still further south. He
describes also the Astapus, answering to the Blue Nile, which joined the main
stream 4° 30° south of Meroe and originated in Lake Coloe, now known as the
lake Tzana in Abyssinia. [Bunbury, vol. ii. pp. 612-33.)

The views of Aristotle as to the inundations of the Nile, which had been
carefully studied by Bacon, though with his usual independence, will be found
in Frag. 212 and 213. In De Animalibus, lib. viii. cap. 12, he speaks of the
marshes of the Upper Nile; and in Meteorol. i. cap. 13 he alludes to its origin in
the Silver Mountain. The passage in Post. Analyt. ii. cap. 13, as to the lessen-
ing of the flow at the end of the month, does not seem to represent any real
opinion held by him.

* There was great confusion in antiquity, and throughout the middle ages, as
to the connexion of the Nile with other African rivers; nor, indeed, was it

Its subse-
quent
course.

320 OPERIS MAJORIS PARS QUARTA.

consimiles pisces et monstra conformia et crocodilos enutriant,
sicut arguit Plinius, quia flumina in diversis regionibus videmus
consimilia animalia secundum speciem enutrire: atque se-
cundum ipsum Plinium et alios, flumina in India nutriunt
crocodilos, sicut Nilus. Sed quod allegat Nilum Aegypti
augeri per incrementa imbrium et nivium fluminis Africani,
concedendum est hoc, quia lacus dictus quo absorbetur hoc
flumen Africae parum distat a Nilo secundum Orosium et

occulto meatu in alveum Nili potest transfundi, sicut nos

videmus multotiens in diversis regionibus consimile evenire.
Decursus autem Nili a sua origine per Aethiopiam et
Aegyptum traditur a Plinio et aliis, licet in ortu ejus discordet
ab illis. Fluit igitur ab origine sua, ut ait Orosius, diu ad
occasum solis, et transit per medium Aethiopiae spargens
multas insulas, quarum omnium nobilissima est Meroe, quae et
Saba dicitur. Deinde flexus ad septentrionem inter Meroen
et Syenem, ut exprimit Plinius, et montibus inclusus cataractas
inter occursantes scopulos aperit, ut non fluere videatur sed
ruere, ubi nimio fragore auditum in accolis tollit; propter
quod ad loca convenientiora se transtulerunt. ut dicit Seneca
libro octavo Naturalium. Istud dico propter hoc, quod Macro-
bius Pythagoricus volens docere qualiter infinitum sonum ex

dissipated til] our own time. Pliny (v. 9" speaks of the belief, held by many
in his time, that the ultimate source of the Nile was near Mount Atlas in
North Western Africa, that, proceeding eastward, it sank underground and
reappeared at a distance of several days’ journey and finally reached Eastefn
Aethiopia and took a northerly direction. Pliny distinguished the Niger as
distinct from the Nile, but thought that both arose from the same source.
Orosius also maintained (lib. i. cap. 2) the existence of an African river which,
though distinct from the Nile, yet probably had some subterranean connexion
with it (occulto meatu in alveum ejus qui ab oriente descendit eructat).

The great Arabian geographer of the twelfth century, Edrisi, describes at
great length a Western Nile which flowed through the Soudan, and at last
found its way into the Atlantic. He speaks of it as the Nile of the black people ;
and notes the names of many of the cities on or near it, especially Gana,
a great commercial centre, probably identical with the modern Kano, described
in Mr. Robinson's recent book on the Hausas. This Western Nile Edrisi
believed to originate in the same range of mountains as the Egyptian Nile,
16? S. latitude. His description obtained from the reports of Mohammedan
travellers consulted by Roger of Sicily, Edrisi's patron, corresponds gn the
whole with the Niger; but some parts of it seem to relate to the northern
tributaries of the Congo. '

GEOGRAPHIA. 321

motu coelorum sustinemus illaesi auribus, ponit vanum exem-
plum de gente quae sustinet propter consuetudinem rugitum
Nili pacifice. Sed exemplum suum falsum est, sicut Plinius et
Seneca docent, et exemplatum esse non potest, sicut docet
Aristoteles secundo Coeli et Mundi. Hic locus est prope
Syenem secundum Hieronymum nono libro super Ezechielem ;
et dicit quod usque ad Syenem est Nilus navigabilis a mari
Italico. Et ulterius septentrionalis effectus Nilum includit,
et tandem fauces ejus in mare quod est inter Aegyptum et
Italiam projicit; ostia ejus duo, scilicet Pelusiacum et Cano-
pium. Sicut autem ait Hieronymus quarto libro, super xix
capitulum Isaiae, Nilus ante Caesarem Augustum unus alveus
fuit, sed tunc divisus est in septem, unde ad Pelusium una
pars descendit, et ad Memphim quae est Damiata decurrit :
alteraque extenditur in altum versus meridiem usque ad Kayr
et Babyloniam, a qua nunc dicitur Soldanus Babyloniae, per
circiter tres dietas a Damiata ; et ab illa Damiata extenditur
a latere una pars fluminis per unam dietam quasi inter
meridiem et orientem ad villam, quae vocatur Lancassor !,
ubi exercitus Christianorum devictus fuit, quando Dominus
Lodovicus filius Lodovici filii Philippi illustris rex Franciae
primo crucem arripuit ad partes transmarinas. Alii autem
rivi fluminis Nili descendunt prope Tampnem et Alexandriam
et caetera loca Aegypti.

Nili vero proprietas secundum Plinium et caeteros est, Inundation
quod inundat certis temporibus et plana Aegypti rigat: Sülbe
secundum cujus egressiones stat Aegyptiaca fertilitas vel
negatur. Nam si fines suos naturales egrediatur solum per
xii cubitos, tunc Aegyptus famem sustinet, in tredecim non
esurit, xiv cubiti hilaritatem afferunt, xv securitatem, xvi
delicias. Si plus, temperate tamen affluat, ad abusum delicia-
rum excitat indigenas. Sed si creverit super debitum nocet,
ut dicit Seneca. Incipit autem crescere, ut dicunt, luna
existente nova quacunque post solstitium sensim, id est
paulatim modiceque, Cancrum sole transeunte, abundantissime
vero in Leone, et residet in Virgine. Et iisdem quibus crevit

! O. has Lamassor.
VOL. I. Y

322 OPERIS MAJORIS PARS QUARTA.

modis revocatur intra ripas dum sol est in Libra et centesimo
die a principio fluxus. Causas vero hujus inundationis et
crementi difficile est assignare, quia valde mirabilis est, eo
quod fit in fervore aestatis, quum aquae plus consumuntur
quam in aliis temporibus. Caeterum nullus fluvius sic inundat
secundum Aristotelem in tractatu de Nilo, secundum Plinium
nisi Euphrates; possumus tamen tertium addere, scilicet
Ethiliam, qui est major Euphrate faciens mare Caspium, de
quo superius tactum est. Istud docent illi qui apud Tartaros
fuerunt, ut frater Willielmus et alii. ^ Aristoteles vero et
Plinius locuti sunt secundum suas experientias.

Difficulty Hujusmodi igitur natura singularis, quae in aliis mundi

ing i. . fluminibus paucissimis reperitur, est satis mirabilis. Deinde
sapientum discordia in causis istius incrementi quasi infinita
inducit in nobis perplexitatem, ut in quam partem vertamur
non sit perspicuum ; praecipue cum multi tam probabiles
sententias reprobent quam sunt illae quas affirmant. Seneca
etiam omnibus auctoribus, excepto si volumus Aristotele,
ubicunque figit intentionem certior, tamen in proposito
solum certas dat reprobationes in libro suo de Nilo, qui est
octavus Naturalium, nullam praesumens firmare sententiam,
victus difficultate hac, licet alias victor gloriosus existens.
Aristoteles etiam quamvis opinionem spargat, multis tamen
contradictionibus semper turbari potest. Quae vero magis
aestimo digna relatu propter hanc persuasionem usque ad
tractatum principalem inferam tolerabili brevitate.

Wind Sapientes vero Latini negligentes experientiam in hac parte

reory of adhaerent opinioni Thaletis, qui fuit primus de septem
sapientibus famosis, quae consistit in hoc, quod venti annuales
determinati flant contra ostia Nili revolventes fluctus et
arenas maris, quibus obstruuntur ostia, et aquae Nili penitus
redeunt, et sic exit suas ripas. Sed auctoritate et experi-
mento refellitur. Nam secundum Aristotelem et Senecam et
secundum quod docet experientia eorum qui in Aegypto
fuerunt, aquae Nili incipiunt fluere a superiori parte Aegypti
ab Aethiopia. Nam et Aegyptii prae gaudio exultantes
ascendunt naves et obviam Nilo defluenti occurrunt cum cantu
et instrumentorum musicalium genere multiplici; unde ab

GEOGRAPHIA. 323

ostiis ejus prius dictis non incipit fluere, sed a superiori parte
in ostia.

Anaxagoras vero philosophus inducit opinionem magis Snow
probabilem omnibus, et dicit nivem liquefieri in aestate in !heory of
montibus Aethiopiae, et sic Nilum augmentari, sicut Rhodanus, goras re-
et Padus, et Danubius, et hujusmodi flumina prope Alpes Pedby
crescunt ex nivium liquore. Sed hanc opinionem Aristoteles
et Seneca negant et reprobant. Aristoteles vero redarguit
per hoc, quod ex multa nive parum de aqua generatur, sed
augmentum Nili est maximum, quia regiones infundit latissi-
mas et aliquando usque ad triginta cubitos altitudinis. Iterum
aliter arguit; aquae quae fluunt a longe sunt fortiores in fine,
sicut venti qui a longinquo veniunt ; et qui de propinquo fluunt
sunt impetuosiores in principio. Cujus causa est in aquis,
quia in magna distantia concurrunt multae aquae in unum et
imbres multi fiunt et vapores multi resultant ex terra, et ideo
fortificantur omnia flumina versus finem et sunt ampliora quam
in principio; et sic de ventis propter multiplicationem vapo-
rum ex diversis locis confluentium in unum corpus propter
distantiae quantitatem. Sed inundatio Nili augmentatur in
principio et magis ac magis fortificatur ad tempus, donec
tepescat in fine, ut Aristoteles dicit et Plinius, et experientia
docet. Ergo non veniunt aquae istae ex longinquo, sed et
montes Aethiopiae, ubi probabilius posset dici quod nives
abundent, distant secundum orbem a Nilo per iter quinque
mensium. Ergo non causabitur inundatio Nili a nivibus.
Major propositio istius argumenti est digna valde; nam multam
habet scientiam, quicquid sit de minore propositione. Item
dicit quod in plenilunio omnia congelata tabescunt et resol-
vuntur magis, sed Nilus crescit in fine mensis, ergo non est
ex nivibus. Item Nilus magis fluit quando flat Boreas, quam
quando Auster; sed Auster magis dissolvit nives quia calidus
est. Caeterum Aristoteles dicit-quod in Aethiopia propter
calorem maximum, qui comburit omnia, non possunt esse
nives ; quod facile credendum est. Et his Seneca concordans
addit, quod nives dissolvuntur in tempore verno et liquescunt
tactae temperato calore et faciunt crementum fluviorum ; sed
calor nunquam temperatus est in Aethiopia antequam erit in

Y 2

Aristotle's
rain theory.

Objections
to it.

324 OPERIS MAJORIS PARS QUARTA.

hyeme. Nilus autem post solstitium crescit aestivale. Quid
vero Pythagoras, quid Diogenes, quid Democritus, quid alii
multi et magni philosophi senserint, non est necesse in hac
persuasione praeambula recitare.

Sed inferatur sententia Aristotelis pro omnibus dicentis,
quod in Aethiopia in aestate nostra sunt multae pluviae et in
hyeme nullae, et Nilus in illis regionibus oritur, unde augmen-
tantur ejus paludes et lacus; et addit, quod venti annuales
determinati in aestate et orientales flant, et fugant nebulas ad
regiones unde Nilus fluit, quae dissolvuntur in lacus ejus.
Causa autem quare augmentatur in fine mensis datur ab
Aristotele secundo Posteriorum, quia finis mensis lunaris est
frigidior, et frigus multiplicat humorem et augmentatur per
Boream, quia ille ventus fugat nubes naturaliter propter
impetum suum, quia venit de prope propter hoc quod habitatio
est in septentrionali quarta terrae, et impetuosus est in hac
quarta, ut Aristoteles docet, et propter hoc fugat ante se
nubes, ut congregari possint in paludibus Nili, quae sunt
quasi incomprehensibilis magnitudinis, ut superius tactum est,
et ideo multum capiunt de loco nubium, et possunt sic per
resolutionem nubium in pluvias aquae multiplicari.

Sed sicut objectum est contra alias positiones, sic contra
istam fieri potest. Nam cum terra sit inhabitabilis propter
calorem, id est, pessimae habitationis cum sit combusta, quo-
modo potest ibi esse abundantia pluviae et maxime in aestate,
sicut nec nives, ut ipse Aristoteles objicit contra secundam posi-
tionem? Et contra primam dicit quod idem accideret in aliis
fluminibus, et quod venti annuales non semper veniunt suo
tempore. Cum ergo pluviae sunt in regionibus multis ubi sunt
flumina magna et venti annuales, et tamen non videmus hujus-
modi augmentum ibi contingere; et Boreas similiter fugat
nubes cum majori impetu in regionibus prope, quia minus a sua
origine distat ; igitur magis augmentarentur flumina in nostris
regionibus et similiter in fine mensis; sed non videmus
hujusmodi augmentum. Dubia igitur est Aristotelis positio,
sicut aliorum. Quapropter difficillimum est reddere causas
hujus augmenti singularis, quod non est nisi in Nilo secundum
Aristotelem, vel saltem secundum Plinium non est nisi in Nilo

GEOGRAPHIA. 325

et Euphrate. Est tamen adhuc in tertio flumine superius
tacto, ut fuit in Jordane ante subversionem Sodomae et
vicinarum civitatum, testante scriptura Geneseos. Propter
igitur hujus rei difficultatem sufficit in hac persuasione, ut
sententias philosophorum videamus quatenus per eas excitati
in principaliori ! tractatu certius veritas inquiratur.

Revertendum igitur est ad descriptionem regionum. Et
inveniemus apud Plinium sexto libro, et Alfraganus concordat,
et Lucanus quod antiqui vocabant partem Arabiae totum
quod habitatur a mari Aethiopico et meridie descendendo
per Meroen et Syenem, ita etiam quod Heliopolis Aegypti,
de qua dictum est, in Arabia computetur ; et ideo totum quod
habitatur a Meroe et Syene et Heliopoli versus orientem
inter mare Rubrum et mare Aethiopicum sub Arabia contine-
tur; unde Alfraganus in primo climate ponit insulam Arabum,
et in secundo; quae insula est in mari Aethiopico vel circa
ortum maris Rubri. Et Lucanus dicit,

* Ignotum vobis Arabes venistis in orbem,
Umbras mirati nemorum non ire sinistras.'

Hoc dicit de Arabibus, qui venerunt Romam in adjutorium
Pompeii, qui mirati sunt umbras sinistras et septentrionales
non ire, id est, non mutari in dextras seu meridianas. Nam
in terra sua, quae est inter tropicum Cancri et aequinoctialem,
habent in aliqua parte anni meridianas umbras quando sol
transit ultra eos versus tropicum Cancri, quia tunc sol est in
aquilone respectu eorum ; et quando transit ultra eos versus
aequinoctialem, tunc oportet quod habeant aquilonares, quia
sol est in meridie eorum. Tota igitur haec pars Aethiopiae
citra Meroen et Syenem et Heliopolim versus orientem sub
Arabia continetur. Et non solum hoc, sed quicquid est circa
linguam, id est, extremitatem maris Rubri et super littus ejus
versus orientem a cuspide linguae usque ad sinum ejus Persi-
cum. Etextendit se a mare Rubro usque ad Pelusium Aegypti
ad occidentem, et dilatat se ad septentrionem per totum

! [t will be noticed that this discussion of the Nile problem contains three
references to the systematic work in which this and many other questions were
to be more thoroughly investigated ; the Opus Majus being merely a fersuasio
pracambula.

Arabia ; its
boundaries.

Desert of
Sur.

Desert of
Sin.

326 OPERIS MAJORIS PARS QUARTA.

desertum, in quo vagati sunt filii Israelis usque ad terram
Philistinorum super mare nostrum conterminam Aegypto, et
extensam ad orientem donec occurrat Amalechitarum regio,
quae est ad orientem terrae Philistiim, et usque ad terram
Edom, seu Idumaeam, quae est ad orientem Amalech et
usque ad terram Moab. . Deinde flectit se magis versus sep-
tentrionem per terram Seon regis Esebon, et Og regis Basan
usque ad montem Galaad et Libanum, et adhuc magis flectit
se ad septentrionem orientalem usque ad Ciliciam et Syriam
Comagenam, et usque ad Euphratem.

Unde Arabia large sumpta est terra magna valde, et con-
tinet in se primo Desertum Sur seu Ethan, nam Ethan dicitur
solitudo ex utraque parte maris Rubri, et in extremitate ejus
juncta Aegypto et Palaestinae. Quoniam in Exodo habetur
quod filii Israelis metati sunt castra in Ethan; et deinde
transierunt mare Rubrum et venerunt iterum in Ethan. Nam
Scriptura dicit quod post transitum maris Rubri venerunt in
desertum Sur, et ibi fixerunt tabernacula in Mara, et ambu-
laverunt per tres dies antequam fixerunt tabernacula, et primo
fixerunt tabernacula in Mara, deinde in Helim. Sed Hierony-
mus dicit in epistola de mansionibus, quod desertum Sur et
Ethan sunt idem. Et in hac Arabia prope Sur versus orientem
ultra transitum filiorum Israelis super littus maris Rubri est
Elamitarum regio secundum Plinium et Hieronymum in libro
interpretationum ; ubi est Elam civitas urbs ultima Palaesti-
norum. Nam in hac parte juxta desertum Sur flectit se angulus
Palaestinae ad Rubrum mare secundum Hieronymum, ut dicit
Plinius, ibi prope est Stagnos !, insula maris Rubri, quam canes
non intrant expositique cuncta littora errando moriuntur.

Post desertum vero Sur versus orientem sequitur Sin deser-
tum, ubi fuerunt quinque mansiones filiorum Israel secundum
Hieronymum in epistola de mansionibus, quarum prima non
habetur in Exodo, sed xxxiii Numerorum, unde dicitur, ‘ pro-
fectique sunt de Helim ad mare Rubrum quod vocatur
Jamsuph. Et Hieronymus quaerit quomodo reversi sunt ad
mare Rubrum, et solvit dupliciter uno modo quod potuit esse

1 This appears to be a mistake for Sygaros, of which Pliny says (vi. 28) ‘Sygaros
insula quam canes non intrant expositique circa errando litora moriuntur.'

— uL LLL eee d

GEOGRAPHIA. 327

quidam sinus maris Rubri qui extenderetur in deserto Sin
a principali corpore maris, nam Jam est Mare et Suph
dicitur Rubrum. Sed convenientius solvit dicens quod Suph
potest signare rubrum vel scirpum, et hic non habet sumi pro
rubro sed pro scirpo; unde dicit quod possumus suspicari
quod venerunt ad paludem quandam et lacum, qui carecto
et juncis plenus fuit. Quod autem Scriptura sacra omnem
congregationem aquarum mare vocet, nulla dubitatio est;
hic igitur secundum Hebraicam veritatem significat paludem
juncorum. Sed quia etiam nimis vulgatum fuit in antiqua
translatione quod haec mansio vocetur mare Rubrum, ideo
Hieronymus dimisit in nostra stare ut fuerat in antiqua, sicut
multa alia per universum corpus scripturae. Ultima vero
istarum quinque, quae est undecima ab egressu filiorum
Israel de Aegypto, est Raphidim in directo ad septentrionem,
cujus est Amalechitarum regio, quae pugnavit cum filiis Israel
in deserto Raphidim, et victa est ab eis. Deinde magis versus
orientem est desertum Sinai, ubi est mons Sina, qui est mons
Dei Oreb, ut dicit Hieronymus in libro Locorum. Sed non est
petra Oreb in Raphidim, de qua Moyses aquam eduxit. Nam
Horeb pro monte Sina scribitur per Heth literam, sed Oreb
non. Et post sunt sepulcra concupiscentiae et Asseroth, quae
sunt duae mansiones post montem Sina in hoc deserto Sinai.

Deinde magis ad orientem est desertum Pharan, ubi incipit Desert of
regio Ismaelitarum tendens versus mare Rubrum ad orientem. haran.
Ad septentrionem vero Pharan est Ebron civitas David, et
ubi Adam magnus et Abraham, et Isaac, et Jacob, sepulti
sunt. Per viam deserti inter Pharan et Ebron misit Moyses
Josuen, et Caleph, et alios exploratores. Et in hoc deserto
Pharan, ut dicit Hieronymus in libro mansionum, fecerunt
filii Israel octodecim mansiones, a quinque usque ad triginta
duo, computando extremas cum mediis, ut ultima sit Asyon-
gaber; unde Pharan desertum est latissimum. -Et hic percussi
sunt ab Amalechitis et Chananaeis, et hic dat Dominus
judicia, et orta est seditio Chorae, et fronduit virga Aaron,
et multa alia facta sunt, sicut a tertio decimo capitulo
Numerorum in vicesimum patens est.

Postquam exiverunt desertum Pharan, transiverunt magis ad

Another
desert
known as
Sin.

Moab.

328 OPERIS MAJORIS PARS QUARTA.

orientem usque ad desertum Sin, quod est Cades Barne, ubi
murmuravit populus ad aquas contradictionis. Sed istud non
est illud desertum Sin. Nam istud desertum multo plus elonga-
tum est a Rubro mari,cui annexa est terra Edom ad orientem
septentrionalem. Nam ab hoc loco miserunt filii Israel nuntios
ad Edom dicentes, Ecce in urbe Cades, quae est in extremis
finibus tuis, positi obsecramus ut nobis transire liceat, sicut
dicitur Numerorum xviii Quod si quis contendat quod
desertum Sin superius dictum possit se extendere aliquando
ad hunc locum, patet quod non ; per Hieronymum in epistola
de mansionibus, tam per interpretationem quam per Scrip-
turam; quoniam Sin primum scribitur per Samech et inter-
pretatur rubus vel odium ; hoc autem per Sade et vertitur in
mandatum. Et ideo filii Israel declinaverunt per viam quae
ducit ad mare Rubrum circumeuntes terram Edom, et
venerunt ad montem Or in ultimis finibus terrae illius, in quo
monte mortuus est Aaron.

Et in finibus terrae Edom fecerunt adhuc alias tres man-
siones secundum Hieronymum usquequo venerunt ad terminos
Moab, unde Moab est in oriente Edom. Nam egressi de
finibus Edom fixerunt tentoria in deserto quod respicit Moab
contra orientalem plagam, sicut dicitur Numerorum xxi.
Deinde, ut habetur Deuteronomiae xi, transierunt urbem
Moab nomine usque ad confinium terminorum Ammon. Et
in his locis incipit ab oriente terra Seon regis Amorraeorum,
et terra Moabitarum et Ammonitarum, et ideo diligenter
consideranda sunt haec loca. Nam hic incipit terra filiorum
Israel, et de his multum loquitur Scriptura et sancti. Est
igitur in confinio horum locorum rupes in sublime porrecta,
quae vocatur Arnon, et haec rupes distinguit extrema filiorum
Ammon et Moab et Seon regis Amorraeorum; et ideo ibi
incipit terra filiorum Israel. Sed sub hac rupe versus occi-
dentem est vallis quae vocatur Arnon, juxta quam a latere
meridiano est civitas Ar, quae est caput regni Moabitarum,
quae postea dicta est Acropolis ex Hebraeo vocabulo et
Graeco composita, id est, civitas adversarii, sicut dicit Hierony-
mus quinto libro super Isaiam prophetam. A rupe autem hac
descendit torrens versus occidentem, quae vocatur torrens

GEOGRAPHIA. 329

Arnon, super cujus ripam situatur oppidum, quod vocatur Aroer
prope Amon. Haec patent ex libro Locorum Hieronymi, et
ex textu in libro Numerorum xxi et Deuteronomiae ii et iii
et Josue xiii et Judicum xi et multis aliis locis Scripturae.

Terra igitur Moab ascendit ab Arnon in occidentem usque Midian,
ad Edom et usque ad mare mortuum, et ubi fuerunt civitates Seon.”
submersae, et usque ad Jordanem contra Jericho, sicut patet
ex locis praedictis Scripturae et Hieronymi. Et infra terram
Moab prope Arnonem et Ariopolim est Madian civitas Jethro
soceri Moysi, sicut dicit Hieronymus libro Locorum. Et
necesse est ut ibi sint Madianitae. Nam ut patet Exodi
xxii et Numerorum xxiii et xxiv et xxv, Balac rex Moabi-
tarum vocavit Balaam hariolum ut malediceret Israeli, qui
dedit eis consilium ut offerrent eis filias Madianitarum, et
peccaverunt cum eis et interfecti sunt multi de Israele. Insuper
Madianitae destructi sunt et deleti postea per filios Israel.
Ex altera parte torrentis Arnon incipiebat terra filiorum
Ammon versus septentrionem et orientem tendens versus
Euphratem, et ad occidentem accedit ejus angulus versus
Jordanem usque ad vadum seu torrentem Jaboc, quem trans-
ivit Jacob quando venit de Mesopotamia Syriae, post cujus
transitum luctabatur angelus cum eo sicut xxxii Genesis
recitatur. Et quod ad hunc torrentem Jaboc sit terminus
filiorum Ammon patet per Deuteronomiam iii capitulo. Et
hic est terminus Ammon et Seon regis Amorraeorum et
Og regis Basan, sicut patet ex Judicum xi. Nam a Jaboc
incipiebat terra Seon, ut ibi habetur; et ubi terminatur ejus
terra, incipit terra Og regis Basan, et descendit etiam usque
prope torrentem Arnon usque ad confinia Esebon urbem regis
Seon Amorraeorum. Et ideo terra quae fuit propria Seon
est inclusa a meridie Moabitis et ab oriente Ammonitis, et
ab occidente habet Jordanem fluvium, et a septentrione habet
terram Og regis Basan. Sed iste Seon potentior factus irrupit
in regiones Moab et Ammon, et abstulit terras eorum. Nam
quod abstulit terram filiorum Ammon habetur Judicum xi.
Et quod medietatem terrae suae amiserunt filii Ammon
habetur Josue xiii Moab etiam multum amisit sicut patet
ex xxi Numerorum.

Other

regions of
Arabia,

Saba, in
which lies
Arabia
Felix.

330 OPERIS MAJORIS PARS QUARTA.

Postquam vero inventae sunt hae regiones a lingua maris
Rubri per mansiones filiorum Israel, adhuc considerandum est
quod in desertis quae sunt inter mare Rubrum et terras jam
nominatas sunt aliae regiones magnae, quae extenduntur ab
Euphrate in circuitu terrarum jam dictarum, scilicet terra
filiorum Ammon et Moab, et desertum Pharan, usque ad
terram Elamitarum, quam superius esse positam dixi super
littus maris: Rubri a transitu filiorum Israel usque versus
orientem. In hac igitur regione pergrandi similiter et in
Pharan habitaverunt filii Keturae et Agar, quos generavit
Abraham, de quibus fit mentio xxv capitulo Genesis. Et
primo ab Euphrate incipit regio Nabathena a filio primo
Ismaelis, qui vocatur Nabaioth, sicut dicit Hieronymus, super
Genesim xxv capitulo, et nunc dicto concordat Plinius primo
libro, nisi quod unam partem Nabathenorum vocat Nomades,
qui. vagantur circa Euphratem prope Chaldaeos; post hos
versus desertum Pharan est Cedar regio, quae ab altero filiorum
Ismael nominatur qui Cedar vocatus est. Et quamvis aliae
regiones filiorum Ismael nominentur usque Sur, nam habitavit
ab Evila usque Sur, sicut dicit Scriptura, tamen omnes vocantur
Cedar, sicut vult Hieronymus quinto libro super illud Isaiae
xxi Onus in Arabia, dicens, Hic loquitur pro Cedar, quae est
regio Ismaelitarum, qui dicuntur Agareni et Saraceni nomine
perverso ; et septimo libro super capitulum Isaiae 1x dicit de
his regionibus Cedar et Nabathena, quod Cedar est regio Sara-
cenorum, qui in Scriptura vocantur Ismaelitae, et Nabaioth est
unus filiorum Ismael, quorum nominibus solitudo appellatur,
quae frugum inops, pecorum plena est. Evila vero est pars
regionis Ismaelis distans a Pharan oppido in deserto Pharan
per tres dietas, ut dicitur in libro Locorum. Est vero et alia
regio Evila in India juxta flumen Gangem de qua primo
Genesis dicitur.

