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SMITH, Albert Mark, III, 1942-
WITELO ON THE PRINCIPLES OF REFLECTION: A CRITICAL
EDITION AND ENGLISH TRANSLATION, WITH NOTES AND
COMMENTARY, OF BOOK V OF WITELO'S PERSPECTIVA
The University of Wisconsin-Madison, Ph.D., 1976
History, medieval
Xerox University Microfilms, Ann Arbor, Michigan
(c) Albert Mark Smith. III. 1976
All Rights Reserved
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UNIVERSITY MICROFILMS
WITELO ON THE PRINCIPLES OF REFLECTION
A Critical Edition and English
Translation, with Notes and
Commentary, of Book V of
Witelo's Perspectiva
A thesis submitted to the Graduate School of the
University of Wisconsin-Madison in partial fulfillment of
the requirements for the degree of Doctor of Philosophy
BY
ALBERT MARK SKITH %£?
Degree to be awarded: December 19 May 19_ August 19 76
Approved! by Thesis Reading Committee:
Major Professor Date of Examination
<%»>?ut \c_-/U_ /ft-<n^y^
Deani, Graduate School
WITELO ON THE PRINCIPLES OF REFLECTION
A Critical Edition and English
Translation, with Notes and
Commentary, of Book V of
Witelo's Perspectiva
BY
jrC
ALBERT MARK SMITH
A thesis submitted in partial fulfillment of the
requirements for the degree of
DOCTOR OF PHILOSOPHY
(History and History of Science)
at the
UNIVERSITY OF WISCONSIN-MADISON
1976
To my parents,
who bore with me for so long.
iii
CONTENTS
Chapter Page
I. INTRODUCTION 1
Witelo's Life 2
The Origins of the Science of Perspectiva 10
Format and Methodological Approach
in the Perspectiva 32
The Sources for Book V 55
Witelo's Theory of Light and Vision 60
Conclusion 74
II. MANUSCRIPTS AND EDITING PROCEDURES 86
Manuscript Sources 87
Editing Methods 94
Editing Procedures 98
Conclusions 103
Critical Text and Translation 105
Notes on the Critical Apparatus 107
III. CRITICAL TEXT—BOOK V OF WITELO'S PERSPECTIVA 110
Prohemio Ill
Diffinitiones 112
Petitiones 114
Theoremata 115
IV. ENGLISH TRANSLATION—BOOK V OF WITELO'S PERSPECTIVA . .. 231
Prologue 232
Definitions 233
Postulates 236
Theorems 236
V. NOTES AND COMMENTARY 358
VI. VARIANT READINGS 446
BIBLIOGRAPHY 484
iv
ACKNOWLEDGMENTS
My first expression of gratitude goes by rights to Professor
David Lindberg whose confidence in me gave me confidence in myself;
I am very much in his debt both for his generosity in allowing me free
and easy access to his microfilm collection and for his balanced
supervision, which was necessarily close yet surprisingly and
satisfyingly unconfining. Thanks too to Professor William Courtenay
who, perhaps unknowingly, first steered me into serious study of
medieval history and whose advice on manuscript editing proved to be
very helpful in this thesis.
On a more pragmatic level I can hardly ignore the kindness
and good humor of my typist, Mrs. Jeanne Zwaska, whose proprietary
interest in this dissertation has far surpassed my own. Indeed, I
cannot begin to guess how much time and trauma her intelligent
editing, punctilio, and patience have saved me in the final composi
tion of this thesis.
Finally, how can I properly express my gratitude to Katherine
Tachau-Auerbach, who filled so many functions from sounding-board to
general editor so selflessly? I hesitate to list her contributions
lest I force myself into acknowledging her as co-author. But suffice
it to say that her grasp of paleography and Latin, as well as her
quick wit, has made its mark in many ways upon this thesis. Yet more
important, her patience and fidelity as a simple friend have helped
make this year of intellectual demands and drudgery far more bearable.
CHAPTER I
INTRODUCTION
2
Witelo's Life
i
What little we know about Witelox has been gleaned primarily
from a handful of geographical and chronological clues scattered
hia ximilien Curtze, "Sur l'orthographe du nom et sur la patrie
de Witelo (Vitellion)," Bullettino di bibliografia e_ di storia delle
scienze matematiche e fisiche, vol. 4 (1871), pp. .49-77, has shown
that, despite the usual rendering of "Vitello" or "Vitellio" found in
later manuscripts and the early printed editions of the Perspectiva,
the proper spelling is "Witelo," which is the diminutive of the fairly
common thirteenth century Thuringian name "Wito" or "Wido."
The first truly comprehensive and critical modern study of
Witelo and his works was Clemens Baeumker's Witelo, ein Philosoph und
Naturforscher des XIII. Jahrhunderts in Beitrage zur Geschichte der
Philosophie des Mittelalters, vol. 3, pt. 2 (Milnster, 1908), pp. 1-686.
Starting a decade later and over a span of four years, Alexander
Birkenmajer published his four "Etudes sur Witelo" in the Bulletin
international de l'Academie Polonaise des sciences et des lettres
(1918), pp. 4-6; (1920), pp. 354-360; (1922), pp. 6-9. During this
time he also published his "Witelo e lo studio di Padova" in Omaggio
dell'Accademia Polacca di Scienze e_ Lettere all'Universita di Padova
nel settimo centenario della sua fondazione (Cracovia, 1922), pp. 147-
168. These etudes, which are actually only abstracts, have been
gathered together with the original papers from which they were ab
stracted into one volume, Studia Copernicana, vol. 4 (Wrociaw, 1972),
pp. 256-434—henceforth I shall not refer to these etudes specifically,
but instead I shall cite the Studia, giving the appropriate page
number(s). This volume also includes an abridged edition of Witelo's
De natura demonum and De_ primaria causa penitentie (pp. 122-141).
