Perspectiva. Book I

339 Pages·1977·14.477 MB·English

by  WITELO, S. Unguru (ed.)

POLISH ACADEMY OF SCIENCES
TIIE INSTITUTE FOR THE HISTORY OF SCIENCE,
EDUCATION AND TECHNOLOGY
WITELONIS PERSPECT1VAE
LIBER PRIMUS
BOOK I OF WITELO’S PERSPECTIVA
* AN ENGLISH TRANSLATION WITH INTRODUCTION
AND COMMENTARY
and
LATIN EDITION
of
THE MATHEMATICAL BOOK OF WITELO’S PERSPECTIVA
by
SABETAI UNGURU
I
f
i
i
WROCLAW • WARSZAWA ‘ KRAKOW ■ GDANSK
OSSOLINEUM
THE POLISH ACADEMY OF SCIENCES PRESS
1977
0
EDITORIAL COMMITTEE
MARIAN BISKUP, JERZY BUKOWSKJ,
PAWEJL CZA RTORYSKJ (editor in chief), JERZY DOBRZYCKI,
KAROL G6RSKI, BOGUS4.AW LESNODORSKI, BOGDAN SUCHODOLSKl
EDITORS OF THE VOLUME
PAWf.I. CZAJRTORYSKI, JERZY BURCTHARDT, ANNA SI.OMCZYNSKA
File cover and cover designed bjr
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Cerm it ISO.—■
1
Table of Contents
Foreword (by Pawel Czartoryski) ................................................................................................ 7
Preface ................................................................................................................................ . . . , 9
I. Introduction.............................................................................................................................. 12
1. Life and Works of Witelo ........................................................................................... J2
2. The First Book of Witelo’s Perspectiva and the Mathematics of the Second Half
of the Thirteenth Century .............................................................................................. 26
3. Manuscripts and Printed Editions ................................................................................... 40
4. Textual Procedures . ........................................................................................................... 43
II. English Translation....................... . . . ............................................................................ 47
III. Notes and Commentaries........................................................................................................168
IV. Latin Text and Variant Readings ........................................................................................215
V. Bibliography........................................ ..................................................................................317
Polish Summary (by Jtrzy Burchardt) ............................................................................................325
Index of Names..........................................................................* , , ...............................................328
List of Plates ....................................................................................................................................331
7
FOREWORD
The present volume of “Studia Copernicam” contains an English translation
of the mathematical book of Witelo’s “Perspectiva” with an Introduction»a Commentary,
and an Edition of the original Latin Text prepared by Sabetai Unguru, professor of
the history of science at the University of Oklahoma, Norman, U.S.A,
We are happy to publish this first modern edition of a part of Witch's lengthy
treatise. ft is worth mentioning that the importance of the “Perspectiva” for the deve­
lopment of the exact sciences in the Middle Ages and the Renaissance has recently
drawn the particular attention of American scholars. A facsimile reprint of Risner's
edition of the “Perspectivae* of Alhazen and Witeh with an introduction by David
C. Lindberg, as well as two important papers by the same author, one published in
“Speculum” (1971) and one in the “Dictionary of Scientific Biography”, vol. 14 (1976),
should be mentioned here. Likewise, cases in point for this renewed interest in Witelo
are S. Unguru’s recent articles in “ISIS. Archive for History of Exact Sciences”,
and the forthcoming article on Witelo in the (tEncic1opedia Biogrqfica degfi Inventori
e degli ScienziatiPerhaps it is not a mere coincidence that in the same period Eugenia
Paschetto from Torino and Jerzy Burchardt from Wroclaw have been working on
Witelo’s treatise t(De causa primariapoenitentiae in hvminibuset denatura daemonum”,
which we hope to publish in one of the forthcoming volumes of **Studia Copernicam'*.
The research mentioned above seems to form, after a break of forty years, a new
and important stage in the “studies on WiteloFor, in the early twenties, previous
relevant results were achieved by Aleksander Birkenmajer in his “Etudes sur Witelo”,
now available again in volume IV (1972) of “Studia Copernicana,\ pp. 97—434.