Et inter Cedar et Elamitarum regionem supradictam exten-
ditur Saba regio super littus maris Rubri secundum Plinium
quinto libro. Et haec regio est thurifera et aromatibus plena,
et habet tres partes. Una vocatur Arabia Eudaemon, quae
includitur inter sinum Persicum maris Rubri et sinum Arabi-
cum, secundum Orosium libro de Ormesta Mundi, et secundum

GEOGRAPHIA. 331

Isidorum libro xiv. Alia est Madian, nominata ab uno filio
Abrahae ex Kethura. Tertia est Epha, regio nominata ab
uno filio Madian, ut patet ex xxv Genesis. Et quod hae duae
regiones sint de regno Saba vult Hieronymus expresse super
xvii Isaiae, dicens, Madian et Epha sunt regiones fertiles came-
lorum, omnisque provincia appellatur Saba; unde fuit regina
Sabae sicut dicit. Et quod Arabia Eudaemon sit pars Sabae
patet, quia illa juncta est Chaldaeis immediate, sicut dicit
Orosius. Et Chaldaei et Sabaei eorum vicini simul invaserunt
armenta Job sanctissimi, ut patet ex capitulo primo libri sui; et
illud patet expresse per Isidorum decimo quarto libro, qui dicit
sic, Arabia appellatur sacra, eo quod regio sit thurifera odores
creans. Hanc etiam Graeci Eudaemon, nostri Beatam nomina-
verunt, in cujus saltibus et myrrha et cinnamonum provenit ;
ibi nascitur et phoenix; ipsa est et Saba appellata a filio
Chus, filii Cham, filii Noe, qui filius Chus Saba appellatus
est; et hoc dicit Hieronymus in Hebraicis quaestionibus. Et
ideo cum Madian et Epha numerantur lx Isaiae, adjungitur
etiam Saba, cum dicit, Omnes de Saba venient. Nam Arabia
Eudaemon nominatur specialiter Saba et principaliter, licet
tota regio illa et Madian et Epha dicantur Saba. Et ideo
tota regio a Chaldaeis supra mare Rubrum usque ad Elam
dicitur Sabaea.

Et considerandum est hic propter aliquas contrarietates, Different
quod Arabia large sumpta habet omnes regiones dictas ex t Por
utraque parte maris Rubri secundum Plinium et Alfraganum Arabia.
et philosophos antiquos. Specialius tamen sumpta accipitur
solum pro regione quae est a lingua maris Rubri usque ad
Euphratem et sinum Persicum versus orientem, et usque ad
Palaestinam Idumaeam versus septentrionem ex una sui parte,
cujus alia pars septentrionalis et magis orientalis extenditur
ad montem Libani, et comprehendit totam regionem Moab et
filiorum Ammon et regna Seon et Og regis Basan, et aliqua
eis conjuncta. Et sic utitur Scriptura ut in Isaia cum dicit,
Onus in Arabia, ubi Cedar comprehenditur sub ea; et mons
Sina sic est in Arabia, secundum quod apostolus dicit ad
Galatas iv. Tertio modo magis stricte accipitur, ut excludatur
Pharan et Cedar et Madian et Epha et Saba Eudaemon.

Syria.

Mesopo-
tamia.

332 OPERIS MAJORIS PARS QUARTA.

Nam sic in tempore Hieronymi et deinceps accepta est Arabia,
quoniam ipse dicit in libro Locorum Pharan trans Arabiam
esse; quarto et decimo septimo libro super Isaiam dicit Madian
et Epha et Cedar et Nabatheam regiones esse trans Arabiam.
Quod vero Saba thurea Eudaemon et tota regio Saba sit
distincta similiter contra Arabiam isto tertio modo dictam
patet per Hieronymum in Hebraicis quaestionibus. Nam
dicit quod cum in Psalmis dicitur, reges Arabum et Sabae dona
adducent, illa est Saba thurea et thurifera praedicta, de qua
adducit auctoritatem Virgilii, Solis est, inquit, thureis virga
Sabaeis. Nam, ut Hieronymus dicit et patet cuilibet scienti
Hebraeum, in Hebraeo dicitur, reges Saba et Saba dona ad-
ducent ; sed primum Saba interpretatur Arabia et scribitur per
sin litteram, secundum scribitur per samec, et est illa Saba
thurifera, et de hac Saba venerunt magi qui adoraverunt
Christum, non de Saba quae est in Ethiopia. Nam illa est
in meridie. Ab oriente enim secundum Evangelium venerunt
magi. Et isti sunt reges Sabae, sive reges Arabum et Sabae.

Post haec sequitur regio praegrandis quae vocatur Syria,
quae, secundum Scripturam et Plinium et antiquos auctores
continet omnes provincias a Tigri flumine ab oriente usque ad
Arabiam a meridie et usque ad mare nostrum seu magnum,
quod dividit Italiam et Syriam et Aegyptum ab occidente
et a Cilicia et Tauro monte altissimo a septentrione. Prima
ejus et principalis regio est Mesopotamia seu Assyria, nam
idem sunt secundum Plinium ; et Hieronymus dicit tertio libro
super Isaiam, quod tota regio inter Tigrim et Euphratem est
regio Assyriorum. . Similiter Mesopotamia inter Tigrim et
Euphratem continetur. Unde dicitur a meson, quod est
medium, et potamus, quod est fluvius, quasi inter duos fluvios
contenta, Tigrim scilicet et Euphratem. Et ideo idem fuit
antiquitus Mesopotamia et Assyria. Et haec Mesopotamia
seu Assyria ab oriente habet Tigrim, ab occasu Euphratem,
a meridie mare Persicum, quod est sinus Persicus maris Rubri,
a septentrione Taurum montem, cujus longitudo est circiter
octingenta milliaria, latitudo trecenta, secundum Plinium. In
hac Mesopotamia sunt Ninive et Babylon, et tota terra Chal-
daeorum, et Babel turris constructa in terra Senaar. In hac

DM 00M Uo7 "0t un Se v7 UC -———— Áo a eS ee ee

GEOGRAPHIA. 333

autem Mesopotamia sunt civitates quas Nimroth construxit,
scilicet Arad, id est, Edissam, et Archad, quae nunc Nisibis,
seu vulgariter Nisibin dicitur, et Calampne, quae postea a
Seleuco rege dicta est Seleucia, sicut Hieronymus exponit
super decimum capitulum Genesis. Et praeterea in Mesopo-
tamia est Aram, sicut in Genesi habetur, quae adhuc nomen
suum retinet. Et Aram distat per duas dietas ab Euphrate,
et Hieronymus dicit quod Aram est trans Edissam ; ergo
Edissa est inter Aram et Euphratem, et Ninive est circiter
decem dietas ab Aram, id est, ad orientem super Tigrim
fluvium, secundum quod vult Scriptura quod Tigris currit
contra Assyrios. Ninivitae enim principaliter vocati sunt
Assyrii. Ab Aram usque ad Baldac versus meridiem sunt
dietae circiter xxvi. Et est Baldac civitas regia, in qua Caliph
Dominus Saracenitae sectae sedem suae dignitatis constituit.
In illis vero partibus est turris Babel, et ruinae Babylonis
magnae, quae fuit caput regni Babyloniorum et Chaldaeorum,
qui cum fuerant Mesopotamii et Assyrii a principio, eo quod
tota terra inter Tigrim et Euphratem dicebatur Mesopotamia
et Assyria, tum quia Babylon Chaldaicarum gentium caput
summam claritatem obtinuit inter urbes toto orbe. Reliqua
pars Mesopotamiae Assyriaeque Babylonia appellata est, ut
dicit Plinius, ita quod tandem Babylonii praevaluerunt. Nam,
ut patet ex libris Regum et Paralipomenon primo nominati
sunt reges Assyriorum, ut Salmanasar et Sennacherib et
caeteri. Deinde Nabugodonosor, rex Babylonis, et ejus
successores vastaverunt Assyrios, et dominati sunt per totum
inter Tigrim et Euphratem. Noe quidem et filii ejus primo
post diluvium habitaverunt in Babylonia, sicut dicit Albumazar
quinto libro in majori introductorio astronomiae. Nam cum
ipsi fuerunt sapientes astronomi et docuerunt primo Chal-
daeos astronomiam, ut ibidem dicit, sciverunt quod quartum
clima est temperatissimum, in quo Babylonia est, et ideo ad
eam declinaverunt.

Quoniam vero Tigris et Euphrates sunt duo de quatuor The Tigris
principalibus fluminibus mundi et Nilo connumerati, ideo de Euphrates
illis aliqua sunt dicenda. Varius autem est ortus eorum.
Nam secundum veritatem primo oriuntur de Paradiso, ut vult

334 OPERIS MAJORIS PARS QUARTA.

Scriptura. Deinde secundum Plinium Tigris erumpit in
Armenia majore et postea cadit in lacum omnia illata pondera
sustinentem et nebulis exhalantem, cui unum genus piscium
est, qui aquae transcurrentis non miscentur alveo, sicut ncque
a Tigri pisces in lacum transnatant. Deinde occurrente Tauro
monte in specum mergitur, et ab altero montis latere erumpit
in lacum, et postea ad formam fluminis revertitur et Euphrati
jungitur, et transit per Ninivem, et post longa spatia currit
in maris Rubri sinum, qui Persicus vocatur. Euphrates vero
secundum Plinium quinto libro in Armenia majore oriens
separat Cappadociam ab illa, deinde occurrit ei mons Taurus
postea fluenti in occasum. Iterum se flectit in meridiem, et
funditur in duo brachia. Unum cadit in Tigrim includens a
septentrione Mesopotamiam, aliud alluit eam ab occidente et
currit per mediam Babyloniam, ut dicit Orosius ad Augustinum,
deinde fluit in paludes, et tandem in mare Persicum. Nam
Chaldaei sunt inter Babyloniam ad meridiem versus Persicum
mare, et Euphrates eos, sicut caeteros Mesopotamios et
Assyrios, alluit ab occidente, separans eos a caeteris Syriae
regionibus et ab Arabia. Euphrates vero, ut dicit Plinius,
crescit Nili modo parum ab eo differens. Nam Mesopotamiam
inundat sole obtinente xx partem Cancri, et incipit minui in
Virgine, Leone transgresso. In totum vero remeat xxxix
parte Virginis. Quod autem Boetius quinto de consolatione et
Sallustius dicunt, quod Tigris et Euphrates uno se fonte
revolvunt, potest intelligi de fonte Paradisi; nam hoc verum
est secundum Scripturam, quam Boetius saltem bene scivit, et
Sallustius ex revolutione historiae Scripturae credere potuit ;
aut hoc verum est de ortu eorum in Armenia, quoniam uterque
ibi oritur secundum Plinium; aut intelligi poterit de ortu
eorum citra Taurum montem, nam occursu ejus absorbentur
in terram, et ex altera sui parte erumpunt.

Other parts Ab Euphrate qui currit in oriente est Arabia, de qua

of Syria.

dictum est, versus meridiem et mare Rubrum. Et versus
septentrionem sunt reliquae regiones Syriae, scilicet Syria
Comagena, Syria Coele seu Coele-Syria, et Syria Phoenicis,
et Syria Palaestinae, quae includunt provincias a Judaeis
possessas, scilicet Judaeam, Samariam, et Galilaeam citra

GEOGRAPHIA. 335

Jordanem, et per eam trans Jordanem, quam possederunt
tribus Ruben et Gad, ac dimidia tribus Manasse, ubi est regio
Decapolis et Ituraea seu Traconitis regio.

Et in his provinciis reperiuntur omnia loca sacra, quae Sacred
calcaverunt primo sancti patriarchae et prophetae, deinde ECoErspby.
Dominus ipse et Mater ejus et apostoli sacrati, et in quibus
crevit ecclesia primitiva et quae resonant evangelia, in quibus
majora mysteria continentur quam auris mortalis possit audire
aut mens humana intelligere, ut vult Origenes xviii Josue.
Quapropter de his diligentius est dicendum.

Primo igitur super mare nostrum, quod dividit Italiam et Cities on
Aegyptum et Syriam, collocandae sunt civitates famosae vel $e Syrian
prope illud, ut sic superius versus orientem facilius depre-
hendantur loca quae volumus. Primo igitur non super mare
sed prope, quasi per tres leucas in confinio Aegypti et
Palaestinae et Judaeae est Gaza civitas insignis Palaestinae,
ut dicit Hieronymus libro Locorum. Deinde sunt novem
leucae usque ad Ascalonem, quae est metropolis Palaestinae
super mare sita. Deinde xii leucae usque ad Joppen. Deinde
usque ad Acon xxiv, vel duae dietae. Nam duae leucae vel
tres usque Assur, quod antiquitus Adotus dicebatur, et postea
decem vel novem usque Caesaream Palaestinae, quae antiquitus
turris Stratonis vocabatur, in qua Petrus baptizavit Cornelium,
ut dicit Hieronymus multis locis, deinde usque castrum pere-
grini quinque leucae; et postea usque Caiphas tres; et quatuor
usque Acon; et postea usque Tyrum in corde maris sunt
novem leucae; et postea quatuor vel quinque usque ad Sarep-
tam Sidoniorum, ubi vidua pavit Heliam prophetam ; deinde
tres vel quatuor usque ad Sidonem; postea novem vel octo
usque Berithum, quod Barut vocatur. Deinde novem usque
Biblium, quod nunc Gibeleth dicitur, unde xxvii Ezechielis
dicitur, Senes Biblii et prudentes ejus habuerunt nautas.
Postea novem leucae usque Tripolim ; postea est una dieta
usque Tortosam, quae ante Radum dicitur. Deinde usque
Laodiceam sunt dietae circiter tres. Nam usque Valaniam
sunt leucae circiter decem. Alii tamen dicunt, quod a Tortosa
usque ad Margat est una dieta; et a Margat usque Laodiceam
una dieta; et a Laodicea usque Antiochiam duae dietae. Sed

Palestine ;
its dimen-
sions and
boundaries.

336 OPERIS MAJORIS PARS QUARTA.

Antiochia est per quinque leucas a mari infra terram. Ab
Antiochia usque ad Tarsum Paulo apostolo gloriosam, metro-
polim Ciliciae, sunt dietae circiter tres. Sed tamen usque prin-
cipium Ciliciae sunt dietae circiter duae, vel una et dimidia.
Redeundum est igitur ad loca infra terram. Abraham et
Isaac frequentabant loca Gerarae. Gerara enim, a qua
Gerarchica regio, ut dicit Hieronymus libro Locorum, fuit
terminus olim Palaestinorum inter Cades et Sur, et ibi est
Bersabe, qui vocatur puteus juramenti, ubi Abraham et Isaac
foedus cum Abimelech iniverunt. Et ab isto loco incipit terra
Hebraeorum ab eis possessa. Nec ultra hunc locum ad
austrum amplius possederunt, sicut dicit Hieronymus in
epistola ad Dardanum de terra repromissionis. Quamvis
terra repromissa eis a Deo incipiebat a torrente Aegypti. sicut
dicit Hieronymus octavo libro super Isaiam et primo libro
similiter. Ille enim torrens, ut dicit Hieronymus, ibi est fluvius
turbidus in finibus Aegypti versus Palaestinam et Judaeam, nec
habens perpetuas aquas, non procul a Nilo, sed juxta castrum
quod Rinocorura dicitur, quod LXX interpretes posuerunt loco
torrentis sicut in eorum translatione habetur in Isaia. A Ber-
sabe vero viginti milliaria versus septentrionem est secundum
Hieronymum libro Locorum Ebron metropolis olim Philisti-
norum, sed decorata nobilium sepultura quatuor patriarcharum
scilicet Adae maximi, Abrahae, Isaac, et Jacob. Et facile
est tunc advertere loca vicina, scilicet convallem Mambre et
ilicem Abrahae et campum Damascenum a meridie Ebron,
qui sic nominatur a Damasco servo Abrahae. Unde non est
Agar ille prope civitatem illam magnam Damascum, quae
caput Syriae est. Nam ab illo loco distat circiter per quinque
dietas, sed est juxta Ebron, in quo Adam plasmatus est, et in
quo Cain interfecit fratrem suum ; sic dicit magister in historiis
et super Genesim. Carmelus, ubi quondam Nabal Carmelus
fuit, et nunc villa est Carmela nomine in sexto lapide oppidi
Ebron ad orientalem plagam, sicut dicit Hieronymus libro
Locorum. Et prope Carmelum ad orientem in octavo milliario
ab Ebron Ziph vicus ostenditur, ubi absconditus est David,
juxta quem mons squalidus idem nomen habet, scilicet Ziph,
in quo sedit David prope Carmelam ut dicit Hieronymus.

GEOGRAPHIA. 337

Quartodecimo vero milliario versus septentrionem est Bethleem,
civitas in qua Dominus natus est. Et secundum Hieronymum
sexto milliario a Bethleem versus septentrionem fuit Jerusalem
longe clarissima urbium orientis, ut dicit Plinius! Haec
autem civitas distat a Joppe per duodecim leucas, et ab Acon
per dietas circiter tres, et ad orientalem plagam distat Jericho
a Jerusalem per novem leucas; et inter Jericho et Jordanem
sunt duae leucae. Et Thecua villa Amos prophetae distat
versus Eurum inter orientem et austrum per duodecim milliaria,
ut dicit Hieronymus secundo libro super Jeremiam.

Et secundum Hieronymum in epistola de epitaphio sanctae Pentapolis.

Paulae prope illam fuit Pentapolis regio continens quinque
civitates maledictas, scilicet Sodomam, Gomorram et caeteras.
Nam ab illo loco describit Paulam reversam Jerusalem, et primo
per Thecuam proximam. Orosius autem primo de Ormesta
Mundi dicit quod Pentapolis regio in confinio Arabiae et
Palestinae sita est; mediamque vallem quam Jordanus irri-
gaverat nunc mare superinfusum tegit. Et hoc est mare
Mortuum, et mare salis, et mare salinarum et lacus bituminis,
et vallis salsa, et vallis salinarum, et mare Araba, id est, de-
sert. Unde in libris Regnorum scribitur, Ab introitu Emath
usque ad mare Araba et mare Asphalti, id est, bituminis,
secundum Hieronymum in libro Locorum, et super Genesim.
Nam in valle salinarum fuerunt putei bituminis ante subver-
sionem civitatum, sed post pluviam sulphuris in mare Mortuum
versum est, quod stagnum bituminis appellatur. Quatuor
autem civitates submersae sunt, et quinta quae Bale post voca-
batur remansit ad preces Loth, ut in ea post ruinam aliarum
posset morari, quae postea Segor dicebatur, et nunc Zoara
Syriace nuncupatur, sicut dicit Hieronymus super Genesim et
in multis locis. Et haec civitas, licet non fuerit cum suis socia-
bus igne sulphuris consumpta, tamen post lapsum temporis
tertio terrae motu subversa est, ut ait Hieronymus, quae re-
parata Zoara dicitur ab incolis, qui Zoari nuncupantur. Et
haec civitas est in termino maris Mortui ad occidentalem
plagam, a qua non longe super mare Mortuum ab occidente

! Pliny, v. 14 ' Hierosolyma longe clarissima urbium Orientis, non Judaeae
modo.'

VOL. I. Z

The Dead
Sea.

338 OPERIS MAJORIS PARS QUARTA.

est oppidum Engaddi urbs palmarum fertilis, unde balsamum
venit et opobalsamum. Nam arbor est distillans balsamum
in vineis Engaddi, de quibus Solomon meminit in Canticis.
Et haec civitas vocatur in Genesi Asasontamar, quod in
lingua nostra dicitur urbs palmarum ; tamar quippe palma
dicitur, sicut Hieronymus dicit. Quamvis vero multi multa
scribunt de conditionibus istius maris et locorum subversorum,
tamen hic principaliter introducam Hegesippum! in quarto libro
historiae de subversione Jerusalem, quia plura scribit quam
alii, et multi aliorum receperunt ab eo quae recitant, ac si sua
essent quae narrant.

De mari vero Mortuo dicit, quod omnia viventia resiliunt et
statim excutiuntur nec mergi possunt in eo, quod aqua ipsa
amara et sterilis est, nihil recipiens generum viventium,
denique neque pisces, neque assuetas aquis et laetas mergendi
usu patitur aves. Lucernam accensam ferunt aquis super-
natare, sine ulla conversione extincto demergi lumine, et
quamvis demersum difficile haerere in profundo. Denique
Vespasianum imperatorem praecepisse ferunt nandi ignaros
revinctis manibus in profundum dejici, eosque omnes illico
supernatasse quasi spiritu quodam venti levatos, et ad superiora
vi magna repulsos resiluisse. Vagari super aquas bituminis
glebas certum est atro liquore, quas scaphis appropinquantes
colligunt, quibus id muneris est ; haerere sibi fertur bitumen ;
ut ferro haudquaquam vel alia peracuta metalli specie
recidatur; sanguini sane cedit mulierum quo menstrua
solventes lavari feruntur, cujus attactu, ut allegant quibus
experiendi usus fuit, interrumpi proditur. Utilis ad com-
pagem navium fertur, et corporibus hominum salubris admixta
medicamentis. Longitudo lacus hujus ad Zoaros Arabiae
dirigitur stadiis diIxx. Latitudo in stadiis cl usque ad viciniam
Sodomorum, qui quondam uberrimam regionem inhabitabant.

1 The Hegesippus here spoken of is not the Christian writer of the second
century, but the unknown author of a work probably written in the fourth
century, De bello Judaico, or De excidio urbis Hierosolymitanae. It was sup-
posed to have been translated from Greek into Latin by St. Ambrose. The
book is principally composed of extracts from Josephus. Some have thought
that Hegesippus was a misreading of an early copyist who had before him the
words, Ex Josippo. (See Smith's Dict. of Christ. Biog.)

GEOGRAPHIA. 339

Quatuor itaque urbes incensae sunt, quarum umbra quaedam
et species in favillis videtur. Arsere terrae, ardent aquae, in
quibus coelestis ignis reliquiae adhuc manent. Aspicias illic
ad speciem poma viridantia, formatos uvarum racemos, ut
edendi gignant spectantibus cupiditatem ; si carpas, fatiscunt
et resolvuntur in cinerem, fumumque excitant quasi adhuc
ardeant. Quicquid vero Isidorus et Solinus de mirabilibus
mundi et Hieronymus decimo quarto libro super Jeremiam et
Plinius et alii multi dicunt, sub sententia Hegesippi compre-
henduntur. Nam si ipse aliqua summatim perstringat, dicens
nihil vivum ibi posse nutriri nec mergi, alii specificant. Nam
Plinius et Solinus dicunt quod nullum corpus animalium
recipit; tauri camelique fluitant!. Et Hieronymus dicit, quod
propter amaritudinem maris nihil spirans ibi invenitur, unde
nec pisces nec serpentes, sed et pisces a Jordanis inundatione
delati in hoc mare statim moriuntur. Isidorus vero in
Etymologiarum libro verba Hegesippi exponens dicit, quod
nec ventis movetur, resistente turbinibus bitumine, quo aqua
omnis stagnatur, nec ullam materiam sustinet, nisi quae
bitumine illustratur. Et extenditur inter Jericho et Zoaram,
quae est Segor.

Quoniam vero Jordanes influit in mare Mortuum, et ibi The Jor-
nomen suum et virtutem amittit, atque regiones Hebraeorum dan.
et multae aliae notificantur per Jordanem, ideo de illo nunc
dicendum est. Quamvis vero Hieronymus eleganter et
veraciter loquatur de ortu manifesto et discursu Jordanis,
atque Plinius et Isidorus et alii, tamen omnibus merito
praeponendus est Hegesippus, qui in tertio libro explicat
certius et abundantius istius fluminis originem. Omnes enim
auctores praeter Hegesippum, qui per experientiam procedit,
aestimant Jordanem fluvium oriri ex duobus fontibus ad
radices montis Libani juxta Daneadem, quae nunc Caesarea
Philippi nominatur; quorum fontium unus Jor, et alius Dan,
qui sua profluvia divisim protendentes tandem concordant in
unum, unde Jordanes efficitur; et per aliquod spatium terrae

! Plin. v. 16 * Nullum corpus animalium recipit: tauri camelique fluitant ;
inde fama nihil in eo mergi.'

Z2

Cities and
districts of
Palestine.

340 OPERIS MAJORIS PARS QUARTA.

fluminis jura defendens se postea transmittit in lacum qui
Genesar dicitur cui contiguatur lacus Tiberiadis et deinde
Jordanes erumpens decurrit ad orientem Jericho ct fluit in
Mortuum mare supra dictum. Sed totum illud praeter
ortum ejus certum est. Ortus etiam manifestus et vulgatus
se habct, ut dictum est, a duobus fontibus. Sed Hegesippus
probat quod ibi non est primus ejus ortus, immo a Phiala
fonte, qui est ex altera parte Jordanis in Traconitide regione
distans ab urbe Caesarea cxx interjacentibus stadiis. Ab hoc
igitur fonte labitur aqua subterraneis meatibus, et ubi
Caesarea est rursum ebullit. Nam Philippus tetrarches
lraconitidis regionis misit paleas in Phialam, quas ad
Caesaream fluvius subterraneus ebullivit; unde liquet non
exordium primum esse Jordanis in Caesarea, sed fluentum, -
ut paleis resurgentibus manifestatum est. Addit etiam ad
decursum ejus, quod a Paneade seu Caesarea, non latente jam
neque abdito per cava terrae meatu, sed visibili per terras
atque aperto flumine incipiens se superfundere Semeconitim
lacum, paludesque ejus intersecat. Inde quoque cursus suos
dirigens centum viginti stadiis progreditur usque ad urbem,
cui Julias nomen est. Postea lacum istum qui Genesar dicitur
in medio transit fluento, quibus ex locis plurima evagatus
deserta Alfacio suscipitur lacu atque in eum conditur. Itaque
duos lacus victor egressus tertio haeret.

