Archimedes in the Middle Ages. II. The Translations from the Greek of William of Moerbeke. Parts i-ii.

393 Pages·1976·8.57 MB·English

by  Marshall Clagett

Memoirs of the
AMERICAN PHILOSOPHICAL SOCIETY
held at Philadelphia
for Promoting Useful Knowledge
Volume 117 Part A
A R C H I M E D E S
in the M iddle Ages
VOLUME TWO
THE TRANSLATIONS FROM THE GREEK
BY WILLIAM OF MOERBEKE
PART I: INTRODUCTION
PART II: TEXTS
MARSHALL CLAGETT
THE AMERICAN PHILOSOPHICAL SOCIETY
Independence Square
Philadelphia
Copyright © 1976 by The American Philosophical Society
Library of Congress Catalog Card Number 76-9435
International Standard Book Number 0-87169-117-5
US ISSN 0065-9738
To Harold Cherniss

\ ' Preface
Though Volume Two of my Archimedes in the Middle Ages has been
near completion for a number of years, I have held up its publication
until the completion of the third volume in an effort to correlate the
two volumes closely. In now publishing Volume Two (with Volume
Three soon to follow), I have been forced by the rising cost of publica­
tion to certain economies. Chief of these is the separation of the
diagrams from the Introduction and the Latin text of William of
Moerbeke’s translation (except for Fig. 2.2.1, which appears in place
on page 67). However, the diagrams are all carefully labeled and the
pages of the Introduction and Latin text on which they are mentioned
are indicated at the top of each page of diagrams. Hence the reader
should be able to locate the figures without undue difficulty. I have
also reluctantly agreed to the separation of the Variant Readings from
the Latin text. But the fact that the Variant Readings, Commentary
and Diagrams are bound separately in Part III should make easy the
simultaneous consultation of the separated material and the Latin
text.
I should also note that a considerable economy was achieved by the
preparation of the Greco-Latin Glossary and Index of Latin Terms
on an IBM typewriter. As the result of this, there are minor differ­
ences in the Greek fonts used on the one hand in the Introduction, Text
and Commentary and on the other in the Glossary and Index. Further,
the system of photo-compositing used in the Introduction-Text-Com­
mentary has significantly reduced the cost of publication. But it has
produced certain trivial infelicities. For example, it has forced the
use of a cedilla (instead of a reverse cedilla) to mark the e standing for ae
and the addition, by hand, of a number of signs that could have been
more aesthetically added by normal printing methods. Mrs. Carolyn
Brown of Tempa Communication Graphics in Princeton deserves
special thanks for her skill in solving many difficult printing problems.
A general bibliography that includes works used in both Volumes
Two and Three and several indexes that locate manuscripts, persons
and works treated in both volumes will be included in Volume Three.
Vll
/
As usual, I owe thanks to many individuals and institutions for help in
preparing and publishing these volumes. Dr. Lorenzo Minio-Paluello
of Oxford University kindly read the Introduction to Volume Two
and made many useful suggestions. My colleague Professor Harold
Cherniss, to whom I affectionately dedicate this volume, has been a
constant source of wisdom in matters Greek and otherwise. I have
had assistance in checking references and reading the successive type
scripts from a series of indefatigable research assistants: Drs. Jim Otte,
Bert Hansen, Joe Brown, and Charles Zuckerman. I owe particular
thanks to Hansen and Zuckerman for their contributions to the indexing
of Volumes Two and Three, and to Mrs. Ann Tobias for her expert
secretarial help over the many years during which the volumes have
been written and particularly for preparing the final form of the dia­
grams. And though the reading of proof is justly said to be thankless,
I nevertheless thank Mrs. Tobias, Dr. Zuckerman, and my wife Sue
for the many hours they have spent in such unrewarding toil.
Also noteworthy is the generous assistance I have obtained from the
principal European libraries that have allowed me to consult the large
number of texts cited in these volumes and that have supplied me with
films of countless manuscripts. I should single out for special thanks
the Bibliotheca Apostolica Vaticana, where I have again and again
consulted the autograph of William of Moerbeke’s translation of
Archimedes. Finally, I must thank the American Philosophical
Society for its help in publishing this volume and the Institute for
Advanced Study for providing the ideal home in which to write it and
the funds to complete its publication.
vm
Contents
Part I: Introduction to the Texts of William of Moerbeke’s Archimedean
Translations
Chap. 1: William of Moerbeke as the Translator of Archimedes
I. The Life and Scientific Activity of William of Moerbeke 3
II. The First Use of Moerbeke’s Archimedean Transla­
tions................................................................................ 13
III. William of Moerbeke and the Archimedean Transla­
tions................................................................................ 28
Chap. 2: The Text of William of Moerbeke’s Archimedean
Translations
I. The Greek Manuscripts Used by William of Moerbeke 54
II. William of Moerbeke’s Autograph (MS 0) and its
Derivatives.................................................................... 60
III. Textual Procedures......................................................... 73
Part II: The Texts of William of Moerbeke’s Archimedean Trans­
lations
1. Liber Archimedis de quam pluribus theorematibus ['de figuris
Aids'] (11vA-16vT).............................................................. 81
2. Liber Archimedis de centris gravium vel de planis eque re­
pentibus (17rA-20vD).......................................................... 115
3. Liber Archimedis qui dicitur quadratura parabole (20vE-
22vPI)............................................................... 141
4. ['Archimedis circuli dimensio'] (22vl-23rl)............................ 157
5. Liber ^Archimedis] de spera et cylindro (23vA-33vV)........... 161
6. Eutokii Ascalonite rememoracio in libros Archimedis de
spera et chylindro (34rA-44vP)............................................ 221
ix
/
7. Liber Archymedis de conoydalibus et speroydalibus (45rA-
52vO)...................................................................................... 287
8. Euthocii Ascalonite rememoracio in libros Archymedis de
equerepentibus (53rA-55rW)................................................ 339
9. Liber Archimedis de insidentibus aque (55vA-60rA)............. 357
Part III: Variant Readings, Commentary, Diagrams and Indexes
Variant Readings........................................................................... 385
Commentary................................................................................... 429
Diagrams......................................................................................... 589
Greco-Latin Glossary.................................................................... 641
Index of Latin Terms.................................................................... 657
x
Open qtMr in (jac tialuminr continantur ■
inbtllw <dt fprcrdis cpmpvrfnhlnis
•
Sirtf M.lbrv folio prnm-
- Xibtllns de ■hitRSitn: pondnn >n 'tigda dafutptnr
t j fvnr- cMirt •
htcqvmtdu dr Vo 'txvquy y(a falter: wear.*
- •
Arc^mtdis dr flaws cqttnrfmVttff ji»t~
Crntrngwmttn libri duo ■ ■ is ■
Arthimtdf QMimtursi parnealV- . ijr~
fadimtM drntli mmfrmtio ■ . tf-
- Avcfavridu dt-ffltt* n Cylmdtalifai duo-1£~.
• JLtittci/ Afiglmkcr cormntnmrtj in
otefamtdii h(>7?r dr fp far it ft cylindro- X7-
Arcfavitdrs cfr COUPt’dituf cr
Sffancudibcf ■ -Si-
T-utceu Afcnlsmu*t-zovnnmtflrta wltbrofAr ■
ctfamtdi's dr firms eqti*rrfmttl> ns -imr- c entris
jrrwwm ■
kxdnimtdis d( rnpdtnttbvs libri dtw ■' 4>&~ ■
■ (fal/wdijfttltvm fpttidmt ,/j,
rijftoltrr.ii lib*r cir findrrr.nuitr. .//.
\
lXite I: MS 0, folio 7b verso.