Previous stages of scholarly interest in Witelo were marked by Clemens Baeumker’s
monograph of 1908 and. as far back as the sixteenth century, by Risner's important
notes in his edition, now reproduced in a facsimile version. It is hoped that the present
publication of a crucial book of the “Perspectiva”, conforming to modem standards
of historical scholarship, will perform the function of a pilot study and help organize
and stimulate further work on a complete edition of this important source for the history
of science.
Thus, as a pilot study, the edition of the Latin text of Book I leads to important con-
.8
elusions concerning the manuscript tradition of Witelo's text and its relation to the
Risner edition. According to the present author’s opinion: “there are very few subs-
tantive differences between the readings and content of the various manuscripts’'’
(p. 42) and" ... it is certainly correct to say thatt in general, there are no substantive
differences of great import between Risner's edition and the manuscript tradition
as far as the first book is concerned” (p. 43).
The "modern” cftaracter of Sabetai Ungurus book ties mainly in his English
translation (which in itself is an “interpretation” of the medieval text) and,
first of all., in his “Notes and Commentaries” which include a detailed identification
of Witelo’s sources. It should be explained here, that Risner did not intend his citation s
as clear-cut identifications but rather as designations of authors who had dealt with
the same or similar propositions as Witelo did. Though nineteenth and twentieth cen­
tury scholars (Birkenmajer, Baeumker, etc.) repeated largely Risner's identifications
of Witelo's sources, none of them, however, including Risner, identified as many sources
as did Unguru, and most importantly, none of them analyzed in detail Witelo's in-
debtedness, proposition by proposition, to his precursors, both with respect to availa­
bility of sources in Latin and with respect to Witelo's mathematical understating.
Finally, Unguru's balanced view on the position of Witelo in the development
of medieval and early modern mathematics is based on a comprehensive and highly
exciting list of his readers and admirers through the ages, such as Nicole Oresme,
Johannes Regiomontanus* Leonardo da Vinci, Erasmus Re inhold, John Dee, Tycho
Brahe, Michael Maestlin, William Gilbert* Simon Stevin, Johannes Kepler, Thomas
Harriot, Rene Descartes, Galileo Galilei, Francesco Maria Grimaldi and Giovanni
Riccioli.
For Witelo's contribution to the development of mathematics consisted maitdy
in the fact that he was the only medieval scholar who stimulated the translation of
Greek mathematical texts into Ijitin in order to incorporate this rtew knowledge
in the first book of his “Perspectiva”. Only two centuries later, a similar initiative
taken, at the peak of the Renaissance, by Cardinal Bessarion.
This first-hand Greek heritage (among other things), made available in the pages
of the “Perspectiva"* explains why it re/mined a standard reference book until the
limes of Copernicus, Kepler, and Newton. Convincing evidence of this important
tine of tradition is provided by Sabetai Unguru's study.
Pawel Czartoryski
1
To Yochi, Michal, and Yoram, who suffered the
brunt of the (tool) long “creative processes'* begetting
this uson of old age", a highly unsuitable offering.
PREFACE
Witelo, a natural philosopher and perspectivist of the second half of the Xlllth
century, wrote in the 1270's an extensive optical treatise, Perspectiva, in ten books,
the first of which is exclusively mathematical in character, including the mathematics
deemed necessary in the development of the remaining nine books. The whole work
is patterned after Ibn-al-Haitham’s Perspectiva, from which Witelo appropriated
many propositions and their proofs, sometimes verbatim but usually adding to the
number of words used. The Mathematical Book, however, is nonexistent in Alhazen,
and its composition and the place it occupies in Witelo’s Perspectiva indicate the
systematic and didactic approach of our author.