Notificato Jordane urbes et regiones distinguendae sunt.
Nam vicinia Jericho se extendit ad urbem Scythopolim a
parte septentrionali Jericho secundum Hegesippum, quae
civitas in biblia vocatur Bethsan, ut dicit Hieronymus in libro
Locorum, et est oppidum in tribu Manasse, a quo accolas
pristinos non potuerunt filii Manasse expellere. Descendendo
vero ad occidentem usque in septentrionem Jerusalem est
civitas sacerdotalis et insignis ortu Jeremiae prophetae, quae
vocatur Anathoth, tribus milliaribus ab Hierosolymis separata,
sicut dicit Hieronymus quinto libro super Jeremiam. . Deinde
magis ad septentrionem per xii leucasa Jerusalem, et per xii a
Caesarea Palaestinae in directo Caesareae est Samaria civitas
famosa, metropolis decem tribuum, quae nunc Sebaste dicitur.
Super autem regionem Caesareae Palaestinae, et mari magno

GEOGRAPHIA. 341

usque ad fines Ptolemensis regionis incumbit mons Carmelus
per dietas circiter duas in longitudine distensus, in quo oravit
Helias propheta, oleis consitus, et arbustis ac vineis, sicut vult
Hieronymus in quinto et primo libro super Jeremiam. Post vici-
niam Samariae ad orientem septentrionalem sequitur planities
Sabae nunc vocata, sed antiquitus dicebatur campus magnus
Estrelon de quo! .... Et campus Magido in quo Josias rex
optimus fuit occisus. ... Et per fines ejus ad septentrionem
decurrit torrens Fison usque in mare magnum inter Caiphas
et Acon. Deinde ad septentrionem illius campi, et ab Acon
versus orientem ab ea septem leucis distans est Nazareth
beata civitas Domini Salvatoris. Deinde ulterius ad orientem
per duas leucas est mons Tabor gloriosus, in quo Dominus
suam gloriam discipulis tribus et Moysi et Heliae ostendit.
Et deinde ad orientem est Tiberias civitas, quae antiquitus Lakes of
Cenereth dicebatur, ut dicit Hieronymus decimo quarto libro Tiberias
super Ezechielem, et prope hoc mare Tiberiados et Cenereth nesaret.
dicitur lacus, super quem sita est civitas, qui secundum Isidorum
decimo tertio libro, ‘ omnibus aquis in Judaea est salubrior, et
circuit stadia centum sexaginta, cui conjungitur lacus Genesar
amplissimus in Judaea; longitudine clx stadiis extenditur,
latitudine xl diffunditur, aquis crispantibus aura non ventis,
sed de se ipso sibi excrispans, unde et Genesar dicitur Graeco
vocabulo quasi generans sibi auram. Deinde per diffusiora
spatia lacus frequentibus auris spirantibus agitatur. Unde et
purior haustus ejus et ad potandum dulcis et habilis, Haec
Isidorus, qui distinguit hos lacus quantitate et naturali
proprietate, quamvis glossa sexto Matthaei dicit quod idem
dicitur stagnum Genesareth, et mare Tiberiadis, et lacus
salinarum. Sed lacus salinarum secundum omnes, ut prius
dictum est, mare Mortuum vocatur, et ideo haec glossa magi-
stralis magis ex rumore locorum habita est quam ex auctoritate
sanctorum vel experientia. Quod tamen dicit unum esse
mare Tiberiadis et Genesar, hoc potest referri ad vicinitatem
corum. Nam contigua sunt et cchaerent, et ideo pro uno
computantur. Quoniam diversos esse lacus evangelium
Johannis ostendit, quia sexto capitulo dicit, quod abiit Jesus

1A hiatus occurs here in all the MSS.

Cities of
North
Palestine.

342 OPERIS MAJORIS PARS QUARTA.

trans mare Galilaeae quod est Tiberiadis, et deinde venit in
desertum Bethsaidae secundum Lucam; et postea venerunt
discipuli Bethsaidam, secundum Marcum ; deinde ascenderunt
mare ut irent Capharnaum, secundum Johannem, quod non erit
proprie mare Tiberiadis,quia ultra illud prius transierant. Ergo
hoc est mare Genesareth, et ideo diversa sunt, sed cohaerentia.
Deinde versus septentrionem, deserto interjacente, in quo
Dominus pavit quinque millia hominum ex quinque
panibus hordeaceis et duobus piscibus, est Bethsaida civitas
principis apostolorum et Andreae ac Philippi; deinde
Capharnaum. Et quod hic sit ordo istorum locorum patet ex
evangeliis. Nam ante miraculum de panibus dicit Johannes,
abiit Jesus trans mare Galilaeae quod est Tiberiadis ; et tunc
occurrebat multitudo quam pavit; et post discipuli ascen-
derunt in navem, ut transfretarent in Capharnaum, sicut
dicit Johannes ; sed antequam illuc devenerunt, et antequam
pavit multitudinem, venit in desertum locum, qui est Beth-
saida, cum discipulis suis, ut Lucas refert, et Marcus dicit
quod venerunt ad Bethsaidam. ^ Quapropter primo est
Tiberias, deinde ultra mare Tiberiadis versus septentrionem
est desertum Bethsaidae, et juxta illud est Bethsaida, et postea
lacus Genesareth et tandem Capharnaum super oram ejus, et
haec omnia docentur in glossa magna sexto Marci. Deinde
post Capharnaum est Julias oppidum de quo supra ; deinde
Caesarea Philippi ad radices montis Libani.

Amplius ab Acon in orientem versus septentrionem magis
quam Nazareth est Cana Galilaeae, in qua Dominus mutavit
aquam in vinum. Et distat Cana ab Acon per quinque
leucas. Et inter Canam et Nazareth sunt duae leucae.
Item ab Acon in oriens septentrionale per novem leucas est
Sapheth civitas Tobiae ultra Cana quasi per quinque leucas.
Deinde per leucam et dimidiam est Corazaim civitas, et inter
Corazaim et Tiberiadem sunt leucae circiter duae. Et in his
locis scilicet Tiberiade, Bethsaida, Corazaim, Capharnaum,
Cana, Nazareth, Dominus maxime conversatus est praedicando
et faciendo miracula,sicut evangelia referunt. Mons vero Libani
extenditur a Paneade seu Caesarea a regione Tyri et Sidonis,
et Baruch, et Biblii, et Tripolis, per mille quingenti

GEOGRAPHIA. 343

stadia, ut dicit Plinius, et contra Tyrum descendit aqua de
Libano sub terra, et currit prope Tyrum ad unam leucam, et
ibi erumpit in puteum latissimum, et altitudinis ad modum
turris, qui per canalem descendit in terram et irrigat loca
vicina. Et hic puteus est puteus aquarum viventium, qui
fluit cum impetu de Libano, de quo in Canticis habetur.
Contra vero Tripolim est fons hortorum juxta colles Libani et
fluit usque ad montem peregrinum, a quo flumen emanat, et
cadit in mare inter Tripolim et Tortosam, prope tamen
Tripolim. Sed et ab eodem fonte peregrini currit aquae-
ductus in Tripolim. Fons hortorum et Libanus distant a
Tripoli per tres leucas. Sidon distat a collibus Libani per
leucas circiter tres, a monte magno per leucas circiter quinque.

Et cum nunc tactae sunt civitates et montes citra Jordanem Cities
et versus mare nostrum, possunt aliqua addi versus Euphratem. Telden.
Et primo super mare Mortuum est Machaerus, quondam arx
secunda post Hierosolymam, ut dicit Plinius, a qua incipit
tribus Ruben a meridie; et in septentrione super Jordanem
juxta montem Libanum est Pella! civitas, quae est ultimus
terminus terrae Hebraeorum ultra Jordanem in septentrione
prope Caesaream Philippi. Est autem ad orientem finis istius
terrae secundum Hieronymum libro Locorum civitas Phila-
delphia, quae dicitur in Biblia Rabath filiorum Amon. Et in
termino regni Seon, et Og regis Basan, est Jaboc fluvius ut
dictum est, ubi est Ramoth-Galaad, de quo satis habetur in
bellis regum Israel. Circa Pellam et Caesaream Philippi est
mons Hermon Caesareae imminens ; et e regione Libani ad
orientem terrae filiorum Israel, ut dicit Hieronymus libro
Locorum, de quo aestivae nives Tyrum ob delicias deferuntur.
Sed, ut dicit Plinius, valle interjacente post Libanum, huic
par mons exoritur qui Antilibanus nominatur, et est in
orientalem partem montis Libani, ut dicit Hieronymus libro
Locorum. Et secundum Hieronymum libro Locorum, Galaad
mons est ad terminum Phoenicis et Arabiae collibus Libani
copulatus ad meridiem, extenditurque per desertum usque ad
locum illum, ubi trans Jordanem habitavit olim Seon rex

! Pella is twenty miles south of the sea of Tiberias, and sixty miles away from
Caesarea Philippi.

Division of

Syria into
provinces.

344 OPERIS MAJORIS PARS QUARTA.

Amorraeorum. Et cecidit hic mons in sortem tribuum
Ruben, Gad, et dimidiae tribus Manasse: sed et Jeremias
loquitur, ‘Galaad, tu mihi caput seu principium Libani.
Antilibanus vero, secundum Hieronymum libro Locorum,
extendit se circa regiones urbis Damasci, quae cecidit in
sortem tribus Manasse, et haec est Damascus, quae in libris
Regnorum caput Syriae nominatur, quae distat a Jerusalem per
dietas circiter quatuor, ab Acon circiter tres, a Tripoli circiter
duas, a Baruch per unam. Deinde a Damasco per dietas
circiter septem vel octo in septentrionem est civitas famosa Alap,
quae antiquitus mansio fuit Abrahae, quae ab Euphrate distat
circiter per duas dietas et ab Antiochia per dietam et dimidiam.
Deinde in fine terrae repromissionis ad septentrionem in
oriente est et Amath civitas, ut habetur Numerorum xxxiv, de
qua etiam scribitur secundo Regum viii, et primo Paralipo-
menon xviii, et pluribus aliis locis. Et Hieronymus dicit libro
Locorum quod diligenter inquisivit de hac civitate et invenit
quod vocatur Epiphania. Deinde est Comaga civitas prope
Ciliciam, ubi malta bitumen ardens reperitur, quod projectum
super militem armatum comburit eum, nec est remedium per
aquam nec per aliud liquidum, sed per terram apponendum.
Diu vero turbatus est exercitus Romanus et confusus per hoc
bitumen projectum in milites, usquequo remedium per terrae
pulveres sparsos super locum a bitumine tactum didicerunt.
Haec Plinius narrat libro secundo !.

Postquam civitates, et montes, et aquae, et caetera loca
particularia sunt assignata, nunc juxta haec facilius provinciae
et regiones capi possunt. Haec autem tota Syria citra
Euphratem situm habet porrectum in immensam longitu-
dinem, sed in lato angustior est, ut dicit Isidorus, et Plinius
ait quod ejus longitudo a Cilicia usque ad Arabiam tenet
cccclxx milliaria ; habet autem multas provincias, quae omnes
nomine Syriae continentur. Nam in ea nominatur Syria
Comagena, Syria-Coele, Syria Phoenicis, Syria Palaestinae,
Galilaea, Samaria, Judaea. Nam hae regiones ad Syriam per-
tinent Palaestinam secundum auctores. Syria vero Comagena,
ut dicit Isidorus decimo quarto libro, nominatur a vocabulo

! Pliny, ii. 10«.

Bn ——— ——— ————— -— MM ————— — vV— Mn 9 n Án HIP oe

GEOGRAPHIA. 345

Comagae urbis quae quondam ibi metropolis habebatur. Haec
ab oriente habet Euphratem, a septentrione Ciliciam et
Cappadociam, ab occasu mare nostrum, a meridie Syriam-
Coele, quae per diphthongum scribitur, et Coele-Syria nuncu-
patur. In hac est caput et principalis civitas Antiochia in
occidente, cui super mare adnectuntur Laodicea, et Ateradum,
et vicinae civitates usque ad provinciam Phoenicis, et in
oriente est Emath. Nam Hieronymus dicit libro Locorum,
quod diligenter investigans invenit quod haec civitas Emath
fuerit in Coele-Syria, et hoc dicit Plinius. Et similiter Alap,
quae est prope Antiochiam et multum distans a Damasco,
quae est in Syria Phoenicis. Habet igitur haec ab occidente
mare magnum, a septentrione Syriam Comagenam, ab oriente
Euphratem, a meridie Syriam Phoenicis, quae incipit in
septentrionali termino montis Libani. Nam Plinius dicit
quod porrigitur hic mons usque in Coele-Syriam et hoc est
circa Tripolim ; in qua sunt Tripolis, et Tyrus, et Sidon, et
Acon, usque ad Caesaream Palaestinae.

Nam Plinius dicit, quod in ora Phoenicis est Ptolemais,
quae Acon dicitur, et Caesarea Philippi est de provincia
Phoenicis, ut dicit Hieronymus, et totum citra Jordanem
usque ad Palaestinam; atque continet montem Libani et
Antilibanum et Damascum cum sua regione, et totum ultra
Jordanem continet usque Pellam et montem Hermon et
montem Galaad, et illas terras filiorum Israel super Jordanem.
Quod autem contineatur Damascus in Syria Phoenicis patet.
Nam Hieronymus dicit libro Locorum, Damascus est nobilis
urbs Phoenicis. Et super Genesim comprehendit Damascum
sub Syria Phoenicis, cum dicat, quod Hus filius Aran
possedit Damascum, et usque ad Coele-Syriam. Principales
tamen civitates Phoenicum sunt Tyrus et Sidon. Nam, ut
dicit Isidorus decimo quarto libro, Phoenix Cadmi frater
de Thebis Aegyptiorum in Syriam profectus apud Sidonem
regnavit, eamque provinciam suo nomine Phoenicen appel-
lavit. Et isti similiter condiderunt Tyrum; a quibus tota
terra in circuitu vocatur Phoenicea. Haec tamen in duas
partes principales distribuitur, scilicet in regionem Tyriorum,
Syriorum, et Sidoniorum, et Aconensium, et totam terram

Phoenicia.

Judaea.

346 OPERIS MAJORIS PARS QUARTA.

inter Libanum et Tripolim; et alia ejus pars principalis est
Syria Damasci, quae civitas Damascus quantum ad regnum
Syriae inter Euphratem et montem Libanum usque ad terram
Hebraeorum vocabatur caput Syriae. Nomen enim Syriae in
tempore regum Israel attribuebatur Damasco et regioni ejus.
Haec igitur provincia Syriae Phoenicis habet terram
Hebraeorum a meridie et terram Philistinorum ; sed terra
Philistinorum incipit a finibus Aconensis territorii usque ad
turbidum fluvium Aegypti, et antiquitus continebat fere
totam terram Judaeorum citra Jordanem.

Quia tamen Judaei multa occupabant de regione Philisti-
norum et coarctabant eos in civitatibus maritimis, scilicet
Caesarea, Joppe, Ascalone, et Gaza, et caeteris; ideo distin-
guendum est hic quod citra Jordanem sunt tres regiones
principales Judaeorum, scilicet Galilaea, Samaria, Judaea
specialiter dicta, secundum quod xix Matthaei dicitur in
glossa. Omnis Judaeorum provincia ad distinctionem aliarum
gentium Judaea dicitur, sed specialiter meridiana plaga, in
qua Hierosolyma, ad differentiam Samariae, Galilaeae, Deca-
polis et caeterarum regionum ejusdem provinciae. X Hanc
autem terram Judaeorum totam trans Jordanem et citra
Josephus in antiquitatum libro distinguit in partes et ordinat ;
quem secutus est Hegesippus tertio libro, et exponit ea
quae obscurius apud Josephum reperiuntur. Tota autem
regio trans Jordanem vocatur ab eis Pera. Longitudo ejus
a Macheronte super mare Mortuum usque ad Pellam prope
Caesaream Philippi et montem Hermon; latitudo ejus a Phila-
delphia usque ad Jordanem. Duas vero partes principales
invenimus in ea; una est Decapolis regio continens decem
civitates, quarum una est Pella, ut dicit Plinius, et caeterae ei
annexae ad meridiem Libani et Antilibani secundum Plinium
versus Philadelphiam, quam cingunt, ut dicit, duae tetrarchiae,
scilicet Paneas seu Caesarea Philippi ab occidente et Traconitis
regio a meridie super Jordanem. Et ideo Decapolis haec est
prope Libanum et Caesaream Philippi, et jungitur finibus
Tyri et Sidonis, secundum quod Marci viii habetur ; ‘ Exiens
jesus de finibus Tyri venit per Sidonem ad mare Galilaeae
inter medios fines Decapoleos. Et post hanc ad meridiem

GEOGRAPHIA. 347

super Jordanem est Ithuraea seu Traconitis tetrachia, in qua
est Phiala fons Jordanis, ut prius dictum est, parum distans
a Caesarea, et Gerasenorum regio, cujus caput est Gerasa.
Et dicit glossa Marci quinto, Gerasa est urbs Arabiae trans
Jordanem juncta monti Galaad in tribu Manasse non longe a
stagno Tiberiadis, in quo porci praecipitati sunt. Hic igitur
habitabant Geraseni seu Gergaseni, ut ex hoc loco accipitur.
Deinde versus meridiem est alia pars Ithuraeae seu Traconi-
tidis regionis, de qua dicit Hieronymus libro Locorum.
Traconitis regio sive Ithuraea, cujus tetrarches Philippus
juxta evangelium Lucae, est trans Bosram Arabiae civitatem
in deserto contra australem plagam, et in septentrionem
respicit versus Damascum. Quae Bosra est in deserto trans
Jordanem, quae cecidit in tribu Ruben ad orientalem plagam
Jericho et extenditur versus Macherontem et terminos
Moabitarum. Sed ne fiat quaestio de Bosra, dicendum est
quod alia est civitas in Idumaea, de qua dicit Isaias: * Quis
est iste qui venit de Edom, tinctis vestibus de Bosra?' sicut
distinguit Hieronymus libro Locorum. Et quod hic Ithuraea
extendatur usque prope Decapolim et Caesaream patet per
hoc, quod Plinius dicit quod Ithuraea cingit Decapolim.

Regiones vero citra Jordanem sic dividuntur. Nam Galilce.

secundum Josephum et Hegesippum primo est tota Galilaea,
quae habet a septentrione fines Tyri et Sidonis, ab occasu
Aconense territorium cum monte Carmelo, ab ortu Decapolim,
a meridie Samariam et Scythopolim superius assignatam.
Duplex tamen est Galilaea, una gentium et superior, quae
finibus Tyri et Sidonis adhaeret. Quae ideo dicitur Galilaea
gentium, quia Solomon dedit in ea Hiram regi Tyri viginti
civitates; et ideo quia gentes in hac Galilaea mixtae sunt cum
Judaeis, et quia est prope nationes gentium a septentrione, et
ortu solis, et occidente, vocatur Galilaea gentium ; et haec
terminatur circa Tiberiadem, et infra campum magnum
Esdrelon. Et in illis locis incipit Galilaea inferior, quae
dicitur Galilaea Judaeorum, quae est in tribu Zabulon. Sed
hic cavendum est, ne putetur esse trans Jordanem, ut multi
aestimaverunt propter verbum Isaiae et evangelium Matthaei,
cum dicit, ‘terra Zabulon et terra Nepthalim via maris trans

Samaria.

Extent
of the

348 OPERIS MAJORIS PARS QUARTA.

Jordanem, Galilaea gentium.’ Sed glossa super Matthaeum
dicit Galilaea gentium quae est in tribu Nepthalim vicina
Tyriis; et ideo cum tribus Nepthalim sit citra Jordanem, tunc
haec Galilaea similiter, et hoc dicit : Hieronymus in libro
Locorum; et Josephus, et Hegesippus, et omnes volunt hoc.
Sed considerandus est modus loquendi in hac parte. Nam
pluries invenimus hunc modum loquendi in evangeliis. Quo-
niam sexto Marci dicitur, ‘ et ascendentes in navim abierunt
in locum desertum, et viderunt cos abeuntes et cognoverunt
multi, et pedestres de omnibus civitatibus concurrerunt illuc
et praevenerunt eos.’ Ubi dicit glossa, non ad aliam maris
ripam sive Jordanis pervenerunt, sed transito aliquo freto vel
stagno a Domino et discipulis ejus, proximos ejusdem regionis
locos indigenae adierunt quo pedestres pervenire potuerunt.
Ex quo accepimus quod trans Jordanem hic significat fieri
trans ejus aliquam partem, non totum. Similiter cum
dicatur sexto Johannis, ‘Post haec abiit Jesus trans mare
Galilaeae quod est Tiberiadis, non transivit usque ad aliud
littus, ubi est regio Gerasenorum, sed angulum maris transivit
ex eadem parte, scilicet citra Jordanem, et ideo hic sicut
prius ponitur pars pro toto. Et cum eodem capitulo dicat,
* Venerunt trans mare in Capharnaum, adhuc in eadem
regione et citra Jordanem semper fuerunt. Et ideo non
totum mare accipitur, nec fit transfretatio ad aliud littus, sed
pars pro tota accipitur ex eadem parte Jordanis: et ita hic,
cum dicitur trans Jordanem Galilaea gentium, sumitur pars
pro toto. A loco enim Isaiae, in quo haec dicebat, fuit
magna pars Jordanis usque ad Galilaeam gentium, quam in
eundo de uno loco ad alium oportet transmeare, et ideo dicit
trans Jordanem, id est, trans magnam partem Jordanis, quae
extendebatur a loco Isaiae usque ad Galilaeam superiorem.
Deinde ad meridiem Galilaeae Judaeorum est Samaria, quae
non est solum civitatis nomen, sed regionis, quae incipit in
campo magno et extenditur usque ad Judaeam, cujus Judaeae
latitudo est a Jordane usque ad Joppen secundum Josephum et
Hegesippum, cujus longitudo usque ad Bersaben extenditur.
Et nunc in fine solvenda est quaestio notanda, ut sciamus
quantum est terra repromissionis et quantum est possessum

GEOGRAPHIA. 349

a Judaeis. Sed Hieronymus certitudinaliter hoc in epistola promised
de terra repromissionis determinat, dicens quod nec David, and.
nec Solomon, nec alii possederunt unquam nisi a Dan usque
Bersaben, licet post victoriam multos inimicos et tributarios
receperunt. Et hujus terrae longitudo inter Dan et Bersaben

vix continet centum et sexaginta milliaria, ut ipse dicit et infert.
Pudet dicere latitudinem, nam a Joppe usque ad viculum
nostrum Bethlehem sunt quadraginta sex milliaria, et a Beth-
lehem usque ad Jordanem est circiter una dieta ; quapropter
parum fuit possessum a Judaeis. Sciendum tamen est,
quod hoc quod nunc tactum est, solum fuit possessum citra
Jordanem.

Ultra tamen habuerunt suas possessiones duae tribus et Judaea
dimidia, ut patet, sicut Hieronymus etiam in hac epistola Jordan.
exponit. Sed repromissum fuit eis ab Euphrate ex parte
orientis, usque ad mare nostrum ex parte occidentis, et a
Cilicia et Tauro monte a parte aquilonis usque ad fluvium
turbidum Aegypti, et usque ad terram Edom, et Moab, et
Ammon, ex parte meridiei. Nam octavo libro super Isaiam
dicit Hieronymus quod ab Euphrate usque ad rivulum Aegypti
fuit Judaeis repromissum, immo usque ad Nilum. Nam ille
rivus est prope Nilum. Et Euphrates est ab oriente istius
terrae. Rivus autem Aegypti cum mari nostro, in quod in-
fluit, est ad occidentem, et in primo libro dicit illud idem. Et
addit quod ex parte aquilonis fuit eis repromissum a Cilicia et
Tauro monte, et decimo quarto libro super Ezechielem dicit,
quod plaga septentrionalis incipit a mari nostro usque ad
Zephirum Ciliciae oppidum, et usque ad Taurum montem
altissimum, et usque Emath, quae est civitas Coele-Syria,
quae nunc Epiphania dicitur, et in occidente durat a torrente
Rinocorurae urbis influente in mare magnum super mare
istud usque ad eum locum maris qui est contra Emath urbem
Syriae, de qua supra. Meridiana vero pars incipit a torrente
Aegypti, ubi cadit in mare magnum, ascendendo per desertum
Sin et Cades, et per terram Edom, Moab et Ammon, usque
ad Euphratem. Nam si Euphrates est in oriente, et mare
in quod cadit rivus Aegypti in occidente, tunc meridiana pars
extenditur inter illud mare et Euphratem. Hoc sequitur

Jerusalem.

The Tauric
range, in-
cluding
Caucasus.

350 OPERIS MAJORIS PARS QUARTA.

necessario. Sed non habetur hoc una auctoritate, sed ex
multis colligitur et sequitur ex praedictis. Quod enim xxxiv
Numerorum, et xiv super Ezechielem multis locis habetur,
quod mare Cenereth et Jordanis et hujusmodi sunt in oriente,
hoc est verum respectu terrae possessae a Judaeis citra
Jordanem. Sed ultra Jordanem multa possederunt, ut patet
per duas tribus et dimidiam, et plura fuerunt eis repromissa,
quoniam usque ad Euphratem.

1In medio Judaeae est Hierusalem variarum opum dives,
unde secundum gratiam elementorum putaverunt Judaei eam
promissam fluentem lac et mel, cum hinc eis Deus resur-
rectionis praerogativam pollicetur. Scissura decem tribuum
nomen dedit Judaeis, nam ante Hebraei sive Israel nomina-
bantur. Ex quo autem in duo regna Dei populus est divisus,
duae tribus quae de stirpe Judae reges habebant Judaei dicti
sunt. Reliquae decem tribus quae in Samaria regem sibi
constituerunt Israel dictae sunt. ]

Ad caeteras regiones accedendo oportet describere Taurum
montem ?, quoniam ipse disterminat regiones infinitas. Ab
oriente et Indico mari incipit, et transit in occasum per fines
Indiae et Parthorum regna, et Mesopotamiam et Syriam,
quas provincias relinquit versus meridiem, et ab aquilone
totas Scytharum regiones et partem Armeniae majoris et
Cappadociam relinquit et transit in Ciliciam. Sed secundum
varietatem regionum diversa sortitur nomina. Aliquando enim
Caucasus, ubi altior est propter abundantiam nivium, nam
illorum lingua quibus attollitur Caucasus significat candidum ;
alibi Caspius vocatur, alibi Taurus, et aliquando Hyrcanus ;
et multis aliis nominibus, pluribus quam viginti, secundum

! This paragraph, which is missing in the other MSS., is found in a MS. of
Corpus Christi Coll, Cambridge, containing the geographical section of the
Opus Mayus, which I was kindly permitted to collate.

? This conception of the continuity of the great Asian chain seems to be due
to Eratusthenes. ‘He considered it as a vast range of mountains occupying
in parts a width of not less than 2,000 stadia, and stretching in a direct line
nearly parallel with the equator from the interior of Lycia and Cilicia . . . north
of the plains of Mesopotamia and Assyria as well as of the table-land of Persia,
and the plains of India, till they ultimately ended in the unknown ocean that
formed the eastern boundary of Asia, Bunbury, Hist. of Ancent Geography,
vol. i. p. 641. Cf. Pliny, v. 27.