Relying upon evidence that Baeumker did not possess, Birkenmajer
corrected some of Baeumker's chronological errors while disproving his
false assumption that Witelo was the author of the Neo-Platonic tract
De intelligentiis, ascribed by Birkenmajer to Adam Pulchre Mulieris,
who purportedly wrote it sometime between 1220 and 1230. This false
assumption, in fact, invalidated much of Baeumker's subsequent analysis
of Witelo's philosophy.
Although Birkenmajer's work stands as the definitive modern
biography of Witelo, there are some additional useful sketches, the
best of which is undoubtedly D. C. Lindberg's introduction to the re
print of Frederick Risner's 1572 edition of the Opticae thesaurus
(Johnson Reprint Corp., N.Y., 1972), pp. vli-xiii. The biographical
details of this introduction have been greatly abridged in Lindberg's
forthcoming article on Witelo in the Dictionary of Scientific Biography.
There is also a good outline of Witelo's life in Sabetai Unguru's
"Witelo as a Mathematician: A Study in Xlllth Century Mathematics,"
3
2
throughout the Perspectiva —for example, the reference to "nostra
3
terra, scilicet Poloniae," which, when complemented by a passage
4
suggesting more than passing familiarity with Silesia, hints strongly
at a Polish birthplace for Witelo, probably within the territorial
ambit of present-day Wroclaw. This implication is, of course, further
buttressed by Witelo's claim to Polish and Thuringian ancestry —a
Ph.D. dissertation, University of Wisconsin, 1970, pp. 1-23. Less
useful than these is Eva Tea's "Witelo, prospettico del secolo XIII,"
L'arte, vol. 30 (1927), pp. 3-30; and least useful, because of its
very limited topical range, is Baeumker's "Zur Biographie des Philo-
sophen und Naturforschers Witelo," Historisches Jahrbuch der Gorres-
Gesellschaft, vol. 33 (1912), pp. 359-361.
2
With the exception of references from book V itself, all
citations from Witelo's Perspectiva will be made from the reprint of
Risner's Opticae thesaurus. Citations from book V will always be made
from my critical text, pp. 111-230 of this dissertation.
3
Witelo, Perspectiva, book X, proposition 74, p. 467.
Henceforth, I shall omit "book" and "proposition" from such references
so that, for example, this citation would read X, 74.
4
Ibid., IV, 28. Risner rendered this passage in the following
way: "Et huius simile accidit iuxta civitatem Vratislaviae apud nemus
villae Boret . . . iuxta lignum et castrum Poloniae." Now, if "Boret"
is changed to "Borec" ("t" and "c" being virtually indistinguishable
in medieval Latin), and if "lignum" is rendered as "Ligniz" while "et"
is dropped (upon checking this passage in Cambridge, Emmanuel College,
MS 20, I find that it clearly does read "Ligniz castrum Poloniae"),
the sentence reads, "Et huius simile accidit iuxta civitatem Vratis
laviae apud nemus villae Borec . . . iuxta Ligniz, castrum Poloniae."
Actually, "Vratislavia" is the ancient city of Breslau, or present-
day Wroclaw; Liegnitz, which is present-day Legnica, does lie in the
near vicinity; and it is probable that a town named Borek (a variant on
"burg") did exist near Wroclaw during much of the middle ages. See
Baeumker, Witelo, pp. 204-213.
Witelo makes this claim in the dedicatory epistle to William of
Moerbekc (Perspectiva, p. 1): "Veritatis amntori fratri Guilielmo de
Moerbeca, Witelo fillus Thuringorum et Polonorum ..." (my emphasis).
4
claim moreover which, in view of the large influx of Thuringian
colonists to Poland In the thirteenth century, argues implicitly that
it was Witelo's mother who was Polish.
For all our reasonable certainty about Witelo's place of birth,
we are commensurately uncertain about the date, the one normally agreed
upon being based somewhat tenuously upon a possible allusion in the
De primaria causa pc-.itentie to the infamous contretemps between the
secular and mendicant faculty that disrupted the University of Paris in
the years between 1252 and 1259. That he did indeed attend the Univer
sity of Paris can be inferred from a p£issage in the De natura demonum
Q
alluding to his return to Poland from Paris, so it is reasonable to
assume that his purported knowledge of the protracted squabble was
firsthand. Hence, if Witelo matriculated at a normal age as an arts
9
student any time during this seven-year interval, his birthdate ought
to lie somewhere in the early 1230s.
See Birkenmajer, Studia, pp. 416-417. The rationale behind
this conclusion is undoubtedly that, assuming one of Witelo's parents
to have been a Thuringian colonist, it would have been far more likely
for that immigrant parent, especially if unmarried, to have been male
than female.
Ibid., p. 139, lines 104-105. Here Witelo claims that he had
a prophetic dream in which he saw "aquam loco turbationum molendum vero
loco scholarum." Birkenmajer's interpretation of this rather vague
passage as a direct reference to the troubles in Paris seems to me to
be highly forced. See Birkenmajer, Studia, p. 402.
o
Ibid., p. 127, line 169: "Et istud audivi in Polonia, cum de
Parisius rediissem."
9
Actually, if Birkenmajer is correct in his assumption that
Witelo's prophetic dream concerned the disturbance at Paris, then
Witelo must have entered the university by 1252 at the latest (if
indeed his dream was prophetic).