The period during which the Perspectiva was written was one of stark sterility
in the development of mathematics, an interregnum preceded by the earliest inde­
pendent medieval contributions to mathematics in the West, made by Leonardo
Ftbonnaci and Jordanus Nemorarius and succeeded by another remarkable period
in the second quarter of the fourteenth century, when the application of mathematics
to physics led to the development of the concept of function and to the first appearance
of infinite series at the universities of Paris and Oxford.
A mathematical work written during such a barren period in the history of
mathematics should be a good indicator of the extent and depth of mathematical
knowledge at the time and of the sources of this knowledge. This is indeed the case
with Book I of the Perspectiva. It contains sixteen definitions, five postulates, and
137 propositions. Knowledge of the Elements is taken for granted; moreover, Witelo
envisaged his first book as supplementing Euclid’s Elements with additional mathema­
tical propositions lacking in the latter but required in matters optical. Such pro­
positions Witelo compiled from all the sources available to him although the only
mathematicians he mentioned by name were Euclid and Apollonius. His other
sources, in addition to Alhazen, were Campanus of Novara’s and Theon’s recensions
of the Elements, Eutocius's Commentary on Archimedes’. On the Sphere and the
Cylinder, Pappus’s Mathematical Collection, Jordanus’s Geometria, Theon’s recen­
10
sion of Euclid’s Optics, Theodosius’s Sphaerics, and Serenus’s De Sectione Cylindri.
However, Witelo’s use of the mathematical knowledge of his predecessors betrays
the approach of the compiler, not of the crcator.
Witelo, though not primiarily a mathematician, undoubtedly deserves to be
included in historical accounts of the evolution of mathematics. Despite the primitive
character and chronic lack of rigor of his mathematics (which, after all, should
be expected), he displayed an uncommon knowledge and understanding of geometry
for the second half of the thirteenth century. Though essentially a compilation
from widely different sources, some of which Witelo was among the first to use,
the arrangement of those sources in Book I and their understanding are clearly Witelo’s
achievements. His erudition and interests, his drive to put to use all the information
he could gather, coupled with his talents of exposition, are also merits which explain
the great success of the Perspectiva as a whole. Finally the influence that the Perspecti­
va exerted during the coming three and a half centuries (becoming a significant
part of the university curriculum in the later Middle Ages) represents another very
important reason why Witelo is entitled to a place in histories of medieval mathema­
tics.
There is an acute need for a critical edition of all ten books comprising the Per­
spectiva. Risner’s edition of 1572, though essentially reliable, can hardly fulfill such
a need. This work constitutes a first step in this direction. In addition to an edition
and an English translation of Book I, it includes in its Notes and Commentaries
a close analysis of all 137 propositions included in that book with respect both
to mathematical content and rigor and to the sources employed by Witelo.
The writing of this study would not have been possible without the help, under­
standing, and support of many people. Foremost among them is David C. Lindberg,
Professor of the History of Science and Chairman of the Department of the History
of Science at the University of Wisconsin in Madison. It was he who introduced
me to the Perspectiva. Due to his critical judgement and historical acumen my work
has been spared many errors and it has benefited of many improvements. His friend­
ship and interest in my work have been of cardinal importance to me.
I also owe a debt of gratitude to Professors Robert Siegfried and Erwin Hiebert,
as well as to the Graduate School of the University of Wisconsin for its financial
support. Professors Mark M. Ingraham, Menahem Mansoor, and William D.
Stahlman have also been helpful at various times and in different respects during
the initial stages of this work. To all of them are extended my sincere thanks. Pro­
fessor Leon Zelby from the School of Engineering of the University of Oklahoma
has helped me with the translation of some Polish texts. I thank him for his efforts.
I would also like to thank Professor Pa wet Czartoryski, Editor in chief of Studia
Copernicana, for his very helpful editorial comments. 1 have also benefited from
the comments of Dr. Jerzy Burchardt. Needless to say, I am the only one responsible
for any and all errors. In this connection, 1 can do no better than quote Dummett’s
words:
i
it
I will not indulge in the conventional fatuity of remarking that [others] are not responsible for
the errors this book may contain. Obviously, only I can be held responsible for these: but, if I toukl
recognize the errors, I should have removed them, and since I cannot. I am not in a position to
know whether any of them can be traced back to the opinions of those who have influenced me1.