GEOGRAPHIA. 351

Plinium. Nam novem nomina habet ab oceano Indico in
oriente, antequam vocetur proprio nomine Taurus, deinde
Caucasus, et postea tria sortitur nomina extranea, et iterum
Taurus vocatur. Sed ubi se aperit et portae fiunt Caspiae,
ibi vocatur Caspius, et Hyrcanus, et multis aliis nominibus,
de quibus non est curandum ad praesens. Haec secundum
Plinium, quamvis Orosius velit aliter, et multi alii aliter quam
ille. Unde totus ille mons a multis vocatur ab India Caucasus
et postea Taurus. Alii e converso, sed non est curandum, quia
diversae imaginationes et diversa vocabula hic sunt circa rem
eandem. Quod tamen magis est in usu sapientum describentium
mundi regiones, est quod vocetur in orientali parte Caucasus,
deinde Caspius et Hyrcanus, postea Taurus, et iterum Cau-
casus. quia ubi se maxime attollit vocatur Caucasus, et tum
postea adhuc Taurus nominatur. Totus etiam Caucasus dicitur,
et totus Taurus secundum diversas considerationes.
Revertendum est igitur ad regiones orientales supra Meso- Media and

potamiam, Assyriam et Babylonem, ct dicendum est secundum P*rthis.
Plinium et omnes, quod ibi sunt regna Medorum et Persarum
et Parthorum. Et haec regna habent ab occidente Tigrim
fluvium, ab oriente Indum fluvium, a meridie mare Persicum,
sive sinum Rubri maris Persicum, a septentrione habent Arme-
niam et Taurum, et Caucasum montes, et portas Caspias, seu
Hyrcanias, et terram Hyrcanorum et mare Hyrcanicum, quod
est et Caspium. Nam idem est mare Caspium et Hyrcanium,
sicut dicit Plinius. Et Persarum regna nunc Parthorum
intelligimus, ut dicit Plinius. Veruntamen illa pars quae est
super mare Persicum est prope Persida; nam ab illa mare
Persicum nominatur. Sunt enim Parthorum regna octodecim,
ut dicit. Undecim dicuntur superiora et septentrionalia, quae
incipiunt a confinio Armeniae et Caspiae littoribus seu
Hyrcanicis, et hi proprie dicuntur Parthi, et pertinent ad
Scythas, cum ex aequo vivunt qui adhaerent montibus et
mari Caspiis et Hyrcanicis. Alia septem regna Parthorum
sunt meridionalia, et adhaerent mari Persico et proprie
vocantur regna Persarum, et ili sunt Elamitae, id est
principes Persidis, sicut Hieronymus dicit super Genesim
et in libro Locorum. Nam Elam est civitas principalis

India.

Indus and
Ganges.

352 OPERIS MAJORIS PARS QUARTA.

Persarum, in qua fuit Susis vel Susa castrum, de quibus
habetur octavo Danielis, ubi fuit caput regni Persarum. Et
Plinius dicit, quod prope Tigrim et a mari Persico per ccl
milliaria est Susa Persarum regia, a Dario Hydaspis filio
condita in septentrionali Tigris alveo. Et ibi prope est
oppidum ubi mortalium soli aurum in odium contrahunt,
idque fodiunt ne cui in usu sit. Medi vero sunt vicini tam
Parthis quam Persis. Nam una pars Medorum scilicet sep-
tentrionalis est sub Parthis et Caspiis, et incipit recte a portis
Caspiis, et in confinio Armeniae. Et ideo habent hi Parthos ab
oriente, et a septentrione Armeniam et portas Caspias, ab occi-
dente vero Tigrim, quia Parthi sunt supra eos versus Indum .
fluvium. Alia pars Medorum meridiana flectit se inter regna
Parthica superiora et inferiora, ita quod inferiora, scilicet regna
Persidis habeat non recte ab ortu, sed magis a meridie vergente
in occasum secundum intentionem Plinii. Nam Media includit
utraque regna Persarum et involvit secundum Plinium.

Supra vero Indum fluvium versus orientem est tota India
usque ad mare! Scythicum, quod est ab aquilone, et montes
Himanus, Hemodus, et multi qui sunt partes Caucasi ; et
extenditur usque ad mare Eoum, quod est orientale, et usque
ad mare Indicum meridianum, in quod cadit Indus fluvius, ut
dicit Plinius, quia jam evanuit mare Rubrum. Unde India
habet Indum fluvium ab occidente, et regna Persarum et
Medorum ; et habet mare Scythicum, montes Caucasum et
Taurum a septentrione et Scytharum regna, et Indicum mare
a meridie, et Eoum ab oriente; cujus dispositio in principio
tacta est in multis, quia ibi est principium habitabilis. Et ideo
ab ea fuit incipiendum, ut ulterius curreret stylus per longitu-
dinem habitabilis usque ad occidens per regiones Aethiopum,
et iterum ab occidente revertendo secundum longitudinem.

Tactae sunt regiones succedentes prioribus usque in Indiam,
de qua adhuc aliqua dicenda sunt. Habet enim flumina
maxima, inter quae praecipue sunt Indus et Ganges, de quo
loquitur Scriptura. De magnitudine vero Indi, dicit Plinius,
Alexander magnus nullo die minus sexcenta stadia navigavit
in Indo, nec potuit ante quinque menses enavigare totum,

1 Reg. has Scythicum: O. Sericum.

L2. —--— T - a —— — --————— —--— 0-2 .0.—————-— —-- -—— —— —- 0 -——- —- Ce -- o —— eet

GEOGRAPHIA. 353

adjectis paucis adhuc diebus. Et tamen Ganges major est ut
dicit, et hic fluvius, sicut Scriptura dicit, circuit omnem terram
Evilat, ubi aurum nascitur optimum. Nam a montibus
Caucasi oriens in septentrione dividit Indiam, decurrens ad
orientem ubi sunt ejus ostia magna, quibus in mare Eoum,
id est, orientale delitescit.

Bragmani vero, de quibus habetur in epistola Hieronymi Brabmins.
Bibliae praeposita, sunt in India. Et quia sancti et philosophi
et historiae narrant mirabilia de eis plus quam de aliis genti-
bus, ideo aliqua hic inseram de illis, et praecipue adducam ea
quae volo de scripturis beati Ambrosii propter majorem certi-
tudinem. Dicit igitur in epistola ad Palladium de vita
Bragmanorum quod habitant juxta flumen Gangem, ubi in
mare oceanum quod est Eoum ingreditur, sed viri ultra flumen
versus oceanum, foeminae vero citra inhabitant propter in-
signia castitatis: Nam solum propter spem prolis conveniunt
mares cum foeminis certis temporibus, scilicet Julio et Augusto,
ut refert sanctus praedictus. At ubi quadraginta cum foeminis
suis compleverunt dies, mox ad propria revertuntur. Et cum
fuerit alicujus uxor enixa edideritque unum et alterum partum,
non transit ulterius ad ipsam ejus maritus, singulis enim filiis
loco patrum substitutis per totam in reliquum ab hujusmodi
coitu abstinent vitam. Si autem acciderit, ut quisque sterilem
sortiatur uxorem, usque ad annos quinque maritus ejus transit
et cum uxore propria dormit, quae si gravida per illud tempus
omnino non fuerit, mox abstinet penitus ab ea. Et sicut ex
hac epistola patet et ex libro principali, quem de vita Bragma-
norum scribit beatus Ambrosius, illi habent aerem temperatis-
simum, ita ut vestimentis non utuntur, sed foliis arborum se
tegunt. Nec colunt terras, nec arbores, nec panem habent,
nec vinum ; sed herbis et foliis et fructibus sponte nascentibus
vescuntur, et aquis optimis sitim extinguunt. Sani sunt sine
infirmitate, et vitam protendunt longissimam.

Ad aquilonarem vero partem Indiae, ut dictum est, sunt The.
mare Scythicum et montes illi magni, qui Caucasus et Taurus C*9Pi2n-
et multis aliis nominibus vocantur secundum diversitatem loco-
rum et gentium. Et ad occidentem est Persida seu Parthia,
et Media. Deinde sub eis ad occidentem est Mesopotamia

VOL. I. Aa

354 OPERIS MAJORIS PARS QUARTA.

et tota Syria, ut dictum est. Sed in confinio Mediae et
Parthiae est porta ferrea Alexandri, quae est civitas denomi-
nata a portis, et illae portae dicuntur Caspiae ', non Caucasiae,
ut dicit Plinius. Nam aliae sunt portae Caucasi, ut postea
dicetur, quia in littore maris Caspii sunt hae portae. Est enim
mare quoddam, quod fit ex concursu maximorum fluminum
venientum ab aquilone, et Caspium vocatur, atque Hyrcani-
cum secundum Plinium. Nam Caspii et Hyrcani super
littora illius maris inhabitant; non igitur est hoc mare
veniens ab oceano?, ut Isidorus et Plinius, et omnes auctores
occidentales scribunt. In hoc enim casu non habuerunt
experientiam certam per se nec per alios, sed ex rumore
scripserunt. In libris autem de moribus Tartarorum, ut
per fide dignos qui in illis regionibus fuerunt patet, quod
hoc mare fit ex concursu fluminum, et est mare satis magnum.

1 This pass is ‘ still traversed by the most frequented route from Teheran to
Meshed and Herat. The identity of this pass with the one now known as the
Sirdar pass, between Veramin and Kishlak in Khowar, has been fully established
by modern travellers. Bunbury, Amc. Geog. vol. i. p. 477.

The pass called by Bacon Caucasian, and carefully distinguished by him from
the Sirdar pass (cf. p. 364), is described by Marco Polo (i. ch. 4) when speaking
of Georgia. ‘ This is the country beyond which Alexander could not pass when
he wished to penetrate to the region of the Ponent, because that the defile was
so narrow and perilous, the sea lying on the one hand and on the other lofty
mountains impassable to horsemen. Alexander caused a very strong tower to
be built there to prevent the people beyond from passing to attack him, and
this got the name of the Iron Gate. This is the place that the book of Alexander
speaks of when it tells us how he shut up the Tartars between two mountains ;
not that they were really Tartars, however, for there were no Tartars in those
days ; but they consisted of a race of people called Comanians and many
besides.’ ‘This,’ says Yule, in his note on this passage, ‘ refers to the Pass of
Derbend. still called in Turkish Demir Kápi or the Iron Gate, and to the ancient
wall that runs from the Castle of Derbend along the ridges of Caucasus, called
in the East Sadd-i-Iskendr, the Rampart of Alexander. Bayer thinks the wall
was built originally by one of the Antiochi, and renewed by the Sassanian
Kobad or his son Naoshirvan.’

The mediaeval legend, bearing the name of Callisthenes, as to the imprison-
ment by Alexander of twenty-two wild tribes behind those gates, Gog and
Magog among them, is repeated by Aethicus, and by many other mediaeval
writers.

? This is one of the most important corrections made in the geography of
Asia by Bacon, in consequence of the attention paid by him to the reports of
the two Franciscan missionaries, Rubruquis and Carpini Previously to their
travels the Caspian had usually, though not always, been held to be a gulf
communicating with the Scythic, or Arctic, ocean,

GEOGRAPHIA. 355

Nam circuitus ejus est quatuor mensium. Et Hyrcania prope
est super littus meridionale illius maris in termino Parthiae ; et
ubi Parthia conjungitur Mediae in portis illius extenditur a
portis Caspiis versus orientem, ut dicit Plinius; deinde contra
residuum Mediae ad ejus septentrionem, et ad occidentem
Hyrcaniae est major Armenia, et eam dividit Euphrates a
Cappadocia, ut dicit Plinius, propter quod Cappadocia est ad
occidentem Armeniae majoris.

Deinde versus Syriam et mare nostrum est Cilicia, quae AsiaMinor.
dicitur Armenia minor. Unde jacet partim in meridie, partim
in occidente Cappadociae, et ejus principium non distat ab
Antiochia per duas dietas. Sub Cilicia ad septentrionem super
mare comprehenditur Pamphylia, ut dicit Plinius, neglecta
gente Isaurica, vel non computata per se propter parvitatem,
sed sub eis comprehensa. In Cilicia est Tarsus metropolis
ejus, in quo natus fuit beatus apostolus Paulus. Et durat
Cilicia a meridie in septentrionem per Tarsum in latitudine
circiter quatuor dietas versus Turkiam; nam ad septentrionem
Ciliciae est Lycaonia, ubi est Iconium celeberrima civitas, a qua
Lycaonia dicitur quasi Iconia; unde princeps eorum vocatur
Soldanus Iconii et Turkiae, nam Lycaonia vocatur nunc
Turkia. Eta finibus Armeniae usque in Iconium sunt octo
dietae. Nomina provinciarum in his regionibus sunt multum
mutata propter guerras Nam Turkia multas terras occupat,
quae apud auctores habent nomina antiqua, ut est pars Asiae
minoris, et Phrygia, et Lydia. Asia vero major continet plus
medietate mundi, et totum praeter Europam et Africam, unde
continet hanc Asiam minorem. Et haec nunc vocatur apud
Graecos Anatolia, id est orientalis Graecia, in qua est Galatia,
unde Galatae quibus scribit apostolus, Ilium, quod et Troja
dicitur, illa famosissima civitas. Et sunt aliae multae, ut
Ephesus, et septem ecclesiae Apocalypsis, et Nicaea, unde
synodus Nicaena, et multae aliae. Et ab Iconio usque
Nicaeam sunt viginti dietae in aestate; et ab ea usque ad
brachium sancti Georgii, quod apud antiquos vocatur Helles-
pontus, sunt circiter septem, quod brachium exit a mari inter
Italiam et Antiochiam. Et ibi terminatur Asia minor, et hoc
ex parte occidentis. A parte vero meridiei habet mare illud

Aaz

The
Tartars.

The Black
Sea.

356 OPERIS MAJORIS PARS QUARTA.

quod est inter Italiam et Graeciam et Antiochiam et Aegyp-
tum. Ab oriente habet Phrygiam. Nam, ut dicit Plinius
curialiter, Phrygia Troiadi superjecta septentrionali sua parte
Galatiae continua est, meridiana Lycaoniae, ab oriente Cappa-
dociam habet, et dicit quod Lydia Phrygiae ex ortu solis vicina
est, unde fuit Croesus ditissimus rex Lydorum. Brachium
vero sancti Georgii est strictum multum et habet Constanti-
nopolim ab occidente in Europa, et extenditur a mari magno
quod est inter Asiam et Aegyptum, Syriam et Italiam, cir-
citer centum leucas versus aquilonem usque ad aliud mare
quod vocatur Ponticum, et mare majus. Et istud mare habet
formam arcus Scythici, multas regiones disterminans.

Unde hic incipiunt regiones aquilonares, de quibus philo-
sophi meridiani parum sciverunt, secundum quod Ethicus
astronomus refert in suo libro; sed hic perambulavit omnes
has regiones, et mare oceanum septentrionale cum insulis suis
navigavit. Volo igitur ipsum sequi, et nihilominus libros de
moribus Tartarorum, et praecipue fratrem Willielmum !, quem
Dominus rex Franciae, Lodovicus, in Syria existens misit ad
terram Tartarorum anno Domini 1253, qui frater scripsit
Domino regi situm regionum et marium.

Extenditur autem hoc mare majus ab occidente, scilicet a

! William de Rubruquis, to whom several allusions have already been made
in the course of this work, was a Flemish Franciscan sent by Louis IX to the
Emperor of Tartary in 1253, with letters inviting him to cease from his wars
of extermination. In Joinville's memoirs we read how, when Louis IX was at
Cyprus on his way to Egypt, ‘ envoia le grant roy des Tartarins ses messages à
li, et li manda moult débonnairement paroles. Entre les autres li manda que il
estoit prest de li aidier à conquerre la terre sainte, et de délivrer Jhérusalem de
la main aus Sarrazins.' The king sent back many presents, including a tent
embroidered with Christian emblems, ‘ et touz les autres poins dela foy. Et ces
choses leur envoia-il par deux fréres préescheurs qui savoient le Sarrazinois,
pour eulz moustrer et enseigner comment ils devoient croire, Part of the narra-
tive of Rubruquis was published by Hakluyt in 1598, and is to be found in
Purchas's, Bergeron's, and other geographical collections. But two-thirds
remained unpublished till 1839, when the whole was carefully edited by the
Paris Geographical Society (Recueil de Mémoires, vol. iv.).

Of Rubruquis, Yule remarks «Marco Polo, vol. i. p. cxxx), * His narrative in
its rich detail, its vivid pictures, its acuteness of observation and strong good
sense, seems to me to form a book of travels of much higher claims than any
one series of Polo's chapters ; a book indeed which has never had justice done
to it, for it has few superiors in the whole history of travels.'

GEOGRAPHIA. 357

Constantinopoli in oriens per mcccc milliaria in longum, et in
medio ejus coarctatur ex utraque parte in angulos, et in angulo
meridiano est castrum et portus soldani Turkiae, quod vocatur
Sinopolis. A parte vero aquilonis habet aliud castrum in
angulo, quod vocatur Soldaia, et est in provincia, quae nunc
Cassaria dicitur vel Cessaria, et sunt trecenta milliaria inter
Sinopolim et Soldaiam, et haec est latitudo maris inter illos
angulos. Et ista castra sunt duo portus famosi, a quibus
transeunt homines a meridianis regionibus ad aquilonares et
e converso. Et ab istis castris versus occidentem seu Con-
stantinopolim extenditur mare pcr septingenta milliaria in
longum et latum, similiter ad orientem per septingenta. Et
ista provincia Cassaria circumdatur mari a tribus lateribus.
Nam in occidente habet partem maris Pontici, ubi est civitas
Kersona, in qua fuit sanctus Clemens martyrizatus. Et prope
eam est insula, in qua est templum, quod dicitur angelicis
manibus praeparatum, ín quo corpus sancti sepultum fuit. Et
a Kersona usque ad Soldaiam sunt quadringenta castra,
quorum quodlibet fere habet proprium idioma, Et sunt ibi
multi Gothi, qui omnes loquuntur Teutonicum.

Et a parte meridiei Cassariae extenditur mare Ponticum, et The Don.

in oriente ejus cadit flumen Tanais in mare, ubi habet lati-
tudinem duodecim milliariorum, ubi est civitas Matrica. Et
flumen illud versus aquilonem facit mare quoddam habens
septingenta milliaria in longitudinem et latitudinem, nusquam
habens profunditatem ultra sex pedes. Et hoc mare est palus
Maeotis famosissima, de qua philosophi et historiae et poetae
loquuntur. Et flumen Tanais extenditur ultra illam paludem
versus aquilonem usque ad montes Riphaeos, qui sunt in ultimo
aquilonis, a quibus montibus oritur hoc flumen et descendit
per longum terrae tractum in paludem supradictam, faciens
eam. Et ultra eam digreditur et fluit in mare Ponticum, ut
praedixi. Et hoc flumen famosum dividit Europam ab Asia
in locis illis, et palus dicta et plures paludes sunt contiguae,
sed quasi pro una computantur ; et vocantur paludes Maeotis,
vel Maeotidae in adjectivo. Paludes igitur illae, quae vocantur
mare illud vadosum, sunt in oriente Cassariae, et pars
fluminis Tanais quae est inter paludes et mare Ponticum.

Cumanians
destroyed
by Tartars.

Russia and

Scandi-
navia.

The Baltic.

358 OPERIS MAJORIS PARS QUARTA.

Et haec provincia Cassaria habet ab aquilone vastam
solitudinem, quae extenditur a flumine Tanai in oriente usque
ad Danubium in occidente, itinere duorum mensium velociter
equitando, sicut equitant Tartari ; et hoc est una die quantum
est ab Aurelianis Parisius. Unde durat haec terra circiter
quatuor menses secundum quod alii homines communiter equi-
tant! Et haec terra fuit tota Cumanorum, qui dicebantur
Captac; sed Tartari destruxerunt eam totaliter et interfecerunt
Cumanos praeter partem, quae fugit ad regnum Hungariae,
qui sunt ei tributarii, et a Teutonicis dicitur Valana, a Plinio et
Isidoro et caeteris Alania occidentalis. Et haec provincia
habet Danubium et Poloniam et Hungariam ab occidente.

Et ab aquilone istius provinciae est Russia magna, quae
similiter a Polonia in una parte sua extenditur ad Tanaim ;
sed in magna sui parte habet Leucoviam in occidente, quae
est terra ita magna sicut Alemannia. Ad cujus partem
occidentalem sunt multae terrae in circuitu maris cujusdam,
quod mare fit per multa brachia maris oceani, quae veniunt
per medium Daciae; et ultra eam versus orientem dilatat se
in magnum mare, quod ab occidente habet Daciam? et
Sweciam. Sed Swecia est ad aquilonem Daciae, declinans
aliquantulum in orientem ultra Daciam; ultra quas ad
aquilonem est Norguegia. Deinde, mari magno interjecto,
sunt Scotia et Anglia, et mari parvo interposito, Hibernia.
Notae sunt hae regiones, sed tango eas propter notitiam
aliarum. Si ergo a finibus occidentalibus ex parte aquilonis
ascendamus versus orientem, primo est Hibernia, secundo
Britannia major, quae continet Angliam et Scotiam, deinde
Norguegia, Swecia, Dacia. Et postea orientem versus est
magnum mare praedictum, quod vocatur mare orientale, quia

! The distance from Orleans to Paris is seventy miles; eight weeks of such
riding would make the distance from the Don to the Danube 4,000 miles ; about
four times the real distance between Buda Pesth and the easterly bend of the
Don. Obviously the unit of measurement is extremely lax. But cf. p. 366, in
which the Cumani are described as extending eastward far into Central Asia,
prior to the Tartar conquests.

3 Dacia is often found instead of Dania in mediaeval maps, e.g. in the
Catalan map of 1378 given in Lelewel's Atlas, Plate xxix (Géographie du Moyen
Age, ed. 1850).

GEOGRAPHIA. 359

oceanus non se extendit ultra illud mare. Sed super latus .
aquilonare istius maris immediate post angulum Sweciae est
Estonia; deinde Livonia versus orientem illius maris ; deinde
Curonia seu Curlandia declinando ad meridianum |latus;
postea Prussia magna terra in meridiano latere; deinde
Pomerania; postea Lubec, portus magnus et famosus in
confinio Daciae et Saxoniae. In medio vero istius maris est
insula quaedam quae vocatur Gothlandia. Et super Livoniam

ad orientem est Semi-Gallia. Et istas terras, scilicet Estoniam,
Livoniam, Semi-Galliam, Curoniam, circumdat Leucovia
praedicta, et eam circumdat Russia magna ex utraque parte

dicti maris, et terminatur in parte meridiana ad Prussiam et
Poloniam. Polonia vero jacet ad meridiem Prussiae ; et ad Poland and
meridiem ejus est Bohemia, deinde Austria. Et ad occidentem Prussia.
terrarum istarum est Alemannia, et postea Francia et
Hispania; sed hae sunt notae, facio tamen mentionem propter

alias. Ad orientem Austriae et Bohemiae est Hungaria, ad
quam occidentalis pars Albaniae descendit. Nam cadit super
Danubium qui fluit per medium Hungariae, et ultra eam in

mare Ponticum per duodecim ostia magna. In termino vero Hungary.
Hungariae orientalis a parte aquilonis occurrit haec Albania,
contra quam ad meridiem Danubii sunt Balchi et Bulgari, et
Constantinopolis, quae terrae antiquitus vocabantur Thracia. Thrace.
Albania igitur occidentalis extenditur a Danubio post finem
Hungariae versus orientem, usque ad flumen Tanaim, habens
Cassariam a meridie et Balchiam, et Bulgariam, et Constanti-
nopolim ; ab occasu vero Hungariam et Poloniam, et extremi-
tatem Russiae; ab aquilone habet totam longitudinem
Russiae.

Et ultra Russiam ad aquilonem est gens Hyperborea, quae The Hy-
sic nominatur a montibus magnis, qui vocantur Hyperborei. NM
Et haec gens propter aeris salubritatem vivit in sylvis, gens
longaeva usquequo fastidiant mortem, optimarum consuetu-
dinum, gens quieta et pacifica, nulli nocens, nec ab alia gente
molestatur. Sed alii confugiunt ad eam sicut ad asylum.
Qualiter autem potest regio ibi esse temperatissima, tctigi
prius in complexionibus locorum mundi. Et sic habemus
regiones aquilonares in Europa notabiles.

360 OPERIS MAJORIS PARS QUARTA.

Religionsof Ritus vero istarum gentium sunt diversi. Nam Prusceni,
Northern Curlandi, Livonii, Estonii, Semigalli, Leucovii sunt pagani.
Alani vero non sunt, quia Tartari terram illam invaserunt, et
fugaverünt Cumanos usque ad Hungariam ; et Cumani sunt
pagani, et Alani fuerunt similiter, sed deleti sunt. Rusceni
sunt Christiani et sunt schismatici, habentes ritum Graecorum,

Sclavonic Sed non utuntur lingua Graeca, immo lingua Sclavonica, quae

?^8"58**- est una de linguis quae plures occupat regiones. Nam
Rusciam, Poloniam, et Bohemiam, et multas alias nationes
tenet. Tartari vero a Danubio inhabitant terram Alanorum
seu Cumanorum, et ulterius usque fere ad partes ultimas
orientis ; et alias nationes eis vicinas ad aquilonem et meridiem
subjugaverunt pro maxima parte. Nam aliquae gentes sunt
in montanis et locis tutissimis, quas non possunt debellare,
licet sint eis vicini, quia sunt inexpugnabiles.

The Don. | Tanais quidem fluvius descendit a montibus Riphaeis
altissimis, qui sunt in vero aquilone, nec est ultra illos ad
aquilonem habitatio. ‘Et in termino orientali Rusciae et
Alaniae, ubi mercatores et alii qui venerunt de Hungaria et
Cassaria, et Polonia, et Russia, est quoddam casale, ubi
navigio pertransitur flumen Tanais. Et est Tanais ibi ad

The Volga. latitudinem | Secanae Parisius. Et ultra flumen illud est
Albania superior usque ad aliud flumen magnum, quod
vocatur Ethilia, quae major est in quadruplo quam Secana,
et est de majoribus fluminibus mundi, et crescit in aestate
sicut Nilus. Et a parte aquilonis distat hoc flumen a Tanai
per decem dietas, sed versus meridiem multum separantur.
Nam Tanais cadit in mare Ponticum, et Ethilia in mare
Caspium, et facit illud mare cum aliis fluminibus multis, quae
veniunt de Perside, et aliis locis. Nam a Pontico mari secundum
Plinium, sunt ccclxxx milliaria usque ad mare Caspium.

Tartar — Et in hac terra habitabant Cumani, sed Tartari deleverunt
principali- . .
ties. omnes, sicut ex altera parte Tanais fecerunt usque ad

Danubium, ut dictum est. Et Tartari habent pecora infinita

1 The Tartar name for Volga is Ethel, which means bountiful. In May and
June this river is swollen by melting snow, and inundations result. By Marco
Polo the Volga is not spoken of by this name, but under that of Tigeri (cf. i. 9,
ed. Yule). See p. 322.

L0 — — — ——nÁ— | — —7——— —— cc (00 0o on

GEOGRAPHIA. 361

et habitant in tentoriis, non habentes villas nec castra nisi
rarissime. Et unus princeps cum exercitu, et cum suis
armentis gregum vagatur inter duo flumina, ut unus inter
Danubium et Tanaim, alius inter Tanaim et Ethiliam, et sic
ultra versus orientem, quod semper divisi sunt per pascua et
aquas. Eta Januario incipiunt adire partes aquilonares infra
flumina usque ad Augustum, et tunc redeunt versus meridia-
nas propter frigus aquilonis in hyeme. Et versus aquilonem
distat Ethilia a provincia Cassariae per unum mensem et tres
dietas, sicut equitant Tartari.

Haec vero terra Tartarorum inter Tanaim et Ethiliam Northem

habet ab aquilone quasdam gentes. Et primo est gens ject to Tar-
Arumphea prope montes Riphaeos, quae est similis Hyper- tars.
boreis in omnibus. £t hae duae gentes sunt prope polum in
aquilone ; sed remotius ab aquilone ultra Tanaim est primo
gens quae vocatur Moxel subjecta Tartaris; et sunt adhuc
sine lege pure pagani, civitatem non habent, sed casulas in
sylvis. Dominus illorum et magna pars eorum fuerunt
interfecti in Polonia per Polonos et Alemannos et Bohemos.
Nam Tartari duxerunt eos ad bellum cum Polonis. Et
multum approbant Polonos et Alemannos de strenuitate,
sperantes adhuc liberari a servitute Tartarorum per eos. Si
mercator veniat inter eos, oportet quod ille in cujus domo
primo hospitatur, det ei expensas quantum vult ibi morari.
Haec enim est consuetudo illius regionis. Post hos ad
orientem est gens quaedam, quae vocatur Merduim subjecta
Tartaris. Sed sunt Saraceni habentes legem Mahometi.
Post eos est Ethilia flumen praedictum, quod descendit a
majori Bulgaria, de qua postea dicetur.

A meridie vero istius regionis Tartarorum super mare
Ponticum sunt Hiberi et Georgiani Et in Georgia est Georgia.
metropolis civitas, quae vocatur Thephelis, in qua fratres
praedicatores habent domum. Et ulterius versus orientem
est terra Corasiminorum, sed deleti sunt a Tartaris. Et in his
locis solebant antiquitus esse Amazones secundum Plinium et
Ethicum astronomum. . Amazones enim, ut refert Ethicus, The Ama-
fuerunt mulieres ducentes exercitum magnum ex mulieribus antiquity.
sine viris collectum, quae advocantes viros certis temporibus

Armenia.

362 OPERIS MAJORIS PARS QUARTA.

anni conceperunt ; sed masculos genitos interfecerunt foeminas
reservando; quarum in juventute mamillas dextras per
artificium chirurgiae abstulerunt, ne sagittando reciperent
impedimentum per mamillas. Et minotauros ac centauros
monstra ferocissima nutriverunt a juventute mamillis suis ;
unde antecedebant eas sicut matres suas et omnem exercitum
premebant magis per hujusmodi monstra quam per arma. Et
similiter elephantes a juventute nutriebant et assuescebant ad
proelia ; et sic per centum annos vastabant meridianas partes
Asiae et Graeciae, donec ab Hercule fuerunt seductae et
destructae. Haec vero loca Georgianorum et Corasiminorum
habent terram Soldani Turkiae et Cappadociam a meridie.
Nam in latere meridiano maris Pontici est terra Soldani
usque ad Sinopolim, de qua prius dictum ‘est. Et post eam in
eodem latere maris versus occidentem est terra Vastachii,
scilicet Graecia orientalis. Nam occidentalis vocatur ubi
Constantinopolis est, et regiones ei annexae citra brachium
sancti Georgii in Europa.

Sed Armenia major est super Cappadociam ad orientem ;
et ideo illa Armenia etsi meridiana sit respectu Georgiae,
tamen in orientem tendit et extenditur usque Mediam et
Mesopotamiam ; et haec terra tota aestimatur a multis esse terra
Ararath, propter hoc, quod in Isaia dicitur quod filii Senacherib,
interfecto patre, fugerunt in Ararath ; et in libro regum dicitur
quod fugerunt in Armeniam. Sed Hieronymus secundo
libro super Isaiam solvit hoc, dicens Ararath regio est Arme-
nia campestris per quam Araxes fluit, incredibilis ubertatis ad
radices monti Tauri, qui usque illuc extenditur. Quapropter
Ararath non est tota Armenia, sed regio determinata, magna
tamen est. Nam Araxes fluvius, a quo Ararath regio nomi-
natur, extenditur a capite suo per iter trium mensium et
amplius. Caput autem ejus est fons in monte Armeniae, ubi
prope oritur Euphrates ex parte aquilonis et Tigris ad aliud
latus montis versus meridiem. In montibus autem Armeniae,
testante Scriptura, requievit arca Noe; sed non in quibus-
cunque montibus, quoniam non est in istis ubi oriuntur ista
tria flumina magna, sed in altissimo Tauri montis cacumine, ubi
Ararath regio est, secundum quod dicit Hieronymus secundo

GEOGRAPHIA. 363

super Isaiam, arca, in qua liberatus est Noe cessante diluvio ;
non ad montes generaliter Armeniae, sed ad montes Tauri
altissimos, qui Ararath imminent campis.

Et prope illos montes est civitas, quae maxima fuit ante- Destruc-
quam eam destruxerunt Tartari. Nam fuerunt in ea octingentae tion of an
ecclesiae Armenorum ; et in tempore fratris Willielmi, quando churches.
transivit per eam, non fuerunt nisi duae parvulae. Et ibi prope
fuerunt martyrizati beati Bartholomaeus, et beatus Judas, et
Thaddaeus. Et ibi sunt duae prophetiae. Una est beati Me-
thodii martyris, qui fuit de gente illa, et plane prophetavit de
Ismaelitis, quae prophetia impleta est in Saracenis. Alius
propheta eorum vocatur Akaton, qui prophetavit de Tartaris
et de destructione eorum. Dicit enim ‘quod ab aquilone
veniet gens sagittaria, quae omnes nationes orientis subju-
gabit, et venient in regno occidentis, scilicet ad Constanti-
nopolim, et ibi per principes occidentis destruentur. Et tunc
convertentur omnes gentes ad fidem Christi, et erit tanta pax
ubique, quod vivi dicent mortuis, Vae vobis, quod non vixistis
usque nunc. Et imperator Christianus ponet solium suum in
Taurino in Perside. Et Armeni habent istam prophetiam
sicut evangelium. Et haec civitas memorata vocatur nunc
Naxuam!, quae solebat esse caput regni; et est versus partes
aquilonares Armeniae. Nam a festo sancti Clementis ascendit
frater Willielmus juxta Araxem, ubi terminatur versus aqui-
lonem. Et in festo natalis venit ad illam civitatem, et in
octavis epiphaniae recessit ab ea, et per Araxem ivit usque ad
caput ejus, ad quod pervenit in secunda dominica quadra-
gesimae; et ideo longe plus est a civitati illa ad ultimum
Armeniae a parte meridiei quam ad aquilonem.

Deinde superius ad orientem sunt montes Alanorum et Regionsbe-

. . . . . e . . t A -
Aas, qui sunt Christiani, et recipiunt indifferenter omnes menia and

! This is Naxuana or Nachitschuan on the Araxes. It is now in Russian ^ Pian

dominion, about roo miles to the East of Lake Van, between 60 and 70
miles south east of Mount Ararat. On his return journey from Tartary,
Rubruquis after passing through the Caucasian gates at Derbend on the
Caspian travelled up the valley of the Araxes. He mentions the town Vaxua
(probably — Naxua) of which he says, 'solebant esse in ea octingentae ecclesiae
Hermenorum ; modo non sunt nisi duo parvulae. Sarraceni enim destrucrunt
eas.’ (See his journal published by the French Geographical Society, vol. iv.

1839, p. 385.)

Alexander's

Caspian
gates.

364 OPERIS MAJORIS PARS QUARTA.

Christianos tam Latinos quam Graecos, unde non sunt
schismatici, et pugnant cum Tartaris; et similiter Alani.
Post eos ad orientem sunt Saraceni, qui vocantur Lelgi !, qui
propter terrae fortitudinem pugnant cum Tartaris. Post illos
ad orientem sunt portae Caspiae super mare Caspium, quas
Alexander magnus construxit in concursu montium. Nam
cum voluit expugnare gentem aquilonarem, non potuit propter
illius gentis ferocitatem et multitudinem. Et, ut dicit Ethicus,
stetit per annum unum et menses tres, ut defenderet se ab eis,
et ingemuit quod talis gens pessima fuisset in partibus aqui-
lonis, et exclamavit ad Deum ut apponeret remedium, ne
mundus destrueretur per eos. Sed licet non fuit dignus
exaudiri, tamen Deus sua bonitate et propter salutem generis
humani jussit fieri terrae motum maximum, et montes per
stadium distantes conjuncti sunt usque ad latitudinem unius
portae.

Et Alexander tunc fecit fundi columnas aereas mirae
magnitudinis, et erexit portas et linivit eas bitumine quod
nec igne, nec aqua, nec ferro dissolvi posset, quod adquisivit
ex insulis maris, nec potuerunt dirui aliquo modo nisi per
terrae motum; et jam dirutae sunt. Nam frater Willielmus
transivit per medium earum cum Tartaris. Et est ibi civitas
quae vocatur porta ferrea Alexandri: a qua versus orientem
incipit Hyrcania super Hyrcanium mare, quod est Caspium,
ut superius dictum est. Nam Hyrcania jacet super latus
meridionale ilius maris et extenditur usque ad terminos
Indiae, a cujus latere meridionali sunt Media et Parthia, sicut
prius fuit annotatum. Hae vero portae non sunt Caucasiae
sed Caspiae, ut dicit Plinius?, nec Caucasiae sunt Caspiae.
Nam Caucasiae distant a Caspiis per ducenta milliaria versus
mare Ponticum ; et a mari Pontico distant per clxxx milliaria
circa partes Hiberiae et Georgiae. Et ista loca cum montibus
interjacentibus vocantur claustra Alexandri, per quae cohibuit
gentes aquilonares ne irruerunt terras meridianas devastando
eas. Nam Alexander multa bella gessit cum eis, ut refert

! J. has Belgi: O. Lelgi.

* Pliny in the eleventh chapter of his sixth book describes the Caucasian gates :
in the fourteenth chapter, the Caspian gates. See notes on pp. 303 and 354.

GEOGRAPHIA. 365

Ethicus, et aliquando infra tres dies ceciderunt ex utraque
parte decies centena millia hominum. Alexander tamen magis
arte et ingenio vicit quam armorum potestate. Et cum fuerunt
excitati sicut ursi de cavernis suis, non potuit eos reprimere
per violentiam, sed Deus juvit per terrae motum et clausuras
montium. Nunc autem ruptae sunt, et diu est quod fractae
sunt sive terrae motu sive vetustate.

Et considerandum est diligenter de locis istis. Nam Gog These

et Magog, de quibus Ezechiel prophetavit et Apocalypsis, in should be
his locis sunt inclusi, secundum quod dicit Hieronymus secundo carey
libro super Ezechielem. Gog Scythica gens trans Caucasum
et Maeotim ct Caspium mare ad Indiam usque tenduntur ; et
a principe Gog omnes qui subditi sunt Magog appellantur
et Judaei similiter, quos Orosius et alii sancti referunt exituros.
Atque sicut Ethicus scribit, Alexander inclusit viginti duo
regna de stirpe Gog et Magog, exitura in diebus Antichristi,
qui mundum primo vastabunt et deinde obviabunt Antichristo,
et vocabunt eum Deum Deorum, sicut et beatus Hieronymus
confirmat. O quam necessarium est ecclesiae Dei, ut proelati
et viri catholici haec loca considerent, non solum propter
conversionem gentium in illis locis, et consolationem Christia-
norum captivorum ibidem, sed propter persecutionem Anti-
christi, ut sciatur unde venturus sit, et quando, per hanc
considerationem et alias multas.

A portis vero Caspiis incipit mare Caspium! extendi in The Cas-
longum ad orientem ; et in latum ad aquilonem, et est non Pland sea.
minus quam Ponticum mare, ut dicit Plinius, et habet spatium
quatuor mensium in circuitu. Frater vero Willielmus in

1 The changes of opinion in antiquity as to this sea are curious. Herodotus
and Aristotle held the true view that it was surrounded by land. See Arist.
Meteor. ii. 1, $ 10. But Patrocles, an officer of Antiochus I, maintained that it
was a gulf of the northern ocean, and that it would be possible to sail from
it round to the Indian sea (Strabo, xi rz, $ 6). Pliny went so far as to say
that Patrocles had actually accomplished this voyage (J7íst. Nat. vi. 17). And
notwithstanding that Ptolemy reverted to the belief that the Caspian was an
inland sea (Cosmographna, vii. 5, $ 4), Pliny's view continued to be reasserted
through the Middle Ages, till Bacon, on the authority of Rubruquis, confirmed
the fact that it was surrounded by land. Bacon however did not free himself
from Ptolemy's error of supposing its greatest length to be from east to west,
rather than from north to south.

The third
and princi-
pal of the
Tartar
kingdoms;
Cara-
cathaia.

Great
Bulgaria.

366 OPERIS MAJORIS PARS QUARTA.

redeundo ab imperatore Tartarorum circuivit latus occidentale ;
et in eundo ad eum perambulavit latus aquilonare, ut ipse
retulit Domino regi Franciae qui nunc est, anno Domini 1253.
Et a parte aquilonis habet vastam solitudinem, in qua sunt
Tartari. Et ultra eos sunt multae regiones aquilonares ante-
quam perveniatur ad Oceanum ; et ideo non potest illud mare
esse sinus maris Oceani, quod tamen fere omnes auctores
scribunt; sed experientia hujus temporis facta per fratrem
Willielmum et homines alios fideles docet, quod non venit
a mari, sed fit per flumina magna et multa, quorum congrega-
tione fit hoc mare Caspium et Hyrcanicum. Tota vero haec.
terra Tartarorum a Tanai usque ad Ethiliam fuit Cumanorum,
qui vocabantur Canglae, qui omnes sunt deleti per Tartaros.
Et tota ista vocabatur Albania antiquitus. Et hic sunt
canes maximi, ita ut leones perimant, tauros premant, et
homines ponunt eos in bigis et aratris.

Deinde ultra Ethiliam est tertius principatus Tartarorum ;
et destructae sunt gentes indigenae ab eis, et fuerunt Cumani
Canglae, sicut prius. Et durat ille principatus a flumine in
orientem per iter quatuor mensium ex parte meridionali usque
veniatur ad terram principalem imperatoris. Sed ex parte
aquilonari durat per iter duorum mensium, et decem dierum.
Ex quo patet quod Cumania fuit terrarum maxima. Nam
a Danubio usque ad terram hanc, in qua imperator residet,
habitabant Cumani, qui omnes sunt destructi a Tartaris
praeter eos qui fugerant ad regnum Hungariae. Et hic
principatus habet ab aquilone primo majorem Bulgariam !,
a qua venerunt Bulgari qui sunt inter Constantinopolim, et
Hungariam, et Sclavoniam. Nam haec quae in Europa est
minor Bulgaria, habens linguam illorum Bulgarorum qui sunt
in majori Bulgaria, quae est in Asia. Et isti Bulgari de majori
Bulgaria sunt pessimi Saraceni. Et hoc est mirabile; quoniam
illa terra distat a porta ferrea seu a portis Caspiis triginta
diebus et plus per transversum solitudinis; et est in fine

! Marco Polo (i. 9, ed. Yule) mentions the city of Bolgara. Yule remarks on
this, * It was the capital of the region sometimes called Great Bulgaria, on the
Volga. .. . latitude about 54° 54’, 9o miles below Kazan. It was captured by
the Mongols in 1225.

GEOGRAPHIA. 367

aquilonis ; unde mirum est valde quod ad eos tam distantes
a Saracenis pervenit secta Mahometi. Et de hac Bulgaria
venit Ethilia, de qua dictum est. Post eam ad orientem est
terra Pascatyr quae est magna Hungaria, a qua exiverunt
Huni, qui postea Hungri, modo dicuntur Hungari ; qui colli-
gentes secum Bulgaros et alias nationes aquilonares ruperunt,
sicut dicit Isidorus, claustra Alexandri. Et solvebatur eis
tributum usque in Aegyptum, et destruxerunt terras omnes
usque in Franciam; unde majoris potentiae fuerunt quam
adhuc sunt Tartari; et magna pars eorum resedit in terra
quae nunc vocatur Hungaria, ultra Bohemiam et Austriam,
quae est modo apud Latinos regnum Hungariae. Et juxta
terram Pascatyr sunt Balchi! de Balchia majore, a quo venerunt
Balchi in terra Assani inter Constantinopolim, et Bulgariam
et Hungariam minorem. Nam populus ille dicitur nunc a
Tartaris Ilac, quod idem est quod Blac. Sed Tartari nesciunt
sonare 6 literam. A parte vero meridiei istius solitudinis
Tartarorum est mare Caspium. Et deinde montes Caucasi
usque in orientem.

Et extenditur hic principatus ab Ethilia usque in Cathaiam
nigram, unde vocatur Caracathaia. Et Cara idem est quod
nigra; et dicitur Cathaia nigra ad differentiam alterius
Cathaiae, quae est longe ultra hanc ad orientem multis
regionibus distantem ab ista Cathaia nigra; de qua postea
dicetur. Et haec terra cum sibi adjacentibus est terra
imperatoris Tartarorum praecipua, in quibus vagatur semper
cum curia sua, ascendendo in aestate ad frigidas regiones, et in
hyeme ad calidas Et haec Cathaia nigra fuit terra Presbyteri
Johannis, sive regis Johannis, de quo tanta fama solebat esse,
et multa falsa dicta sunt et scripta.

Hic vero oportet exprimi originem Tartarorum, non solum
propter evidentiam distinctionis regionum majorem, sed
propter ipsam gentem, quae nunc famosissima est, et subdit
mundum pedibus suis. Sciendum igitur est, quod quando
bellum fuit Antiochiae tunc regnavit in terra ista Coir Cham?.

! J. has. Blaci and Blacia ; O. has Balchi and Balchia.
- * Yule, in his notes on Marco Polo, i. 46, remarks that during the last two-thirds
of the twelfth century there was a great empire in Northern Asia called Kara

Origi
the

powe

of
artar
r.

Prester
John.

368 OPERIS MAJORIS PARS QUARTA.

Nam in historia Antiochena legitur, quod Turci miserunt pro
succursu contra Francos ad regnum Coir Cham, qui tenebat
monarchiam in regionibus aquilonis tempore illo quo capta
fuit Antiochia, qui fuit de Caracathaia. Coir vero est nomen
proprium, et Cham est nomen dignitatis, et sonat idem quod
divinator. Nam principes ibi regunt populum per divinationes
et scientias quae instruunt homines in futuris, sive sint partes
philosophiae, ut astronomia et scientia experimentalis, sive
artes magicae, quibus totum oriens est deditum et imbutum.

Omnes igitur imperatores Tartarorum vocantur Cham,
Sicut apud nos vocantur imperatores et reges. Mortuo vero
isto Coir, fuit quidam pastor Nestorinus in terra illa potens
et dominus super populum, qui populus vocatur Naiman, qui
erant Christiani Nestorini, qui sunt mali Christiani, et tamen
dicunt se esse subjectos Romanae ecclesiae. Et isti Nestorini
non solum sunt ibi in terra Naiman, sed per omnes regiones
usque in orientem sunt dispersi. Iste vero pastor erexit se in
regem, et vocatus est Presbyter et Rex Johannes. Huic
Johanni erat frater quidam pastor potens, nomine Unc !, habens
sua pascua ultra fratrem suum per iter trium septimanarum,
et erat dominus cujusdam villae, quae dicitur Caracarum ?, quae
Khitai : founded by a Prince of the Khitan dynasty of Liao, who had escaped
from North China on the overthrow of that dynasty by the Kin or Niuché
about 1125. His empire extended over Eastern and Western Turkestan. He
took the title of Gur-khan, said to mean universal khan ; and fixed his centre of
government at Bala Sagun north of Thian San. This Gur-khan is the Coir
Cham of Rubruquis,

1 Prester or Presbyter John is a shadowy and almost mythical personage
whose habitat shifts between Abyssinia and the wall of China. Marco Polo
(i. 46) identifies him with Unc Cham. Rubruquis, a somewhat earlier
authority, regards him as his brother. Unc, or Ung, Cham, says Yule, is called
Tuli by the Chinese and Togrul by the Persian historians. The Kin sovereigns
of North China had conferred on him the title of Wang (king) of which
probably Aung or Ung is a corruption. He was the king of the Keraites who
had professed a nominal form of Christianity since the eleventh century. The
wide diffusion of Nestorian Christianity through Central Asia is very emphatically
marked in Rubruquis's narrative. It was a somewhat colourless creed.

* Near the upper course of the river Orkhon, about 250 miles south of
lake Baikal. After the overthrow of Prester John, Okkodai the successor of
Chinghis established his capital here. ‘It continued to be the Mongol head-

quarters till 1256, when Mangu Khan decided to transfer the seat of government
to Kaiping, far north of Peking.’ [Yule’s ed. of Marco Polo, vol. i. note to

P- 204. ]

GEOGRAPHIA. 369

est nunc civitas imperialis, et major in terra imperatoris, et
tamen non est ita bona, sicut sanctus Dionysius juxta Parisius
in Francia, sicut scripsit frater Willielmus domino regi. Et
ultra pascua illius circiter duodecim dietas erant pascua Moal,
qui erant pauperes homines et stulti ac simplices sine lege.
Juxta quos fuerunt alii pauperes, qui vocabantur Tartari,
similes eis. Mortuo igitur Johanne rege elevavit se in regem
Unc frater ejus, et vocavit se Cham, unde Unc Cham dicebatur
qui misit armenta sua versus terminos Moal.

Inter quos Moal erat faber quidam nomine Cingis! furans icinghis

animalia et rapiens ipsius Unc Cham, quo congregante
exercitum Cingis fugit ad Tartaros qui dixit ad eos et ad
Moal, Quia sumus sine duce ideo vicini nostri opprimunt nos.
Et factus est dux eorum ; et congregato exercitu irruit super
Unc Cham et vicit eum, et factus est princeps in terra, et
vocavit se Cingis Cham, et accepit filiam Unc et dedit eam
filio suo in uxorem, ex qua natus est Mangu Cham qui
regnum divisit istis principibus Tartarorum, qui nunc regnant
et discordant ab invicem. Ad hunc enim Mangu Cham fuit
frater Willielmus missus. Et ipse Cingis Cham ubique
praemittebat Tartaros in pugna, unde exibat fama Tartaro-
rum, qui fere deleti sunt per crebra bella. Et licet propter
hanc causam nos istam gentem vocemus Tartaros apud quos
est imperium et dominium, tamen semper sunt imperatores
et principes de gente Moal. Nec volunt vocari Tartari, sed
Moal; quia primus eorum imperator, scilicet Cingis Cham,
fuit natione Moal. Unde non habuerunt adhuc ante istos

! Cingis, or Chinghis, was born in 1155. His original name was Temijin.
The resemblance of the name to Temurji, the Turkish word for blacksmith,
probably gave rise to the legend of his origin (Marco Polo, ed. Yule,i.234). In
the list of Mongol sovereigns Bacon, following Rubruquis, omits Chinghis's son,
Okkodai, who succeeded him. Okkodai was succeeded by his son Kuyuk, the
Keu of Rubruquis ; Kuyuk by his cousin Mangu, a son of Tuli, and grandson
of Chinghis. Mangu was followed by his brother Kublai, in whose time Marco
Polo visited thc Tartar court. Another grandson of Chinghis, Batu son of
Juji, held dominion between the Volga and the Don at the time of the
Franciscan mission ; he had led the great Mongol invasion of Europe 1240-2.
It need hardly be said that Moal is Bacon's reading, after Rubruquis, for
Mongol.

The war between Chinghis and Ung Cham is described at somewhat greater
length by Marco Polo.

VOL. I. Bb

Present
extent of
Tartar
dominion.

370 OPERIS MAJORIS PARS QUARTA.

qui nunc regnant, nisi tres reges, scilicet Cingis Cham, et Keu
Cham, et Mangu Cham: qui Keu fuit filius Cingis, et Mangu
filius ejus.

Haec igitur gens Moal est stultissima ab origine prima et
pauperrima, quae tamen permissione divina paulatim omnes
nationes vicinas subjugavit, et totam mundi latitudinem in
parvo tempore prostravit. . Quae si esset concors, primo
egressu Aegyptum et Africam vastaret, ut sic ex omni parte
Latinos circumdaret. Nam nunc a parte aquilonis regnant
usque in Poloniam, quia tota Ruscia est eis subjecta; et tota
terra ab oriente usque ad Danubium et ultra Danubium,
scilicet Bulgaria et Blachia sunt eis tributariae. Ita quod
usque ad terram Constantinopolitanam tenet eorum imperium.
Et Soldanus Turkiae, et rex Armeniae, et princeps An-
tiochiae, et omnes principes in oriente usque in Indiam sunt
eis subjecti, praeter paucos, qui aut nimis distant aut habent
loca in montanis tutissima quae expugnari non possunt.
Primo igitur in terra ubi imperator moratur est Cathaia nigra,
ubi fuit Presbyter Johannes. Post eam terra fratris sui ultra
per iter trium septimanarum, deinde terra Moal et Tartarorum
ultra eos per iter quasi duodecim dietarum. Sed tota haec terra
est in qua moratur imperator vagans per diversa loca. Terra
tamen, in qua primo fuerunt Moal, vocatur Oznam Kerule;
et ibi est adhuc curia Cingis Cham; sed quia Caracarum
ejus cum regione fuit prima adquisitio eorum, ideo civitatem
illam habent pro imperiali, et prope illam eligunt suum Cham,
id est imperatorem. Deinde post Moal et Tartaros ad orien-
tem sunt fortes homines, qui vocantur Tangut !, qui ceperunt
primo Cingis Cham in bello; sed, pace facta, iterum subju-
gavit eos. Isti homines habent boves fortissimos, habentes
caudas plenas pilis, sicut equi, quorum vaccae non permittunt

! * Tangut is a name very conspicuous in the Mongol era. The name Tanggod
is properly a Mongol plural designating certain tribes of Tibetan blood called
by the Chinese Tanghiang, who established an independent kingdom on the
North-West frontier of China with their capitalat Ninghia on the Yellow River,
. .. This kingdom, called by the Chinese Hia and by the Mongols Tangut, was
several times invaded by Chinghis, and it was on the campaign of its final
conquest that he died in 1227. In a general way Tangut corresponded to the
modern province of Kansuh.' [Yule's ed. of Marco Polo, vol. i, note to p. 186.)

—— — —À— M ae - — —

GEOGRAPHIA. 371

se mulgeri, ni cantetur eis; et si isti boves vident hominem
indutum rubris pannis, insiliunt in eum volentes interficere.
Post istos ad orientem sunt homines qui vocantur Thebeth, Nations to

qui solebant comedere parentes suos causa pietatis, ut non ast or
facerent eis alia sepulchra nisi viscera sua, de quibus scribunt
philosophi, ut Plinius et Solinus, et alii, et frater Willielmus
testatur in libro suo, ac frater Johannes de Plano Carpini!
similiter in libro quem composuit de Tartaris, inter quos fuit
anno Domini 1246, missus a Domino papa in legationem
ad imperatorem Tartarorum. Sed quia fuerunt ex hoc facto
abominabiles omni nationi, ideo jam mutaverunt hunc ritum,
et tamen adhuc de ossibus capitum faciunt scyphos, in quibus
bibunt propter memoriam parentum suorum. Post istos ad
orientem sunt parvi homines et fusci sicut Hispani, et dicuntur
Solangi, quorum nuntii quando veniunt ad curiam alicujus
habent in manu tabulam de ebore, in qua inspiciunt quando
narrant ea quae volunt ac si omnia essent ibi scripta. Et
ultra istos est quidam populus, quorum animalia non appro-
priantur alicui nec habent custodem, sed si aliquis indigena
vult habere aliquod animal, stat super collem et vociferat sicut.
vult, et veniunt ad vocem suam, et accipit quod vult. Quod
si extraneus veniret, odore suo fugaret omnia et faceret ea
sylvestria. Et ideo quando homines veniunt extranei, clau-
dunt eos in domo, et dant eis necessaria vitae, donec habeant

1 Carpini was a native of Perugia, and was amongst the earliest disciples of
St. Francis, who sent him in 1221 to Germany to assist Caesar of Spires as
provincial of that country. At the Council of Lyons, held by Pope Innocent IV
in 1245, it was decided to send a mission to the Tartar emperor (at that time
Kuyuk, the grandson of Chinghis) inviting him to cease from slaughter and adopt
Christianity. Carpini was charged with the mission. Starting in the spring
of 1246 from Poland, he reached the Khan's headquarters near Kara Korum
on July 22. The story of his journey is full of interest, though not equal to
that of Rubruquis. It is to be found complete in the fourth volume of the
Memoirs of the Paris Geographical Society, 1839. Carpini devotes much
attention to the military problem of arresting Tartar invasions. His description
of the marvellous manceuvring of their huge hordes of cavalry is most vivid.
He was much struck by their discipline and loyalty, and their abstinence from
internal quarrels. ‘Sunt magis obedientes dominis suis quam aliqui homines qui
sunt in mundo sive religiosi sive saeculares, et magis reverentur eosdem ; neque
de facili mentiuntur eis. Verbis ad invicem raro aut nunquam contendunt;
factis vero nunquam."