S. V.
March 1975
University of Oklahoma
Norman
1 Michael A. Dummett, Frege; Philosophy of Language (New York, 1973), p. XII.
I. INTRODUCTION
I. LIFE AND WORKS OF WITELO*
Whatever is known about Witelo is ultimately drawn, by way of inference, from
his Perspective and Tractatus deprimaria causapenitentie et de nature demonum2, which
are his only extant works. From an analysis of the latter, where Witelo refers specifi­
cally to the time he spent in Paris and mentions the prophetic dreams he had there,
1 The standard secondary sources on the life and works of Witelo are: Alexander Btrken ma-
jer, "Witelo e lo studio di Padova”, Omaggiodell’ Aeeademia Polctcca di Scteme e Letiere air Uni~
versitd di Padova nelsettimo cewenario delta sua Fomtazione (Cracovia, 1922), pp. 147—168, Birken-
majer, „Studia nad Witel<mem’\ I, Archiwum Komisji do Badania Historii Filozofii w Polsce, vol,
2, pt. 1 (1921 >. pp. 1 149; Birkenmajer’s four “Etudes sur Witelo”, Bulletin international de
FAcademic polonaise des sciences et des let/res, (1918), pp. 4—6; (1920), pp. 354 — 360; (1922), pp.
6- 9; (the first two references represent "Etudes" IV and I. respectively); A. Birkenmajer, “Etude
sur Witelo. Partie III Bis", Bulletin inter national de P Academic polonaise des sciences et des ietttvs,
1926, pp. 5—10, reprinted in Aieksander Birkenmajer, Etudes tThistoire des sciences cn Poktgne
(Wroclaw, Warszawa, etc., 1972), pp. 408 - 412. This work represents vol. 4 in the series Studia
Copernicand and will be referred in the future as Stud Cop. 4. In this volume, pages 97—434 are
devoted to Witelo; Gemens Baeutnher, Witelo, ein Philosoph utid Naturforscher das XIII. Jahrhun-
derts(Beitrage 2ur Geschichie tier Philosophic des Minetalterst vol. 3, pt* 2 (Munster, 1908)), which,
notwithstanding its value should be used with great care, because of Baeumker’s attribution or
De intelligentiis to Witelo and the totally unwarranted conclusions Ke draws from I his mistaken
attribution; Baeum kcr’s “Zur Biographte des Philosophen und Nalurfor sellers Witelo", Historisches
Jahrhuch der Gvrres-Gesellsihaft, vol. 33 (1912), pp. 359—361; Maximilian Curtze*\ Sur I’orlho-
graphe du non) et sur la partie dc Witelo (Vileilion)”, Buflettino di bibtiogrejfia e di storia deft? scieme
maiematiche e fisiehe* vol. 4 (1871), pp. 49—77; Martin Grabmann, Gugiiebno di Moerbeke O. P.
it traduttore dette opere di Aristotek (Roma, f 946), pp. 56 60. The most recent and comprehensive
account, containing aJ! the information gathered from the above sources, can be found in the follo­
wing articles by D. C. Lind berg: Introduction to a facsimile reprint of the Risner edition of the
Per spec tivac of Alhazen and Witelo (New York and London: Johnson Reprint Corporation, 1972),
pp. V—XXXIX, the article on “Witelo”, Dictionary of Scientific Biography (vol 14, I976f, and
“Lines of Influence in Thirteenth-Century Optics: Bacon. Witelo. and Pec ham”, Speculum, vol.
46, no. 1 (1971), pp. 66- 83.1 had the privilege of using these works, on which I rely heavily, and
which, among them, answer the major questions concerning Witelo’s life and works.