Bba

Great
Cathay, or
China.

Religions
of Tartary.

372 OPERIS MAJORIS PARS QUARTA.

responsum de eis pro quibus veniunt; nec permittunt eos
vagari per regionem.

Sed ultra hos est magna Cathaia, quae Seres dicitur apud
philosophos, et est in extremitate orientis a parte aquilonari
respectu Indiae, divisa ab ea per sinum maris et montes.
Et hic fiunt panni serici optimi, et in magna copia, unde
ab hac terra deferuntur ad alias regiones. Et hic populus
aspirat multum per nares, et sunt optimi artifices in omni
arte, et sunt boni medici apud eos in omnibus praeterquam de
urina, cujus judicio non utuntur, sed per pulsum et alia signa
optime dijudicant, et bene cognoscunt vires herbarum, et
totius medicinae potestatem. Multi ex eis sunt apud Tartaros.
Et istorum Cathaiorum moneta vulgaris est carta de Bam-
basio!, in qua imprimunt quasdam lineas. Nec mirum, cum
Rusceni qui prope nos sunt habent pro moneta faciem
Hesperiolorum. Et ista Cathaia non distat per octo et viginti
dietas? a terra in qua moratur imperator. Et in illa terra sunt
rupes exaltae, in quibus habitant quaedam creaturae habentes
per omnia formam humanam, non tamen genua flectunt, sed
ambulant saltando; sed non sunt longitudinis majoris quam
cubiti, et vestitur totum corpus crinibus, et non loquuntur. Et
venatores portant cerevisiam et faciunt foveas in rupibus ad
modum scyphorum, et illa animalia veniunt et bibunt cere-
visiam et inebriantur, et dormiunt, et sic capiuntur. Et
venatores ligant eis manus, et pedes, et aperiunt venam in
collo, et extrahunt tres vel quatuor guttas sanguinis, et
dissolvunt ea ac dimittunt ea abire, et ille sanguis est pre-
tiosissimus pro purpura.

Sciendum vero est quod a principio Cathaiae nigrae usque
in finem orientis sunt principaliter idololatrae?, sed mixti sunt

! Not Gombasio, as in J. For an account of the Chinese paper-money see
Marco Polo, Book ii. ch. 24. It was made of the inner bark of the mulberry
tree. Its use began in the ninth century A.D. and rapidly extended.

3 28 days journey at 20 miles would come to 560 miles, which is nearly
the distance between Caracorum and the nearest point of the Great Wall.
The reading of some of the MSS., cxxviii, is quite inadmissible.

* Marco Polo, like Rubruquis and Bacon, usually denotes Buddhists by this
tern. We do not know, says Yule (Marco Polo, vol. i. p. 187), whether the
Buddhism found here at this time was a recent introduction from Tibet, oc

GEOGRAPHIA. 373

inter eos Saraceni et Tartari, et Nestoriani, qui sunt Christiani
imperfecti habentes patriarcham suum in oriente, qui visitat
regiones et ordinat infantes in cunabulis ad sacros ordines, quia
ipse solus ordinat, et non potest venire ad unum locum nisi quasi
in quinquaginta annis; et ille dicit se habere auctoritatem
a Romana ecclesia ab antiquo, et paratus est obedire, si via
esset aperta. Et isti docent filios nobilium Tartarorum
evangelium et fidem et alios quando possunt; sed quia
parum sciunt, et sunt malorum morum, ideo Tartari despi-
ciunt eos. Et consecrant in missa unum panem latum ad
modum palmae, et dividunt primo in duodecim partes secun-
dum numerum apostolorum ; et postea illas partes dividunt
secundum numerum populi, et sacerdos dat unicuique corpus
Christi in manu sua, et tunc quilibet assumit de palma sua
cum reverentia. Sed idololatrae praevalent in multitudine
in omnibus his regionibus, et omnes conveniunt in hoc, quod
habent templa sicut nos et campanas magnas. Et ideo
ecclesiae Graecorum, Armeniae, et totius orientis nolunt
habere campanas propter idololatras. Rusceni tamen habent
et Graeci in Cassaria. Omnes sacerdotes eorum radunt
totum caput et barbam, et servant castitatem ex quo radunt
caput, et vivunt centum vel ducenti in una congregatione.
Diebus quibus intrant templum ponunt duo scamna, et sedent
e regione chorus contra chorum in terra, habentes libros in
manibus, quos aliquando deponunt super ila scamna; et
habent capita discooperta quamdiu sunt in templo, legentes
in silentio, et nullo modo loquerentur in templo, nisi verba
officii sui. Habent etiam in manibus quocunque vadunt
quandam chordam centum vel ducentorum nucleorum, sicut
nos pater noster, et dicunt semper haec verba, On man
baccan, id est Deus tu nosti!. Haec sunt communia omnibus
idololatris. Sed tamen Ingeres, qui habitant in terra ubi
imperator moratur, differunt ab aliis: Nam alii non ponunt
unum Deum, sed plures, et creaturam adorant. [Isti vero

a relic of the old Buddhism of Khotan and other Central Asian kingdoms,
but most probably it was the former.

! This is evidently a perversion of the Buddhist formula, often imprinted in
flags and revolved in prayer-mills, Om Mani Padme Hum, Ah, the jewel is in the
lotus (the self-creative force is in the Cosmos).

Various
modes of
writing.

Brief notice
of Southern
Europe.

Greece.

374 OPERIS MAJORIS PARS QUARTA.

propter viciniam Christianorum et Saracenorum ponunt unum
Deum. Et sunt optimi scriptores, unde Tartari acceperunt
literas eorum, et illi sunt magni scriptores Tartarorum. Et
isti scribunt a sursum in deorsum, et a sinistra in dextram
multiplicant lineas et legunt. Thebeth scribunt sicut nos,
et habent figuras similes nostris. Tangut scribunt a dextra

in sinistram, sicut Arabes, sed multiplicant lineas ascendendo.

Cathai orientales scribunt cum punctorio quo pingunt pictores,
et faciunt in una figura plures literas comprehendentes unam
dictionem, et ex hoc veniunt characteres qui habent multas
literas simul; unde veri characteres et physici sunt compositi
ex literis, et habent sensum dictionum.

Et tota terra a Danubio usque in orientem vocatur apud
antiquos Scythia, a quo Scythae et omnes regiones
Tartarorum sunt de Scythia, et etiam Ruscia, et totum usque
ad Alemanniam.

Descripsi igitur regiones omnes Asiae et Africae, et aqui-
lonares Europae. Nunc orientales et meridianas Europae et
occidentales breviter annotabo. Nam fere omnes notae sunt
omnibus. Dictum quidem est quod Albania occidentalis
terminatur ad Danubium sub mari Pontico, et ad Hungariam
minorem extenditur. Sed ex altera parte Danubii sub eodem
mari antiquitus prima regio occurrens dicebatur Thracia, in

qua est Constantinopolis. Cui ad occidentem super Danubium

jungebatur Moesia. Sed nunc in illis locis sunt Balchia et
Bulgaria minor. Deinde Hungaria ad occidentem. Et postea
Moravia, quae est sub regno Bohemiae. Cui a meridie est
Histria, quibus in occidente succedunt Bohemia Moraviae,
et Austria Histriae. Deinde tota Alemannia ad occidentem,
et postea Francia, quae notae sunt.

Post Thraciam versus meridiem est Macedonia regibus
inclyta maximis, Antigono, Philippo, Alexandro magno;
quae alio nomine dicebatur Emathia. Post eam ad meridiem
est Magnesia ; deinde Thessalonia, quibus apostolus scripsit.
Deinde adhuc ad meridiem est Boeotia, ubi Thebae civitas
famosa, a qua in orientem xviii milliaribus est civitas nota,
quae Niger Pons vocatur. Sub istis terris ad occidentem
primo contermina Macedoniae Thessaloniae et Bulgariae est

GEOGRAPHIA. . 318

Sclavonia. Sub Boeotia est Attica dicta ab Athenis civitate,
quae est nutrix philosophorum, ubi Socrates et Plato et
Aristoteles et caeteri famosi docuerunt. Et haec est Attica
pars Arcadiae secundum Ethicum philosophum, quae est
illustrissima provincia non solum propter Athenas, quam vocat
Ethicus umbilicum Graeciae, sed propter potentiam militarem.
Nam haec a Scycione rege dicebatur Scycionia, unde regnum
Scycioniorum dicitur, unum de quatuor principalibus regnis
mundi quae fuerunt a principio, scilicet regnum Scytharum
sub Reu atavo Abrahae exortum; et regnum Aegyptiorum
sub Seruch proavo Abrahae: et regnum Assyriorum, et
Scycioniorum sub Nachor avo Abrahae; sicut scribit Beda
libro Temporum; et hoc est regnum Graecorum. Nam, ut
ait Ethicus, tota Graecia conspiravit in nomen Scycioniae
quoniam regnum Graecorum dicebatur regnum Scycioniorum,
propter hoc quod principale robur militiae fuit ad Scycionios,
qui sunt Arcadi. Haec gratis expressi abundantius, quia
historiae omnes faciunt magnam mentionem de regno
Scycioniorum ; et apud solum Ethicum philosophum manifeste
potest inveniri ratio vocabuli, et quid sit quod per nomen
designatur. Secundum vero Plinium postea est Achaia,
postea Peloponnensis provincia, in qua est Corinthus nobilis.
Deinde Locris et postea Epirus, et sic est terminus Graeciae.
Sub qua ad occidentem est Dalmatia, in qua Duracium.
Et sub ea Illyria, a qua dicitur mare Illyricum, quod
extenditur a flumine Arsiae usque ad flumen Dirinum, quod
totum alio nomine Libnia dicitur. Sed proprie circa flumen
Dirinum sunt Illyrii, et ejus longitudo est a flumine Arsia
usque ad flumen Dirinum; et jacet super mare Adriaticum,
quod est mare Venetiarum. In cujus extremitate occidentali
sunt Venetiae. Et habet haec Illyria multas parvas insulas,
et habet haec longitudo dxxx milliaria, latitudo vero cccxv
milliaria. Haec de Illyrico recitavi verbo ad verbum secundum
Plinium, propter hoc, quod nos moderni nescimus intelligere
verbum apostoli, cum dicit se replevisse evangelium usque ad
Illyricum. Et in multis historiis invenimus Illyricum et
Illyricos, et non intelligimus quae dicuntur; unde Illyrii
jacent inter Dalmatiam et Histriam. Et ideo ubi nunc

The Adri-
atic, Italy,
Spain.

376 OPERIS MAJORIS PARS QUARTA.

Sclavonia est et forum Julii et circa partes Venetiarum sole-
bant esse Illyrii. Et hae omnes nationes sunt inclusae inter
brachium sancti Georgii, et mare magnum ab oriente ; et
inter Danubium qui vocatur Hister in magna sui parte a
septentrione; et inter mare Adriaticum a meridie. Distantia
vero penes milliaria et dietas potest in aliquibus notari. Nam
a Venetiis per littus maris sunt plus quam cccc milliaria usque
ad Duracium. Deinde superius ascendendo usque ad Patras
civitatem famosam sunt xl, a qua usque Corinthum Ix, a qua
usque ad Athenas xl,a qua usque Thebas xl, deinde usque
Nigrum pontem xviii, a quo per mare usque Constantinopolim
quingenti milliaria ; eta Nigro ponte usque Cretam insulam ccc
milliaria. Deinde ex altera parte maris Adriatici, inter ipsum
et mare quod ab Adriatico decurrit in Hispaniam, jacet tota
Italia, et deinde Provincia, et tandem Hispania. Sed quia
notae sunt, non oportet nunc plus de istis regionibus dici.
Haec igitur est historia, quam volui hic texere secundum
experientiam naturalium et itinerantium de locis et gentibus
totius habitabilis, usquequo Vestra Reverentia requirat princi-
palem scripturam !.

Outlines of. Post locorum descriptionem deberent sequi alia quatuor,

logical - scilicet certificatio naturarum stellarum fixarum et planetarum,

treatise. ut certior haberetur per haec certitudo complexionum omnium
locorum et rerum locatarum, quatenus posset fieri judicium de
praesentibus, praeteritis, et futuris, ut tandem fierent, quinto ?,
opera quae promoverent omnia rei publicae utilia et nociva
excluderent. Sed cum non potui propter impedimenta

! * Usquequo. .. scripturam' omitted in C. C. C. (Cambridge) MSS. In O. are
the words : * Finitur quarta pars majoris operis. Nevertheless the MS. proceeds
to the astrological section that follows, and indeed divides this section into
chapters as though it were a distinct treatise. The reference to Prinafalem
scripturam, so often spoken of before, will be noted. °

2 The four previous points are (a) the nature of the zodiacal signs ; (b) of
the planets; (c) the influence of each over places and things; (d) judgement as
to past and future events founded on these facts.

ASTROLOGIA. 377

perficere descriptionem locorum in figura secundum vias
naturalium, et haec quatuor sequuntur, oportuit ab horum
tractatu cessare ; volo tamen hic in summa tangere intentionem
tractatus horum quatuor, ac si factus esset, sicut de aliis feci
de quibus tractavi; quatenus videat Vestra Sapientia quid
requirendum sit pro utilitate rei publicae procuranda, et
qualiter scripturas et opera sapientiae petatis a quocunque.

Superius quidem dictum est quod sunt 1,022 stellae fixae, Qualities of
quarum quantitas potest deprehendi per instrumenta astrono- 4) signs
miae, quae habent virtutes varias in calore frigore humore et
siccitate et omnibus aliis passionibus et alterationibus naturali-
bus. Inter quas sunt principales stellae duodecim signorum,
per quas omnia alia specialiter alterantur. Signa vero sunt,
Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, *
Sagittarius, Capricornus, Aquarius, Pisces; quae sic nomi-
nantur, quia stellae in coelo habent dispositionem rerum sic
nominatarum. Et haec signa Aries, Leo, et Sagittarius
sunt effective ignea; Taurus, Virgo, et Capricornus sunt
terrea ; Gemini, Libra, et Aquarius, sunt aerea; Cancer,
Scorpio et Pisces sunt aquatica. Et Aries, Cancer, Libra et
Capricornus sunt mobilia, quia renovantur in eis quatuor
complexiones principales omnium rerum, scilicet calida et
humida in Ariete ; calida et sicca in Cancro; frigida et sicca
in Libra; frigida et humida in Capricorno. Taurus et sui
sequaces sunt signa fixa, quia dictae complexiones figuntur in
eis et perficiuntur. Gemini et sui sequaces dicuntur signa
communia, quia jam declinat complexio in eis ad novam,
quae renovatur in signo sequente. — Habent autem signa haec
quamplures alias varietates et proprietates, quas caeteri
tractatus habent determinare.

Planetarum prima diversitas est in virtutibus propriis. Qualities of
Nam Saturnus est frigidus et siccus, et omnis pigritiae et planets.
mortificationis et destructionis rerum causativus per egressum
siccitatis et frigoris. Mars vero est corruptivus propter egres-
sum caliditatis et siccitatis. Et isti duo planetae nunquam
faciunt bonum nisi per accidens; sicut aliquando venenum
est bonum per accidens, ut Scammonea, quae purgat materiam
morbi, sed tamen per se laedit naturam. Et vocantur

Their
power

: varies with

their posi-
tion.

It varies in
different
parts of
their orbit.

378 OPERIS MAJORIS PARS QUARTA.

isti planetae inaequales, et infortunia, et malevoli. Jupiter vero
et Venus habent caliditatem et humiditatem; sed Jupiter
magis et melius: et isti duo planetae dicuntur aequalis
fortunae, et benevoli. Mercurius est mediocris inter bonum et
malum, et convertibilis naturae. Nam cum bonis est bonus,
et malus cum malis. Luna vero frigida est et humida. Sol
habet generativum calorem et vitalem, quia est causa vitae et
generationis in omnibus, unde licet sit calidus et siccus, suus
tamen calor non est corruptivus, sed generativus, et sua
siccitas non est mortificativa, et ideo aliter est quam in Marte.

Habent autem planetae virtutes alias a signis; nam quando
sunt in signo calido, habent virtutem calefaciendi, et sic de
aliis. Sed speciales praeter has habent virtutes, de quibus
superius dictum est, quae sunt domus, exaltatio, triplicitas,
terminus et facies, et secundum has dignitates habent effectus
mirabiles. Et iterum penes aspectus, qui sunt conjunctio,
oppositio, &c. Conjuncti dicuntur planetae, quando sunt in
eodem signo; oppositi, quando unus est in septimo ab alio.
Trinus vero aspectus est, quando per quatuor distant signa.
Quartus, quando per tria. Et sextilis, quando per duo. Et
oppositio et quartus aspectus sunt mali ex natura sua. Trinus
et sextilis sunt boni, et conjunctio similiter. Aspectus autem
isti considerantur in quinque planetis, praecipue respectu
Lunae et Solis. Quando ergo malus planeta aspicit in malo
aspectu, detestabile est, quia tunc duplicat malitiam ; quando
vero bonus planeta aspicit in malo aspectu, tolerabile est ;
et si malus in bono aspectu aspicit, mitigatur ejus malitia.
Quando vero malus opponitur aut conjungitur malo, tunc
magnum malum est.

Habent etiam planetae magnam varietatem actionum penes
eccentricos et epicyclos. Nam quando sunt in partibus
superioribus istorum, faciunt operationes fortissimas, quando
vero in inferioribus debiles ; quia quando sunt in superioribus
partibus suorum circulorum, qui vocantur auges, tunc
moventur circa mundum motu diurno in circulis magnis, et
tunc velociter feruntur, et velocitas motus inducit fortitudinem
actionis in rebus quae natae sunt moveri, cujusmodi sunt
stellae. Habent etiam effectus varios penes partes revoluti-

ASTROLOGIA. 379

onum suarum, et penes totas revolutiones. Nam secundum
quod transeunt quartam coeli et medietatem et tres quartas,
et totum circulum, habent sensibiles varietates in effectibus.
Et non solum sic, sed penes quamlibet revolutionum determina-
tarum; sicut Saturnus, completis decem revolutionibus suis,
inducit magnam mundi alterationem, sicut prius tactum est in
sectis. Domus etiam duodecim, in quas dividitur totum
coelum, quae superius tactae sunt, maxime considerantur
respectu virtutum planetarum. Nam varias potestates contra-
hunt planetae ex eis, et varia per virtutes harum domorum
operantur planetae in hoc mundo: et ideo has domos
considerare maxime docent mathematici. Haec igitur sunt
radices principales in actionibus stellarum, quae habent ramos
et flores, et fructus infinitos. Haec igitur est intentio tractatus
quem in hoc opere facere proposui de virtutibus et actionibus
stellarum.

Tertio considerandum est quomodo loca mundi et res The effects
alterantur in complexionibus per jam dictas radices. Quidam of celestial
autem universales sermones facti sunt de hac materia in terrestrial
prioribus, ut oportuit, sed in hac parte operis deberent plura things.
certificari in particulari. Et certum est per Aristotelem, quod
coelum non solum est causa universalis, sed particularis,
omnium rerum inferiorum. Nam Aristoteles dicit secundo! de
Generatione quod elementa debilius agunt respectu coeli quam
organa respectu artificis, ut securis et dolabrum respectu
carpentatoris; et ideo licet per qualitates elementares fiant
omnia hic inferius, non erunt tamen respectu coeli nisi sicut
instrumenta respectu artificis. Et ideo si artifex est agens
principale universale et particulare respectu operis, multo
magis coelum respectü rei generandae. Et Averroes dicit in
septimo Metaphysicae quod idem facit virtus coeli in materia
putrefica, quod virtus patris in seminibus; et ideo quae
generantur per putrefactionem, licet sunt animata, fiunt tamen
immediate a coelo, et multo fortius alia inanimata. Et non
solum in his sed in generatis secundum propagationem in

1 De Generatione, ii. 9. In this chapter Aristotle shows that the elements left
to themselves are like tools without a workman; in the following chapter the
revolution of the heavens is indicated as the efficient cause of generation.

Fouropera-
tions to be
distin-
guished.

380 OPERIS MAJORIS PARS QUARTA.

plantis; quia dicit Aristoteles in libro Vegetabilium, quod Sol
est pater plantarum et -Luna mater. Et in hominibus et
animalibus dicit, quod homo generat hominem et sol!. Sed
Averroes dicit quod sol plus facit quam homo ad productionem
rei. Nam virtus solis continuatur in semine a principio
generationis usque ad finem, virtus autem patris non, sed fit
semel, scilicet solum in seminis decisione, et ideo nihil faceret
nisi esset virtus coeli continue multiplicata et infusa, regulans
totam generationem.

Per coelum ergo complexiones omnium rerum habentur, et
non solum regiones diversificantur per coelum, sed res ejusdem
regionis et partes ejusdem rei et non solum in generatione
recta sed monstruosa, et peccatis ac erroribus naturae. Nam
per diversitates horizontum, secundum quod singula puncta
terrae sunt centra in horizontibus novis, patet omnia variari,
ut superius notatum est de herbis diversarum specierum, quae
nascuntur quasi in eodem puncto terrae, et de diversitate
gemellorum in eadem matrice ; propter hoc quod coni diversa-
rum pyramidum continentium virtutes stellarum et partium
coeli super capita habitantium veniunt ad singula puncta
terrae, ut cadat diversitas plena in rebus. — Sed alia diversitas
est per elongationem a polis et a medio mundi. Et hujus
causa duplex est. Una est causa universalis, scilicet solis
distantia vel propinquitas secundum quod superius in locis
mundi est memoratum. Alia est causa particularis, scilicet
diversitas stellarum fixarum super capita habitantium. Nam
specialiter per has variantur res naturales in diversis regioni-
bus, et homines, non solum in naturalibus, sed in moribus, in
scientiis, in artibus, in linguis, et in omnibus. — Tertia est ex
praedominanti virtute duodecim signorum. Nam diversa signa

" dominantur in diversis regionibus, aut quia in mundi principio

fuerunt in directo illarum creaturarum recipientium virtutes
primas, et quod nova testa capit inveterata sapit; aut quia
sunt similes in natura cum stellis quae super capita habitan-

1 Nat. Auscult. ii. 2 dvOparwos yap ávOporroy yevvg xal fjuos. The reference to
the apocryphal work De Plants seems to be incorrectly given. See Lib. i,
cap. 6 ’Avataydpas . . . ($n spós Aexiveoy brc } y prop wey ton rey Quràv,
6 3 fpuos warhp.

A

ASTROLOGIA. 381

tium revolvuntur. Et quarta causa est per planetas. Nam
planetae assignantur diversis regionibus per dominium sicut
signa, et hoc ex duplici causa dicta. Nuncde signis, quomodo
aut in quibus regionibus assignentur signa et planetae, difficile
est certificare, nam auctores diversificantur. Tractatus tamen
de his habet hic expedire.

Sed non est plena certitudo de his, sicut non de aliis s These est
difficultatibus multis, nisi ex libris Hebraeorum, quos primi unde stood
composuerunt astronomi qui revelationem a Deo habuerunt DY rologers.
in omnibus specialem. Nec solum quidem accidit diversitas
complexionis in diversis regionibus per stellas, sed in rebus
ejusdem regionis. Quaedam enim sunt de complexione solis,
et quaedam de complexione lunae, et sic de aliis; quae secun-
dum quod sui planetae habent quinque dignitates suas ante-
dictas, vigorantur, confortantur, augmentantur, et roborantur.
Quando vero sunt in oppositis locis suarum dictarum dignita-
tum, deteriorantur et destituuntur a naturali vigore. Et
similiter accidit de signis, nam res diversae sequuntur
complexiones diversorum signorum. Nam secundum quod
quaedam sunt ignea, et secundum quod planetae sunt ignei,

id est, calidi et sicci, penes hoc sunt res aliquae de complexione
ignis, et hujusmodi res vocantur martiales a planeta, et de
complexione Arietis, Leonis, et Sagittarii, quae sunt signa
calida et sicca ; et sic de aliis rerum complexionibus et signorum
et planetarum. Nominare tamen et signare res singulas
respectu suorum planetarum et signorum, est satis difficilis
certificationis et impossibilis, nisi per libros Hebraeorum, ut
ad fontem certitudinis recurratur. Ista vero quae nunc dicta
sunt de assignatione signorum et planetarum rebus diversarum
regionum et ejusdem regionis, sunt de majoribus difficultatibus
philosophiae, et ubi major diversitas est auctorum Latinorum.

Et non solum sic variantur res ejusdem regionis, sed partes Action of
ejusdem rei et maxime in homine, quia omnia sunt propter m epeeal,
hominem. Nam caput est de complexione Arietis; collum de parts of the
complexione Tauri; et humeri et brachia de complexione ?
Geminorum, et sic ulterius. De qua divisione satis concordant
auctores et ratio sufficiens dictat, et experientia, quod plus
est. Nam si Luna sit in Geminis, quod est signum respondens

Planetary
action on
special
hours and
days.

382 OPERIS MAJORIS PARS QUARTA.

brachiis et humeris, periculum est tangere hujusmodi membra
ferro, ut minutione, scarificatione, seu ventosa, et maxime
cultello vel ense. Et non solum sic, sed de omnibus medica-
minibus chirurgiae; difficultatem enim magnam recipiunt et
languorem, et aliquando mortem ; quae non fierent si Luna
esset in alio signo. Nam Ptolemaeus dicit in Centilogio, Luna
existente in signo respondente membro, periculum est tangere
membrum ferro. Et Haly medicus, dans causam hujus,
dicit, quod tunc propter existentiam Lunae in tali signo
confluunt humores ad tale membrum, et generant nocumen-
tum; et hoc experientia tota die probat. Nam in anno
praecedente medicus famosior in Francia tibiae fratris sui
fecit chirurgum dare medicamen; sed astronomus peritus
prohibuit ei ne faceret, quia Luna fuit in Aquario, quod est
signum respondens tibiis. Et accidit quod continue invaluit
infirmitas et languor usque ad mortem. Hujusmodi casus
accidunt saepe, sed propter ignorantiam astronomiae non
percipiuntur.

Sed res ejusdem regionis non solum sic variantur in com-
plexionibus per diversitatem signorum et planetarum in
eodem tempore, sed in diversis. Nam omni horae dominatur
unus planeta. specialiter, et medietas signi oritur super.
horizonta in qualibet hora, ex quibus variantur horae semper
et quartae dierum similiter et ipsi dies, qui sicut in omni lingua
dies nominantur a planetis, sic habent diversitatem ab eis, ut.
omnes concordant sapientes. Et hoc est a divina ordinatione
a principio mundi. Unde in prima hora diei sabbati dominatur
Saturnus, et toti diei principaliter, quia per ejus qualitatem
alteratur prima hora, quae est principalis, et principium unde
derivatur virtus Saturni in totum diem. Et tunc Jupiter habet
aspectum ad horam secundam, Mars ad tertiam, Sol ad
quartam, Venus ad quintam, Mercurius ad sextam, Luna
ad septimam, et iterum Saturnus ad octavam, et sic ulterius,
ut dominetur in xv, et tertio in xxii, ut Jupiter dominetur in
xxiii, et Mars in xxiv, et sic completur dies naturalis ipsius
sabbati, ut incipiat Sol dominari in prima hora diei dominici,
qui ideo vocatur dies solis apud omnes nationes. Et per hanc
artem currit variatio omnium dierum septimanae et horarum,

ASTROLOGIA. 383

Ex his patent complexiones quartarum diei et noctis, et quae Applica-
sunt horae sanguinis, quae cholerae, quae phlegmatis, et quae Know eden
melancholiae. Sed medici, qui nesciunt astronomiam, non to Medi-
judicant de qualitate horarum, nisi per intentionem et remis- ^.
sionem caloris solaris, vel per absentiam. Nam. solum
considerant quod sex horae diei naturalis sunt calidae. et
humidae, et reliquae sex sunt calidae et siccae ; aliae sex sunt
frigidae et siccae, et ultimae sex frigidae et humidae. Sed
cujus complexionis sit signum quod oritur in duabus horis, et
quis planeta dominetur in hora secundum regulam praedictam,
insuper quis et qui planetae oriantur super horizonta, non
considerant, cum tamen haec et quaedam alia necessario
debeant considerari. Haec tamen diversitas dierum et horarum
bene debet ab omni homine sciri, et maxime a medicis, et
a quolibet qui vult suam sanitatem servare. Nam secundum
diversitatem complexionis cujuslibet et secundum diversitatem
aetatis et occupationis, oporteret eligere diversas horas pro
minutionibus, pro medicinis, et omnibus aliis actibus vitae, et
pro negotiis et occupationibus et aggressionibus operum, seu
sapientia aliorum, quia virtutes coelorum in his horis et diebus
diversimode movent complexiones sanorum et infirmorum
diversas. Et ulterius secundum quod complexiones variantur,
excitantur animi et ducuntur ut gratis velint sequi complexi-
onis motum, etiam in omnibus operibus voluntariis, salva in
omnibus arbitrii libertate. Unde in die sabbati et maxime
in hora prima, non esset minuendum, nec aliquod dignum
incipiendum quod ad complexionem pertinet, sive primo in
naturalibus, sive secundario ut in voluntariis. et hoc propter
malitiam Saturni, qui in omnibus generat infortunium quan-
tum est ex parte sui, nisi aliud impediat. Et tamen ex
errore omnes homines faciunt se minui in die sabbati, quod
faciunt propter quietem diei dominici ab occupationibus et
laboribus.

Et non solum in horis et diebus accidit variatio magna Influence
consideranda per coelestia, immo in septimana, et hoc praecipue 9f te
per aetatem Lunae. Nam dum crescit Luna, omnia crescunt ;
dum decrescit, omnia decrescunt, sive decrementum patiuntur.

Hoc non solum astronomi, sed medici considerant; ut Galenus

The lunar
mansions.

384. OPERIS MAJORIS PARS QUARTA.

in libro Dynamidiarum !, et alii considerant in superiori expe-
rientia, ut in maribus, cerebrisque hominum, medullis, et
conchyliis et omnibus. Nam augmentantur et plena sunt
cum Lunae plenitudine, et deficiente Luna deficiunt. Nam
et lapis Lunae, qui vocatur Selenitis, crescit et decrescit
secundum Lunam, quo varietates lunationis paschalis festi

,sancti antiquitus probaverunt, ut suo loco in opere recto.

Nam quaedam malva in prima Luna ascendit super ipsam,
et crescit usque ad plenam Lunam, et deinde cum Luna
decrescit. Et est herba mirificae virtutis; cum prima Luna
duo folia nascuntur ex utroque latere stipitis, et in secunda
Luna duo alia, et sic usque ad plenilunium, et deinde ordine
consimili cadunt secundum quod Luna decrescit. Caeterum
ut Ptolemaeus ait, et Haly exponit lvi propositione Centilogii,
humores in corporibus prima septimana Lunae, et tertia,
recedunt ab interioribus ad exteriora, sicut flumina fluunt
a suis canalibus. In secunda vero septimana et in quarta
retrocedunt ab exterioribus ad interius, et in hoc est magna
rerum transmutatio et mirabilis. Ex quo sequitur satis
veridice, quod in prima septimana et in tertia utendum est
evacuationibus exterioribus, ut est phlebotomia, et in secunda
et in quarta septimana medicina laxativa ; quia Hippocrates
in prima particula aphorismorum dicit, undecumque reperit
natura, inde ducere per convenientem regionem, id est per
partem corporis ad quam humores naturales decurrunt. Sed
hoc medici astronomiam ignorantes non attendunt, saepius in
praejudicium patientum.

Et etiam est alia alteratio magna rerum per mansiones
Lunae, quae sunt xxviii. Mansio quidem est spatium zodiaci
quod pertransit Luna in die. Istae autem mansiones dis-
tinguuntur, quia quaedam sunt temperatae, quaedam distem-
peratae in sicco, frigido, calido vel humido. Et secundum
hoc quolibet die si homo aspiciat mane in qua mansione sit
Luna, poterit de pluvia et alterationibus aeris judicare, sicut
docet Albumazar in majori introductorio, et patet per ex-
perientiam. Et praecipue considerandum est de dispositione

! The two books, De Dynamidsss, are among the spurious works attributed to
Galen.

ASTROLOGIA. 385

Lunae in novilunio; nam talis debet esse dispositionis, saltem
prima septimana vel quindena, et aliquotiens totus mensis;
igitur in principio secundae septimanae, tertiae, et quartae,
currit eadem observatio. Nam in istis quadraturis fortissima
operatio Lunae est, ut Galenus in libro de Crisi et criticis
diebus, secundum quod transit quartas sui circuli. Nec solum
septimanae, sed menses integri variantur praecipue per motum
solis in singulis signis, secundum quod recedit a nobis vel
accedit ad nos. Sed quartae anni mutantur manifeste in
complexionibus suis, quum ex his communiter oriuntur qua-
tuor complexiones principales, ut calida et humida in vere,
calida et sicca in aestate, frigida et sicca in autumno, frigida
et humida in hyeme. Nam fortissima est mutatio stellarum
in quadraturis suorum circulorum, ut auctores docent et
experientia certificat.

Annorum vero mutatio est major per hos caeteros planetas, Influence of
qui secundum suas revolutiones in quadraturis suorum circu- Marb Jape
lorum et in totius circuli revolutione mutant annos; et maxime Saturn.
tres superiores, scilicet Saturnus, Jupiter et Mars; ut in rebus
maximis, quae tarde veniunt, quia hi planetae sunt tardi motus,
et ideo effectus eorum non sunt quotidiani vel mensivi
sicut Lunae vel Solis. Hujusmodi autem effectus sunt
diluvia, terrae motus, et pestilentia, fames valida, cometarum
et caeterorum ignium in aere apparitio, sicut docet Albumazar
in Conjunctionibus, et omnes sapientes concordant ; unde cum
anno Domini 1264 mense Julii fuit apparitio cometae horribilis,
per virtutem Martis fuisse generatus approbatur. Nam Mars
cum fuerit tunc in Tauro et cometa ortus sit in Cancro, non
cessavit decurrere ad suam causam, scilicet Martem; sicut
ferrum currit ad magnetem. Sicut enim magnes trahit ferrum,
sic planeta, cujus virtute sublimatur vapor ignitus et assimilatur
coelesti naturae, attrahit cometam, et ideo cum ad Martem
motus est, et ibi delituit, necesse fuit eum a Marte causari,
Deinde cum natura Martis sit ignea, cujus natura est multi-
plicare choleram, et per consequens excitare homines ad iram
discordiam et bella, ideo accidit quod cometa ita significabat
super iras et discordias hominum et bella, sicut sapientes
astronomi docent. Sed verius experientia totius ecclesiae

VOL. I. Cc

Planetary
conjunc-
tions.

Medical
authorities
as to their
effects on
health.

386 OPERIS MAJORIS PARS QUARTA.

comprobavit per bella Angliae, Hispaniae et Italiae, et aliarum
regionum, quae circiter tempus illud et a tempore illo acci-
derunt. O quanta utilitas ecclesiae Dei potuisset procurari,
si coeli qualitas istorum temporum fuisset praevisa a sapien-
tibus, et praelatis et principibus cognita, et pacis studio
mancipata! Nam non fuisset tanta Christianorum strages
nec tot animae positae in infernum.

Et non tantum dico hoc propter revolutiones planetarum
generantes cometas et hujusmodi, sed magis propter con-
junctiones superiorum planetarum a tempore memorato.
Conjunctiones autem planetarum multiplicatae sunt nimis
his temporibus ; sed in capitulo superius de sectis et Christi
professione confirmanda adducta est praeclara astronomorum
scientia de istis conjunctionibus, quomodo consuetae naturae
jura mutantur, et animi hominum excitantur ad seditiones et
immutationes consuetudinum et legum, ad discordias et bella,
et mutantur dominatus et regna, et vices principum renovantur.
Albumazar et caeteri sapientes docent hoc evidenter. Et si
haec exempla sint nimis sublimia, converte stylum ad exempla
vulgata et utilia corporibus humanis. Nam Ptolemaeus dicit
in nona decima propositione Centilogii, si quis purgationem
receperit Luna conjuncta cum Jove, abbreviabitur opus ejus et
effectus minuetur. Et dicit Haly, quod hujus causa est, quia
ex beneficio Jovis in tantum confortatur natura, quod impedit
effectum medicinae. Et si Luna conjungatur Saturno, potio-
natus patietur torsiones et in periculo erit propter malitiam
Saturni, nec se poterit expedire propter Saturnalem siccitatem ;
qua, retinebitur medicina in corpore, quia siccum est bene
retentivum.

Sed qualiter cognoscuntur infirmitates penes hujusmodi
conjunctiones et aspectus caeteros et dignitates planetarum,
egregie designant auctores medicinae ; et praecipue Hippocrates
in libro suo de alterationibus corporum humanorum, quae
contingunt ex motu Lunae suscipientis conjunctiones et
aspectus caeteros planetarum. Et Galenus dicit tertio de Crisi
et criticis diebus!, * Et ego redii ad rem, quam consideravi

! The next three sentences are quoted from Galen. The passage will be
found in the treatise De Diebus Decretorits (lib. iii. cap. 4 and 5).

ASTROLOGIA. 337

cum studio et perscrutatione vehementi, et inveni eandem
veram et certam quae non perit, et est res quam invenerunt
astrologi Aegyptii Et est quod Luna signat super dies
qualiter erit dispositio hominis in aegritudine et sanitate sua;
quod est, si applicentur Lunae quaedam stellae aequales, et
sint stellae quae nominantur fortunae, erunt illi dies illi homini
convenientes. Et si applicentur ilii quaedam stellae egre-
dientes ab aequalitate, erurit illi dies laesionis et tristitiae.
Et sumit hic applicationes pro conjunctionibus et caeteris
aspectibus, et multa dicit hic de hac materia. Atque Haly
medicus in libro de Regimine Regali docet praeclare quod
medici indigerit consideratione hujusmodi, unde ait, medicina
eget astronomia, quae medicaminibus electis utitur temporibus
electis, quibus est Luna bonis et felicibus contemperata planetis
et competentibus figuris zodiaci. Et omnes auctores con-
cordant in istis. Et propter has conjunctiones et revolutiones
planetarum mutuas Avicenna secundo libro de Animalibus dicit,
totam generationem regulari et augmentari, et initium vitae
et mortis. Unde ait, opus est ut termini vitae et mortis essent
positi in specie, donec sit vita concordans cum revolutione
alicujus stellae aut multarum stellarum. Et primus terminus
est dies cum sua nocte: deinde est alius, quem Luna constituit
in quarta sui circuli; deinde est mensis, qui est circulus, qui
completur in conjunctione Solis et Lunae; deinde annus
planetarum ; deinde annus mediarum conjunctionum et re-
versionum ad eas figuras in quibus fuerunt istae conjunctiones,
quae faciunt ad augmentum naturalium et diminutionem
innaturalium. Et non solum haec accidunt in recta genera-
tione, sed in monstruosa et peccatis naturae, secundum quod
ipse Avicenna docet eodem libro, dicens, Si embryo potest
recipere humanitatem, potest recipere animalitatem, sicut in
rebus monstruosis, ut quando filius hominis habuit caput
arietis, et agnus habuit caput tauri, quoniam virtus in eo
induxit formas et figuras coelestes, quae accidunt unicuique.
Nec solum his modis accidunt alterationes complexionum Planets in
rerum inferiorum, sed propter ascensiones planetarum ad auges ‘*, 4/5/46
suorum circulorum, et postea descensiones ad oppositionem orbits.
augium propter fortitudinem motuum in augibus et debili-
Cc2

House of
the planet.

Interpreta-
tion of
thesethings
with refer-
ence to
human
events.

388 OPERIS MAJORIS PARS QUARTA.

tatem in oppositis augium, sicut nos videmus per experientiam.
Omnia enim terrae nascentia circa solstitium aestivale quando
Sol est in auge sui eccentrici, plus crescunt et vigorantur per
unum diem quam alias per septimanam. Et quando Luna
est in augibus suorum circulorum, ut in novilunio et plenilunio,
tunc sunt fortiores operationes ejus, ut patet in fluxibus maris
et in piscibus; tunc enim pisces meliores sunt, tunc saniora
sunt conchylia, sicut auctores docent, et experientia; et sic est
de omnibus planetis.

Sed ultimum quod hic volo tangere est de domibus duo-
decim, quae per divisionem coeli in duodecim partes oriuntur,
scilicet quarum consideratio maxime docetur a philosophis.
Nam Albumazar in libro de Floribus dicit, quod certissime
discutiendae et examinandae sunt. Nam per has primo con-
sideratur, quis planeta dominatur complexioni totius anni;
quae consideratio fit in principio veris, quando Sol ingreditur
primum minutum Arietis in aequinoctio vernali; et per has
significationes scitur, quomodo planetae inducunt complexiones
singulorum dierum et singularum horarum, et omnium rerum,
secundum quod ascendunt super horizontem. Nam ostendunt
hoc manifeste astronomi et experientia manifestat. Hae igitur
sunt radices de alteratione complexionum rerum per virtutes
stellarum, in cujus tractatu debent explicari rami et fructus
et flores cum tabulis et figurationibus nobilissimis, ex quo
manifestior est potestas figurarum et numerationum, nec non
praegrandis utilitas et sapientiae pulchritudo.

Post haec sequitur quartum, quod est consideratio de judicio
et cognitione praeteritorum praesentium et futurorum. Nam
si causa complexionum rerum est coelestis constellatio, poterit
hujusmodi effectus sciri per hanc causam. Et quomodo vel
quando, certificatur hoc per sanctos, et praecipue per pa-
triarchas a principio mundi, a quibus habuerunt philosophi
possibilitatem judicandi. Et considerandum est quod omnes
philosophi in hoc concordaverunt, et Aristoteles certificavit in
libro suo de hac materia, et experientia docet. Nec est con-
tradictio, nisi per ignorantiam infinitam, quae currit in vulgo
et in eis qui praesunt eis, qui omnia quae ignorant reprehen-
dunt et negligunt. Modus autem universalis judicandi per

ASTROLOGIA. 389

planetas consistit in hoc, quod homo sciat per tabulas et
instrumenta aequare motus coelorum et invenire loca planeta-
rum; et considerare quis eorum habeat plures et majores
fortitudines ex loco suo secundum illas quinque famosas, quae
sunt domus, exaltatio, triplicitas, terminus et facies ; et similiter
cum hoc videre fortitudines quae contingunt ex aspectibus
illorum et ex motu in augibus suorum circulorum, et ex
domibus duodecim. Et cum bene examinaverit et viderit haec et
eis annexa, tunc si Sol habuerit plura testimonia et fortitudines
hujusmodi, debet judicare secundum complexionem solarem
in rebus, eo quod illa dominatur in eis; et sic de aliis. Par-
ticularis vero consideratio et specialis in singulis habet suas
leges determinatas secundum rerum conditionem. Et potest
homo revolvere historiam ad tempora praeterita, et considerare
effectus coelorum a principio mundi, ut sunt diluvia, terrae
motus, pestilentiae, fames, cometae, monstra, et alia infinita,
quae contigerunt tam in rebus humanis quam in naturalibus.
Quibus comparatis, revolvat tabulas et canones astronomiae,
et inveniet constellationes proprias singulis effectibus respon-
dere. Deinde consideret per tabulas consimiles constellationes
in futuro tempore propinquo vel remoto sicut vult; et poterit
tunc pronuntiare in effectibus, qui consimiles erunt sicut fuerunt
in practerito, quia posita causa ponitur effectus.

Et istorum judiciorum introductoria habentur sufficienter Authorities
ex libro Albumazar proprio ad hoc, et ex libro Alkabiz, et onthe sub-
Haly Abenragel. Sed radices judicandi ponuntur in centum
verbis Ptolemaei, qui est potentior in philosophia speculativa.
Rami vero extrahuntur in quadripartito Ptolemaei, ut idem
dicunt. Flores vero et fructus in multis aliis libris colliguntur ;
sed praecipue in libro Conjunctionum Albumazar, secundum
quod pervenit hujus scientiae notitia ad manus Latinorum ;
hoc dico, quia nondum habent scientiam completam de his,
quia Latini nihil quod valet habent nisi ab aliis linguis; et
pauci fuerunt interpretes et mali ut ostenditur. Libri enim
Hebraeorum certificant de his, quam certificationem Aristoteles
consideravit et redegit in scriptura Graeca. Nam Averroes
dicit super quartum Coeli et Mundi quod Aristoteles certificavit
hoc in libro suo de impressionibus coelestibus, qui liber est

390 OPERIS MAJORIS PARS QUARTA.

melior tota philosophia Latinorum, et potest per vestram
jussionem transferri.
Our con- Quintum vero annunciatum superius est principale inter
duct should haec, nam nominata omnia sunt propter hoc ; quia non sufficit
by this | . rei publicae ut cognoscantur omnia, sed oportet quod utilia
as advise! cognita promoveantur, et nociva evacuentur. Sed hic licet
by Aris: geometria, et arithmetica, et musica dent maxima et quam-
plurima juvamenta, tamen astronomia regulat omnia, propter
hoc quod omne opus magnificum debet fieri in temporibus
electis. Et ideo operata aliarum scientiarum requirunt tem-
pora idonea, quae consideratione astronomi eligi cognoscuntur,
et ideo praeest omnibus scientiis in hac parte, quamvis etiam
specialia remedia habeat infinita, in quibus aliae scientiae non
habent potestatem. Et quia tam universalis est potentia istius
scientiae, ideo Aristoteles sapientissimus philosophus docet
Alexandrum in libro Secretorum, quod nec comedat, nec bibat,
nec aliquid faciat sine consilio astronomi, quia tempora electa
sunt ad omnia ; omnia enim tempus habent, sicut dicit Salomon
sapientior Aristotele. Et Aristoteles sibi objicit dicens, Deus
praevidit omnia ab aeterno, ergo non potest astronomus ea
impedire vel mutare. Et ipse respondet, quod ea quae Deus
praevidit sunt immutabilia. Sed tamen effectus eorum quae
Deus posuit in potestate hominis ex sua provisione aeterna,
potest homo mutare ut vult, quia in contingentibus ad utram-
libet. Et in rebus humanis Deus non posuit necessitatem,
licet sciverit ab aeterno in quam partem debet terminari con-
tingens, et humani libertas arbitrii. Et ideo potest homo
omnes utilitates suas procurare, et impedimenta removere, si
fuerit peritus in hac scientia. Et ponit exemplum. Si enim,
ut dicit, necessario erit superfluitas frigoris in tempore futuro,
astronomus praevidens potest apponere remedia, ut sine grava-
mine patiatur frigus illud, quod alii incaute non potuerunt
sustinere: potest enim astronomus praeparare loca calida,
nutrimenta calida, vestimenta calida et medicamina multa, ita
ut frigus ei in nullo nocebit, quamvis alii qui haec non prae-
viderint prae frigore moriantur. Et ideo in potestate hominis
periti in hac scientia est ut evadat nociva et consequatur
utilia.

ASTROLOGIA. 391

Et hoc egregie docet Isaac in libro Febrium, capitulo de By Isaac
the physi-

pestilentia; nec solum de infirmitatibus, sed etiam universa-
liter in omnibus, dicens quod anima rationalis dignior est
stellis, nam actio earum minime ei nocet nisi cum ignorantia
teneatur. Dum enim ipse sciverit earum actionem omnino
cavere poterit; et infert, Testificatur autem id quod videmus
ab optimis factum mathematicis, qui cum certissime noverint
dies mortis in eis qui mare ingressuri sunt, satis possunt eos
tueri; similiter et eos qui in bello morituri sunt; et addit,
Homo differt ab animalibus, nam rationis et discretionis est
super inquirere et desiderare bona et respuere mala, et eis
repugnare, quia non est subditus actioni naturali, nist cum
ignorantia tentus sit. Et ideo dicit Ptolemaeus in quinto verbo
Centilogii, astrologus optimus multo magis prohibere poterit
quod secundum stellas venturum est; et in octavo dicit, anima
sapiens adjuvabit opus stellarum, quemadmodum seminator
fortitudines naturales, unde et nociva poterit repellere, et
utilia promovere. Et Isaac ponit exemplum de pestilentia
futura, et facit sibi quaestionem juxta ignorantiam medicorum,
sicut Aristoteles fecit. Quaerit ergo utrum hujusmodi putre-
factio veniet necessario propter coelum, quia tunc medicus non
potest prohibere, et ideo inutile videtur hoc praecognosci.
Sed solvit, dicens quod corruptio aeris non nocet nisi corporibus
praeparatis ad eam; et ideo cum medicus videret significa-
tionem aeris corrupti in unoquoque tempore anni venturo,
poterit mundificare naturam, et malam corporis dispositionem
auferre, ut sciat venienti corruptioni repugnare. Nam si
viderit per motum stellarum fieri in aere calorem et siccitatem
nimiam et ustionem, festinet purgare choleram eorum in
quibus inest complexio cholerica, det frigida et humida calori
venturo repugnantia. Et Haly dat consimilem sententiam in
expositione quintae propositionis Centilogii. Ex his patet quod
astronomus potest dare remedia contra nociva et promovere
utilia, non solum in infirmitatibus, sed in aliis universaliter,
cum ratione electionis temporis apti ad omnia opera, cum
ratione operum utilium, cum remotione nocivorum; et hoc
specialiter in curis corporum humanorum, quo nihil melius est
quantum ad bonum civium particulare.

cian,

392 OPERIS MAJORIS PARS QUARTA.

conÁrmed Sed tamen respectu boni communis civitatis et regnorum,
matters by majora possunt fieri opera per virtutem astronomiae quam
example of aliquis potest dicere, et quam aliquis vult per scripturam
of Solo. €xplanare; nam haec sunt multa de secretissimis operibus
mon, sapientiae. Sed propter rerum magnitudinem et ignorantiam
multitudinis studentium, qui de operibus sapientiae non
curant, et propter fraudes multorum et malitias qui abusi sunt
his, occultantur semper a vulgo et a capitibus ejus; de quibus
tamen Moyses et Aaron, Solomon, Aristoteles, Ptolemaeus et
caeteri sapientes operati sunt nimis admirande. Unde cum hoc
sit unum de maximis, et quasi potens quodammodo in omnia,
non decet ut Vestrae Gloriae occultetur. Et quia praecepistis
ut scriberem de sapientia philosophiae, recitabo Vestrae
Clementiae sententias sapientum, praecipue cum ecclesiae Dei
sit omnino necessarium contra furiam Antichristi. Cum vero
Moyses in juventute sua fuisset dux exercitus Aegyptiorum
contra Aethiopes, et ob bonum pacis acceperat Aethiopissam,
pro qua contra eum duodecimo Numerorum objurgati sunt
Aaron et Maria, quae fuit regina Aethiopum, nolens dimittere
eam ut rediret in Aegyptum propter amoris superfluitatem, cum
esset peritus astronomus, fecit duas imagines in annulis, unam
oblivionis quam dedit mulieri, et alteram memoriae quam sibi
detinuit, et sic ab ea libere cum exercitu et sine bello recessit.
Haec Josephus primo Antiquitatum libro, et magister in
historiis, et multi confirmant. Mira res fuit haec, quae animum
mulieris immutavit. Salomon vero ordinavit de hujusmodi
multis, quae praeter solitum cursum naturae facta sunt, ut
dicit Josephus octavo libro, qui cum fuit sapientior omnibus
praecedentibus et sequentibus, ut scriptura sacra et Josephus
docent, non potuit haec opera negligere, et ideo scripta multa
in aenigmate reliquit, quae postea per magicos in malos usus
conversa sunt atque male interpretata, in quibus multa
enormia sunt per fraudulentos admixta. Sed sapientes sciunt
eligere grana de paleis, et theriacam de serpenti separare.
and of Aristoteles vero summus philosophorum docet haec opera
Aristotle. fieri in libro Secretorum, ut quaeque magnifica utiliter promo-
veantur et omnia nociva destruantur. His enim operibus
Alexandrum magnum fecit Aristoteles cum minus quadraginta

ASTROLOGIA. 393

millibus armatorum mundum superare. Is cum in lecto mor-
tali jacebat, et jam esset in januis mortis, civitatem suam et
regionem ab inimicis eripuit. De primo facto notum est in
gestis Alexandri, de secundo in Valerio Maximo, libro quinto.
Sed constat eum non posse hoc fecisse potentia corporali, sed
magna sapientiae virtute, quam in libris Secretorum reliquit
solum sapientissimis indagandam. Et cum propter pondus
senectutis, devicto Dario, mundum tradidit Alexandro, recessit
in terram suam, dixitque Alexandro quod ei scriberet quae
vellet, et ipse consilium daret opportunum. Et cum Alex-
ander invenit gentes habentes mores pessimos, scribens
Aristoteli quid faceret de eis, ipse princeps philosophiae re-
spondit, Si potes alterare aerem ipsorum, permitte eos vivere ;
si non, interfice omnes. O quam occultissima responsio est,
sed plena sapientiae potestate! Nam intellexit quod secun-
dum mutationem aeris, qui continet coelestes virtutes,
mutantur mores hominum ; eo quod alios mores habent
Gallici, alios Romani, alios Hispani, et sic de singulis regioni-
bus. Voluit ergo quod Alexander in bonum mutaret qualita-
tem aeris illarum gentium, ut secundum mutationem illam
mutarentur mores, et excitarentur ad honestatem morum sine
contradictione liberi arbitrii ; sicut quaelibet natio excitatur ad
proprios mores per aerem proprium habentem virtutes
stellarum quae sunt super capita hominum, et secundum quod
signa vel planetae dominantur singulis regionibus. Ostendo
enim in tractatu quem mitto !, quod induci potest aliquis ad
bonum et malum, tam publicum quam privatum, per virtutes
coelorum sine coactione, sicut exemplariter videmus quod
homines mutant suas voluntates per dominos, amicos, et socios,
et rerum praesentiam novarum, et infinitis modis sine
coactione. Quod satis explano in capitulo de potestate judi-
candi de rebus humanis per coelum, in quo capitulo est ratio

1 This does not refer to the treatise De Multiplicatione Specierum, several
times mentioned in the Opus Tertium as being sent together with the Opus
Majus. The subject of astrology is not dealt with there. The reference may
be to p. 251 ef seq. If so, the fact that the Opus Majus should be in this place
spoken of as a distinct work shows that the whole of this second treatment
of astrology would have been elaborated into a special treatise had opportunity
permitted.

Theo-
logians
avoid this
subject ;
fearing the
imputation
of magic.

394 OPERIS. MAJORIS PARS QUARTA.

omnium quae tanguntur de hac materia!. Philosophus igitur
voluit quod faceret opera sapientiae per debitas constella-
tiones ad modum Moysis, qui excitavit animam mulieris per
coelestes virtutes receptas in materia. Nam qua ratione
potuit illa mulier mutari ad castitatem et oblivionem viri per
imagines, potuit et ad alios mores moveri non solum ipsa, sed
quicunque. Ptolemaeus in nona propositione Centilogii docet,
quod vultus hujus seculi sunt subjecti vultibus coelestibus.
Et dicit Haly, quod in hoc capitulo vult Ptolemaeus imaginum
secreta patefacere. Et patet intentio eorum in universali,
quia si contingit temporibus electis eas sculpere ad vultus
coelorum, omnia nociva repelli possunt et utilia promoveri.
Thebit? inter omnes Christianos summus philosophus, qui in
multis addidit ad opera Ptolemaei et aliorum astronomorum
tam in speculativis quam in practicis, specialiter hanc scientiam
ampliavit, et alii sapientissimi super his insistebant.