2 Considered by Birkenmajer as two independent treatises, while Thorndike (which is dearly
correct as a glance at the MSS reveals) regards them as one treatise. (Cf. the first “Etude sur Witelo”,
"Witelo e Padova”, p. I4S. and L. Thorndike, A History of Magic and Experimental Science>
vol. 5 (New York, 1941), p„ 86; cf. also Bir kenmajer’s “Etude sur Witelo. Partie III Bis”. In the
“Etude 111 Bis”, Birkenmajer realized that De primaria causa penitentie in hominibus et de natura
demonum represents one treatise (cf. Stud. Cop. 4, p. 411)-
13
by means of which he was able to anticipate future events exactly and thus later
verify the accuracy of his dreams, Birkenmajer has reached the conclusion3 that
Witelo was in Paris in 1253, and participated in a nocturnal brawl between the
communal guard and the scholars, which marked the beginning of the University
rebellions that were to last until the end of 12594. "It was at Paris, then, and not at
Padua, that Witelo acquired his philosophical and mathematical training5”. Hence,
if Witelo was a student in the faculty of arts at Paris in 1253, his birth would most
likely fall around 1230—1235*.
After completing his studies at Paris, where he became acquainted with the
Platonic and Aristotelean systems, with the doctrines of Avicenna and Averroes,
and with Euclidean mathematics7, he returned to his homeland, Silesia, a province
of Poland. Witelo’s mixed national origins are revealed by his remark in the dedi­
catory epistle to William of Moerbeke, where he portrays himself as “filius Thuringo-
rum et PoIonorum”H, a remark which has been taken by the majority of scholars
to imply that his father was a Thuringian and his mother a Pole and not vice versa9.
One cannot totally dismiss the possibility that his grandfather had been among
those Thuringians who colonized Silesia in the Xllth century, but it is much more
probable, according to Baeumker, that his father came in the Xlllth century with
the greater wave of colonists from Thuringia who settled in Silesia10. Nothing else
is known about his family, except that he possibly was not the only son, as he addre­
sses his treatise On the primary cause of penitence and on the nature of demons to
his brother Louis11, and that his family was not, presumably, of aristocratic ex­
traction12.
3 “Witelo e Padova”, p. 148.
* Ibid., p. 144. In the above mentioned “Etude lit Bis", Birkenmajer modi6ed his earlier view
that the prophetic dreams of Witelo took place at Paris. His new conjecture was that Witelo’s dreams
happened perhaps at the parochial school in Legnica where Witelo allegedly taught (cf. Stud. Cop.
4, p. 410). Witelo’s stay in Paris, however, remains unaffected by this conjecture,
3 Ibid.: “A Parigr dunque, e non a Padova, il Witelo si procaccio la cultura filosofka e mate*
mat»ca”.
6 Cf. Lind berg's Introduction to the Risner edition (hereafter cited as Introd.) quoted above
in n. 1, p. IX.
7 Birkenmajer, loc. cii.
* Vitellonis Thuringopoloni Opticae Libri Decem, ed. F. Risner (Basel, 1572), p. I; future re­
ferences to this work will be made as follows: Risner, Witelo.
9 Risner, in his preface,-writes, “Ideoque in titulo optici opens cognominatur filius Polo-
norum et Thunngoriun, pat re videlicet Polono et matre Thuringa, aut contra procreatus" (p, I)!
It is clear that Risner interchanged the original order which appears not only in the MSS but also
in his own edition.
10 Baeumker, Witelo, p. 215; cf. also Lindbcrg, Introdp. X.
11 Thorndike, he. cit. Thorndike gives the incipit of MS Sloane 2156: “Domino et fratri
suo magistro Ludovico in Leweberi...” {ibid.). This, clearly, does not rule out the possibility that
the mentioned Louis was not Witelo’s Hoodbrother, but rather his spiritual, Christian brother.
(Cf. Jerzy Burchardt, „Zwiqzki Witelona z Wrodawiem”, Sobdtka, vol. 4 (1974), pp. 445—456),
11 Birkenmajer calls Witelo “il plebeo Witelo” (“Witelo e Padova”, p. 168), but he fails