Sed quia haec opera videntur vulgo studentium esse supra
humanum intellectum, quia vulgus cum suis doctoribus non
vacat operibus sapientiae, ideo vix est aliquis ausus loqui de
his operibus in publico. Statim enim vocantur magici, cum
tamen sint sapientissimi qui haec sciunt. Utique theologi et
decretistae non instructi in talibus, simulque videntes quod
mala possunt fieri sicut et bona, negligunt haec et abhorrent,
et computant inter magica. Vident enim quod magici et
abusores documentorum sapientiae his utuntur, et ideo
aestimant indigna Christianis. Sed non debet veritas damnari
pro ignorantia, nec utilitas pro malitia, quamvis eadem fieri
valeant ; nam tunc deberent homines.carere cultellis in mensa,
quoniam comedentes possunt interficere socios eodem ferro
quo scindunt cibaria, et tunc arma debent deleri ab ecclesia
et brachium seculare, quia multa mala possunt per haec fieri, et

! See pp. 246-53.

4 Thebit, or Thabit ben Corra ben Zahrun el Harrani was born a.p. 836, at
Harran in Mesopotamia, and died a.p. gor. Most of his life was spent at Bag-
dad. He was a friend of the great algebraist Mahommed ben Musa; and he
translated into Arabic the works of Archimedes, Apollonius, and Euclid ; also
the Physics and Analytics of Aristotle, and many of the works of Hippocrates
and Galen. He was not a Mahommedan ; but his Christianity is more than
doubtful.

A

ASTROLOGIA. 395

quotidie peraguntur. Et nihilominus jura debent esse in usu
bonorum hominum, quamvis per cavillationes et fraudes multi
juristae juribus abutuntur. Et nunc videmus quod plus est in
usu studentium quicquid de cavillationibus sit scriptum quam
verus usus demonstrationum ; non tamen propter hoc studium
sapientiae damnandum est. Nam semper mali in malis
convertuntur, ex quibus boni utilitates varias producunt.

Et cum opus animae rationalis praecipuum sit verbis uti
efficaciter et ex intentione formatis, potest astronomus formare
verba temporibus electis quae ineffabilem habebunt potestatem.
Nam ubi intentio desiderium et virtus animae rationalis, quae
dignior est stellis, concurrunt cum potestate coeli, necesse est
sive verbum sive aliud opus produci mirae virtutis in alteratione
rerum mundi hujus, ut non solum naturalia, sed animi
inclinentur ad ea quae velit sapiens operator, salva arbitrii
libertate, quia potest animus sequi coelestes virtutes gratis
sine coactione, ut tractatum est suo loco et declaratum.

Ex hac radice incepit apud sapientes usus characterum et
carminum. Nam characteres sunt sicut imagines, et carmina
sunt verba ex intentione animae rationalis prolata, virtutem
coeli in ipsa pronunciatione recipientia; unde de mira
potestate literarum ego facio mentionem in tertia parte!. Per
hanc enim potestatem sanantur corpora, fugantur animalia

venenosa, advocantur ad manum bruta quaecunque, et ser-

pentes de cavernis et pisces de profundis aquarum. Alteratur
enim mundi materia ad multas passiones mirabiles, si recte
fierent ista, et ideo contra malevolos homines et inimicos
reipublicae possunt mirabiliter valere, sicut et caetera opera
stellificata, ut oportet. Sed magici maledicti induxerunt
summam infamiam in hac parte, quum non solum in malis
abusi sunt characteribus et carminibus scriptis a sapientibus
contra nociva, et pro utilibus maximis, sed adjunxerunt men-
dosa carmina et characteres vanos et fraudulentos quibus
homines seducuntur. Insuper daemones temptaverunt multos
et tam mulieres quam daemones docuerunt multa super-
stitiosa, quibus omnis natio plena est. Nam ipsae vetulae
ubicunque faciunt characteres et carmina et conjurationes, ac

! See pp. 93-4.

Operative
force of
words and
written
characters.

396 OPERIS MAJORIS PARS QUARTA.

ipsi magici utuntur invocationibus daemonum et conjurationi-
bus eorum, et sacrificia eis faciunt. Sed haec omnia sunt
maledicta et extra vias philosophorum, immo contra sententias
eorum ; et per haec defamatur philosophiae potestas. Itaque
theologi nunc temporis et Gratianus et sancti plures multas
utiles et magnificas scientias reprobaverunt cum his magicis,
non attendentes differentiam inter magicam et philosophiae
veritatem propter causas quinque de quibus in prima parte
dictum est ; quod capitulum necessarium est omni homini ad
magnalia sapientiae aspiranti et volenti verum a falso separare.
Nam Gratianus, sicut multa scripsit jura quae nunc abrogata
sunt, sententia saniore praevalente, sic, cum de scientiis
locutus est, multa dixit quae debent in partem alteram
commutari, ut inferius abundantius explicabo.

In this Redeo igitur ad verba et opera sapientum, stellarum virtute

acüonupo" et animae rationalis potestate formata, reddens rationem in

nature the
mind co. summa de his secundum quod docuerunt sapientes. Sicut

operates . . .

with stellar €Dim puer natus, et aeri novo tanquam mundo recenti ex-

forces. ^ positus, recipit impressionem virtutum coelestium, a quibus
habet complexionem radicalem quam nunquam potest amittere,
quia quod nova testa capit, inveterata sapit; sic est de omni
re noviter facta, quae recipit virtutem coeli in prima ejus
existentia, et illam quam in principio recipit nunquam amittit
donec a suo esse naturali destituatur et corrumpatur. Et ideo
in istis imaginibus, carminibus, et characteribus, constellatione
debita compositis, recipiuntur virtutes stellarum et retinentur,
ut possint per eas agere in res hujus mundi, et recedente
constellatione, in qua fuerunt res hujusmodi compositae,
recedunt. Et quoniam anima rationalis dignior est stellis,
ideo sicut stellae et omnia faciunt virtutes suas et species in
rebus extra, de quibus speciebus et virtutibus scribo satis in
quarta parte, ubi de geometricis agitur, potest ergo anima
rationalis, quae est substantia maxime activa inter omnia post
Deum et angelos, facere et facit continue speciem suam et
virtutem in corpus, cujus est actus, et in res extra ; et maxime
quum ex forti desiderio et intentione certa et confidentia
magna operatur. De quibus operibus Avicenna in sexto Natu-
ralium potenter eloquitur. Et ideo hujusmodi opera et verba

ASTROLOGIA. 397

de quibus loquor non solum recipiunt virtutem a coelo, sed ab
anima rationali, quae est nobilior, et propter hoc possunt
habere magnam virtutem alterandi res mundi hujus.

Et si dicatur, quod sicut hujusmodi opera recipiunt virtutem Objection.
coeli, sic alia omnia quae sunt in eadem regione, et in tempore
compositionis hujusmodi verborum et operum ; et ita omnia!
debent habere has virtutes, et homines, et boves, et equi, et
arbores, nam radii coelestis constellationis attingunt infinita in
eodem tempore; dicendum, quod non valet objectum, quia non Reply.
sunt res in eodem horizonte. Nam singula puncta terrae sunt
centra diversorum horizontum, ad quae coni diversarum
pyramidum virtutum coelestium veniunt, ut possint producere
herbas diversarum specierum in eadem particula terrae
minima, et gemellos in eadem matrice diversificare in com-
plexione et moribus, et in usu scientiarum, et linguarum, et
negotiorum, et caeteris omnibus; tum quia res aliae jam
factae prius ante compositionem imaginis, licet sint? cum illa,
tamen ab origine sua receperunt influentiam propriam
radicalem secundum quam operantur, et ideo virtus coeli ad
hanc horam, de qua loquimur, non habet effectum naturalem
in rebus hujusmodi prius factis, sicut habet in istis operibus et
verbis nunc de novo factis ; tum quia ab anima rationali non
sunt facta, aut non tunc ; aut si tunc, multa fiunt? ab homine
alia, non tamen ea intentione, nec desiderio, nec confidentia,
nec ordinantur ad hujusmodi actiones, et ideo hujusmodi aut
non habebunt virtutem alterandi, aut non ita notabiles
operationes. Si dicatur, quod saltem omnis res per virtutem Second
quam recipit in sua origine a coelesti constellatione, cum in Objection.
illa maneat complexio radicalis juxta fortitudinem constella-
tionis, alterabit res extra se et immutabit sensibiliter, et
maxime in novitate sua; et quod per processum temporis, per
continuas virtutes coelorum alias, remittatur et debilitetur
virtus prima paulatim donec deficiat ; dicendum est, quod hoc Repiy.
est verum, et secundum quod oriuntur tales res, fiunt aliquando

1 J. has, oma animalia: but ammala is omitted in O. and the sense is
improved by the omission.

3 J. fuit.

? J. has fuerint : but fiunt, the reading of O., is evidently better.

Fascina-
tion.

398 OPERIS MAJORIS PARS QUARTA.

magnae mutationes, licet non consideremus unde tales altera-
tiones contingunt, sicut accidit de cometis et aliquibus aliis.
Et iterum potest elici quid intelligendum est de fascinatione,
quae licet habeat verbum suspectum, et potest modo intelligi
ut vetulae sortilegae et magici considerant ; tamen certum est
quod multi homines sunt malae complexionis et corruptae
compositionis et infirmae, ita quod contagiosi sint, sicut
homines infirmi multis morbis contagiosis. Et praecipue accidit
complexioni hujusmodi virtus infectiva et contagiosa per
malam constellationem in qua conceptus est puer vel natus.
Nam a sanissimis parentibus et optimae complexionis
nascuntur infiniti qui sunt pessimae complexionis ; et isti, sicut
omnes res suam speciem et virtutem producentes, contaminant
res praesentes, maxime teneras aetate et complexione, et
praecipue per oculos; quia porosi sunt et rari, et exeunt
vapores et spiritus corrupti et inficiunt res. Unde Virgilius,
*Nescio quis teneros oculus mihi fascinat agnos! Sicut
mulier menstruosa, si aspiciat speculum novum et politum,
maculat ipsum nube sanguinea, ut Aristoteles dicit secundo de
Somno et Vigilia !, et experientia docet, et ita inficit alias res,
licet non ita appareat : et sic leprosi inficiunt. Ethaec omnia
naturalia sunt. Quod si ulterius aliqua anima maligna cogitet
fortiter de infectione alterius, atque ardenter desideret et
certitudinaliter intendat, atque vehementer consideret se
posse nocere, non est dubium quin natura obediet cogita-
tionibus animae, ut docet Avicenna octavo de Animalibus et
quarto de Anima, quatenus fortior sit multiplicatio speciei et
infectio violentior ; sicut si leprosus intendat desideret et con-
fidat multum nocere alicui quem odio habet, longe plus laedit
eum quam alium cui malum non cogitat. Omnis enim operatio
hominis est fortior et impetuosior, quando ad eam est multum
sollicitus et voluntarius, et fixo proposito firmat intentionem,
et sperat firmiter se posse consequi quod intendit. Nam
dicunt sapientes, quod sicut scammonea acuit medicinam et
dat ei vigorem, sic intentio et desiderium et confidentia se
habent in operibus humanis ; et adhuc non est magicum.
Nam Plinius docet septimo Naturalium, quod multi homines
1 See p. 142.

A—

"om

ASTROLOGIA. 399

sunt talis complexionis, qui alios inficiunt et laedunt ex sua The eye or
praesentia, et per visum et per verbum'. Nam quia verbum the Spoken
ab interioribus membris naturalibus generatur et formatur ex power for
cogitatione et sollicitudine, et delectatur homo in eo, et pro- good o
priissimum est instrumentum animae rationalis, ideo maximam
efficaciam habet inter omnia quae fiunt ab homine, praecipue
cum ex intentione certa, desiderio magno, et vehementi con-
fidentia profertur. Cujus signum est, quod omnia fere
miracula quae facta sunt per sanctos a principio fiebant per
virtutem verborum, unde in verbis summa est potestas, sicut
explicavi. Et si hujusmodi multiplicatio speciei et verbi
prolatio fiant in constellatione debita, necesse est quod
operatio valida consequatur; et in his omnibus nihil est
magicum vel insanum. Et si hoc vocetur fascinatio, nomen,
si volumus, possumus mutare. Sed res in nullo habet calum-
niam apud sapientes. Feci vero mentionem de fascinatione ? ;
sed hic uberius explicatur. . Sed quia magici et vetulae male-
dictae non considerant fascinationem per has vias, immo
asserunt alterationes subitas indifferenter fieri per homines
quoscunque, cum videtur res in mane vel sero, vel loquuntur
de illa, ideo vana est eorum sententia et a sapientibus
reprobata.

Non solum pro consideratione sapientiali haec scribo, sed
propter pericula quae contingunt et contingent Christianis
et ecclesiae Dei per infideles, et maxime per Antichristum,
quia ipse utetur potestate sapientiae, et omnia convertet in
malum. Et per hujusmodi verba et opera stellificanda, et
magno desiderio malignandi componenda cum intentione
certissima et confidentia vehementi, ipse infortunabit et
infascinabit non solum personas singulares, sed civitates et
regiones. Et per hanc viam magnificam faciet sine bello quid
volet, et obedient homines ei sicut bestiae, et faciet regna et
civitates pugnare ad invicem pro se, ut amici destruant amicos
suos, et sic de mundo faciet quod desiderabit.

Et sic poterunt Tartari et Saraceni facere. Nam constat, The
quod Tartari plus vacant astronomiae quam alii, eo quod ems «f
licet in multis nationibus sint astronomi sapientes, tamen dom may

! Plin. vii, 2. ? Cf. p. 143.

400 OPERIS MAJORIS PARS QUARTA.

avail them- principes reipublicae! non reguntur nisi per eos. Sed illi qui

selves of
this know-
ledge, to
our hurt.

sunt apud Tartaros sicut praelati apud nos, sunt astronomi.
Mangu Cham, imperator Tartarorum existens anno Domini
1253, quando dominus rex Franciae Lodovicus misit fratrem
Willielmum de ordine Minorum ad Tartaros, dixit Christianis
congregatis coram eo, praesente dicto fratre; *Nos habemus
legem a Deo per divinos nostros, et facimus omnia quae ipsi
dicunt. Et vos Christiani habetis legem a Deo per prophetas,
sed non facitis eam.’ Hoc dixit, quia in oriente sunt mali
Christiani, ut Nestoriani et alii multi, qui non vivunt bene
secundum legem Christi. Et ille frater scripsit domino regi,
quod si parum scivisset de astris, ipse fuisset bene receptus
apud eos; sed quia nescivit terminos astronomiae, ideo
despexerunt eum. Et ideo Tartari procedunt in omnibus
per viam astronomiae, et in praevisione futurorum et in operi-
bus sapientiae. Cujus signum est evidens, quod cum sit gens
habens parvos et debiles homines, et quasi non comedentes
nec bibentes quod naturam confortet, et nihil pedibus valentes,
et inermes si proprie loquamur, nisi quod habent sagittas ad
terrorem quibus persequantur fugientes, nec unquam de prope
confligunt potestate bellandi, ut acies contra acies ordinentur,
cum jam totam latitudinem mundi prostraverunt ab aquilone
ad orientem, et ab oriente usque ad meridiem, solum eis
deficiunt duo anguli terrae Christianorum, scilicet Aegyptus
et Africa. Nisi enim Dominus reprimeret eos et permitteret
seminari discordias inter eos frequentes, jam totum mundum
occupassent. Et ideo oportet quod per opera sapientiae
procedant magnifica quibus mundum conculcant. Nam narrat
dictus frater in libro suo de moribus Tartarorum quem Domino

1 Principes et respublicae, J. The report of William Rubruquis, already
referred to, contains (p. 362) a full account of the Mongol diviners. ‘Ipsi sunt
multi et semper habent unum capitaneum tanquam pontificem qui semper
collocat domum suam ante majorem domum ipsius Mangu Cham... Istorum
aliqui sciunt de astronomia, maxime iste princeps, et praedicant eis eclipsim solis
et lunae ... Praedicant dies festos vel infestos ad omnia negotia agenda ; unde
nunquam faciunt exercitum nec ineunt bellum sine dicto eorum. Mangu, in his
interviews with Rubruquis, frequently dwelt on the inconsistency of Christians
with their principles. * Vobis,’ he said * dedit Deus scripturas, et non custoditis
eas; nobis autem dedit divinatores, et nos facimus quod ipsi dicunt nobis, et
vivimus in pace' (pp. 359-60).

ASTROLOGIA. 401

regi transmisit, quod quatuordecim millia Tartarorum devi-
cerunt Soldanum Turkiae, qui habuit secum ducentos millia
equitum sine peditibus. Sed hoc facere non poterant per
potentiam bellandi, ut planum est, et ideo per opera sapientiae,
et maxime per astronomiam, qua profitentur se regi et duci
in omnibus. Similiter Saraceni multum utuntur astronomia,
et sciunt sapientes inter eos facere haec opera. Et timendum
est valde quod Tartari et Saraceni in suis regionibus com-
morantes ad Christianos mittant homines, quibus opera
astronomiae conficiant ad infortunandum et ad ponendum
discordias inter principes, quia ad hoc maxime nituntur
inimici Christianorum, ut ponant inter eos bella et discordias.

Nam multa facta sunt hujusmodi, licet multitudo stulta Proofs of
non consideret unde accidant. Forsan vidistis aut audistis this danger
pro certo quod pueri de regno Franciae semel occurrebant in wanting.
infinita multitudine post quendam malignum hominem, ita
quod nec a patribus nec a matribus nec amicis poterant
detineri, et positi sunt in navibus et Saracenis venditi; et
non sunt adhuc quatuor et sexaginta anni!. Similiter in
temporibus nostris magister Pastor totam Alemanniam et
Franciam commgyit, et cucurrit post eum multitudo hominum,
et gratiam habuit coram toto vulgo laicorum in contemptu
cleri et ecclesiae confusionem. Et dixit Dominae Blanchiae,
quod iret ad filium suum ultra mare, talibus verbis sapientis-
simam mulierem decipiens. Non dubitent sapientes, quin ipsi
fuerunt nuntii Tartarorum aut Saracenorum, et quin habuerunt
aliqua opera unde fascinabant plebem. Et vidi cum oculis
meis portare patenter in manu sua quiddam tanquam esset res

! Matthew Paris relates this under the year 1213, 54 years before Bacon
wrote. The Shepherd, or leader of shepherds. of whom Bacon goes on to
speak was, according to Matthew Paris, a renegade Hungarian, who, in 1251
gathered round him troops of shepherds and other poor people offering to lead
them to the Holy Land, professing to have a mandate for that purpose from
the Virgin. * Addidit fidem dictis suis eloquentia et manus suae indissolubilis
clausura, in qua se mentitus est beatae Virginis habuisse chartulam et mandatum."
He seems to have imposed upon Blanche the queen-regent, until a disorderly
attack made by the leader and his followers upon Orleans undeceived those
who had previously trusted him. Thisimpostor had two successors. Matthew
Paris thought, like Bacon, that they were emissaries from the Mahommedan
camp.

VOL. I. Dd

oh AN" NEGO. een

Papal
authority
may react

inst
these dan-
gers.

402 OPERIS MAJORIS PARS QUARTA.

sacra, ac si homo deferret reliquias, et ivit nudis pedibus, et
erat circa eum multitudo armatorum, ita tamen dispersa in
campis, quod ab omnibus occurrentibus potuit videri cum illo
quod portabat in manu cum magna ostentatione.

Quicquid sit de Tartaris et Saracenis, certum est de
Antichristo et suis, quod haec operabuntur. Et nisi ecclesia
occurrat per sancta consilia ad impediendum et destruendum
opera hujusmodi, aggravabitur intolerabiliter flagellis Chris-
tianorum. Et creditur ab omnibus sapientibus quod non
sumus multum remoti a temporibus Antichristi, sicut in
capitulo de sectis per astronomiam in uno revolutis patet.
Si igitur Christiani scirent haec opera auctoritate papali
facienda ad impedienda mala Christianorum, satis esset
laudabile, et non solum propter mala repellenda, sed ad
promotionem quorumcunque utilium. Et quia personae, et
civitates, et regiones secundum praedicta possunt alterari in
melius, et ut vita quantum sufficit prolongetur, et omnes res
utiliter procurari, atque multo majora fieri, quam praesenti
scripturae debeant commendari, non solum in naturalibus, sed
in moralibus scientiis et artibus, sicut patuit per Moysen et
Aristotelem. Et haec praecipue fieri possunt, quando cum
virtute et specie coeli currit a parte operantis species et virtus
animae rationalis, quae est dignior coelo, ita ut adsit fortis
cogitatio, et ardens desiderium, certa intentio et plena confi-
dentia, et maxime sanctitas vitae; et quia natura obedit
cogitationibus et affectibus animae, et maxime sanctitati.
Nam octavo de Animalibus Avicenna ponit exemplum de
gallina strenua, quae vicit gallum unum miserum, et ex gloria
victoriae statim crevit ei cornu in crure, et dicit ibi Avicenna,
in hoc cognoscimus quod natura obedit cogitationibus animae
sensitivae. Et ponit exemplum in quarto de Anima, de eo qui
ligno posito super aquam ambulans cadit, quia cogitat de casu
et desperans est, et natura obedit cogitationibus et affectibus
animae; unde ait, quod provenit “calor non ex calore, et
frigus non ex frigore, sed ex.sola animae cogitatione et sic
fit infirmitas, et omnis alteratio proprii corporis. Et pro-
culdubio multa fieri possunt in corpore alieno; quia quoddam
genus luporum est, quod reddit hominem raucum, si primo

ASTROLOGIA. 403

aspiciat eum, ut vulgatum est apud auctores. Et multo fortius
anima rationalis potest propter nobilitatem suae speciei multa
immutare cum quinque conditionibus supradictis, et maxime
cum sanctitate, quia nobilior est sanctitas quam cogitatio vel
desiderium, et ideo animae sanctae plus obediet materia
mundi quam aliis quatuor conditionibus. Et hoc videmus
adimpleri in sanctis qui fecerunt miracula, quibus elementa
mundi obediebant. Et Avicenna quarto de Anima docet, quod
anima sancta et munda a peccatis potest universale et
elementa alterare, ut ejus virtute fiant pluvia, tempestates,
et omnes alterationes corporum mundi. Verum est autem
quod gratia Dei multum facit, sed anima sancta cooperatur
gratiae gratum facienti, ut non salvetur homo per solam
gratiam, sed oportet animam cooperari gratiae tali; multo
ergo fortius poterit cooperari gratiae gratis datae quae est
gratia miraculorum. Sed in aliis mirabilibus melius est
cogitare quam scribere, donec apostolica auctoritate requi-
ratur major certitudo, et haec possibilia sunt. Et si vos et
successores Vestrae Beatitudinis velint, poterunt omnia adim-
pleri. Hae sunt radices in summa tractatus, quem proposui
de hujusmodi conscribere ; sed propter impedimenta non
potui plura scribere !.

! With regard to the influence of the Moon on human action, on which so
much has been said in the foregoing pages, the following extract from Bacon's
Commentary on the Secretum Secretorum (Tanner MSS. 116, fol. 86), may be
of interest. It represents Lunar action as modified by each of the planets,
under various aspects.

DE ASPECTU LUNAE AD PLANETAS.

SEXTILIS TRINUS QUADRATUS
ASPECTUS ASPECTUS ASPECTUS OPPosrTIo | Coxjuscrio
VENUS Dieslaudabilis| Dies Dies laudabilis. Dies landabilis. Dies laudabilis, | Dies laudabilis
jungi . juvenibus| Bonum est indui | Bonum estemere | bonum — emere; omnibus operi-

MERCURIUS

et mihtibus et
quaerere dilec-
tionem et orna-
mentum.

Dies laudabilis.
Bonum est in ea
computare scri-
bere et jungi
consulibus et
scriptoribus et
disponere opera.

novis vestibus,
ornari et nubere
et omne orna-
mentum uae-
rere causa dilec-
tionis.

Dies laudabilis.

Bonum jungi
scriptoribus, fir-
mare — pactum,
jungi consulibus,
et disponere
opera.

servos et indui serv

novis vestibus,
adducerc opera-

rios, ornan or- |

namentis, uti
balneis, et delec- |
tari.

Dies laudabilis.
Bonum mittere
cartulas,tractare
de scripturis, se-
dere cum sapien-
tibus, et his simi-
libus.

OS, indui bus et peregri-
novis vestibus, | nationi, uti mili-
uti medicamini- | tibus, emere sub-
bus digestivis, si tilia, et peter-
in scorpione op- | uxorem.

ponitur.

Dies mediocris; Dies landabilis.
in conventione! Bonum — jungi
scriptorum, re-|scriptoribus — et
‘gum, et borum computatoribus,
similium. et agere omnia

opera.

~ —— ————— —-

404.

SATURNUS

JUPITER

MARS

SOL

SEXTILIS
ASPECTUS

Dies fortunata;
bonum est vir-
inibus consuli-
us et senibus, et
agereres cum eis.

Dies laudabilis.
Bonum est jungi
justis judicibus
ct quaerere quod
jus est et lauda-

ile in omni
opere.
Dies laudabilis.

Bonum jungi du-
cibus et regibus,
disponere exer-|
citus, uti armis,
et tractare de!
bello.

Dies fortunata.
Bonum jungi
consulibus et se-
nibus, ac regibus
potestatibus prin-
cipibus et petere
principatum.

TRINUS
ASPECTUS

Dies laudabilis;
bonum est in ea
aedificare plan-
tare et res an.
tiquas agere.

Dies laudabilis
ad augenda justa
judicia et omnem

ustam = inquisi-
tionem et omne
opus bonum et
amicitiam secun-
dum Deum.

Dies laudabilis

fortunata.Bonum

jungi regibus et
eimnere bestias, et
tractare de beilo.

Dies laudabilis.
Bonum est in ea
jungi senibus et
regibus et colere
terras et dis-
ponere omnia
opera.

QUADRATUS
ASPECTUS

Dies timenda ;
cavendum est in
ea jungi regibus
et potentibus seu
divitibus omnino.

Dies laudabilis
ad justa agenda,
et inquisitionem
sapientiae, et
rem quam vult
occultari, et
maxime si fuerit
ipse occultatus
sub radiis solis.

Dies cavenda ;
non bonum jungi
ducibus et regi-
bus. Cavendum
in ea omne opus
in quo speratur
bonum.

Dies laudabilis

omni operi si
fuerit luna re-
cepta. Si non,

nullum bonum,
sed cavenda est
in omni opere.

-— — — — ek —- .-—

OPERIS MAJORIS PARS QUARTA.

OPPOSITIO

Dies cavenda
in omnibus operi.
bus et nullum in
ea est bonum
opus faciendum.

Dies laudabilis
in omnibus operi-
bus; bonum est

' junzi potentibus
et petere venta-
tem ct quod jus-
tum est.

Dies cavenda
in omnibus operi-
bus ; et in ea nul-
lum bonum est.

Dies cavenda
est in omnibus

operibus quia
nullum bonum
est iu ea.

ConjUNCTIO

Dies ista caven-
da est in omni-
bus et nullum
bonum est in ea.

Dies laudabilis
et propria in
minutione san.
guinis et medi-
caminibus et cae-
teris similibus.

Dies cavenda
in omnibus operi-
bus, quia nullum
bonum est in ea.

In hac die erit
luna sub radiis.
Nullum bonum
nisi in his quae
necesse sunt oc-
cultari et con-

tegi.

4