Apollonius: Conics Books V to VII: The Arabic Translation of the Lost Greek Original in the Version of the Banū Mūsā

643 Pages·1990·25.02 MB·English

by  Gerald J. Toomer (auth.)

Sources
in the History of Mathematics and
Physical Sciences
9
Editor
G.1. Toomer
Advisory Board
R.P. Boas 1.Z. Buchwald P.l. Davis
T. Hawkins A.E. Shapiro D. Whiteside
Sources in the History of
Mathematics and Physical Sciences
Vol. I: G.J. Toomer (Ed.)
Diodes on Burning Mirrors: The Arabic Translation of the Lost Greek
Original, Edited, with English Translation and Commentary by G.J. Toomer
Vol. 2: A. Hermann, K.V. Meyenn, V.F. Weisskopf (Eds.)
Wolfgang Pauli: Scientific Correspondence I: 1919-1929
Vol. 3: J. Sesiano
Books IV to VII of Diophantus' Arithmetica: In the Arabic Translation
Attributed to Qusta ibn Liiqa
Vol. 4: P.J. Federico
Descartes on Polyhedra: A Study of the De Solidorum Elementi.\'
Vol. 5: O. Neugebauer
Astronomical Cuneiform Texts
Vol. 6: K. von Meyenn, A. Hermann, V.F. Weisskopf (Eds.)
Wolfgang Pauli: Scientific Correspondence II: 1930-1939
Vol. 7: J.P. Hogendijk
Ibn AI-Haytham's Completion of the Conics
Vol. 8: A. Jones
Pappus of Alexandria Book 7 of the Collection
Vol. 9: G.J. Toomer (Ed.)
Apollonius Conics Books V to VII: The Arabic Translation of the Lost
Greek Original in the Version of the Banii Miisa, Edited, with English
Translation and Commentary by G.J. Toomer
continued after index
Apollonius
Conics
Books V to VII
The Arabic Translation of the
Lost Greek Original
in the Version of the Banii Miisa
Volume I: Introduction, Text, and Translation
Edited
with Translation and Commentary by
G.J. Toomer
In Two Volumes
With 288 Figures
Springer-Verlag
New York Berlin Heidelberg
London Paris Tokyo Hong Kong
Gerald J. Toomer
History of Mathematics Department
Brown University
Providence, Rhode Island 02912, USA
Library of Congress Cataloging-in-Publication Data
Apollonius, of Perga.
[Kiinika. Book 5-7. English)
Conics, books V to VII : the Arabic translation of the lost Greek
original in the version of the Banu Musa i Apollonius ; edited with
translation and commentary by GJ. Toomer.
p. cm. - (Sources in the history of mathematics and physical
sciences ; 9)
Includes bibliographical references.
ISBN-13:978-1-4613-8987-3 (alk. paper)
1. Mathematics, Greek. 2. Conic sections. 3. Apollonius, of
Perga. Konika. Book 5-7. English. I. Toomer, G. J. II. Title.
III. Title: Apollonius, Conics, books V to VII. IV. Title: Conics,
books 5 to 7. V Seties.
QA31.A5 1990
516 -dc20 89-26277
Printed on acid-free paper.
© 1990 by Springer-Verlag New York Inc.
Softcover reprint of t.he hardcover 1st edition 1990
All rights reserved. This work may not be translated or copied in whole or in part without the written permIs
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and Merchandise Marks Act, may accordingly be used freely by anyone.
Camera-ready text supplied by the author
987 6 5 4 ) 2 I
ISBN -13:978-1-4613-8987-3 e-ISBN -13:978-1-4613-8985-9
DOl: 10.1007/978-1-4613-8985-9
VXORI CARISSIMIE
JANET
Prima dicta mihi, summa dicenda Camena
APOLLONII Conica legat. Videbit, esse quasdam materias, quae
nulla ingenii felicitate ita tradi possint, ut cursoria lectione com
prehendantur. Meditatione opus est, et creberrima ruminatione
dictorum.
Kepler, Astronomia Nova, p. 376
Preface
With the publication of this book I discharge a debt which our era has
long owed to the memory of a great mathematician of antiquity: to pub
lish the /llost books" of the Conics of Apollonius in the form which is the
closest we have to the original, the Arabic version of the Banu Musil. Un
til now this has been accessible only in Halley's Latin translation of 1710
(and translations into other languages entirely dependent on that). While I
yield to none in my admiration for Halley's edition of the Conics, it is far
from satisfying the requirements of modern scholarship. In particular, it
does not contain the Arabic text. I hope that the present edition will not
only remedy those deficiencies, but will also serve as a foundation for the
study of the influence of the Conics in the medieval Islamic world.
I acknowledge with gratitude the help of a number of institutions and
people. The John Simon Guggenheim Memorial Foundation, by the award
of one of its Fellowships for 1985-86, enabled me to devote an unbroken
year to this project, and to consult essential material in the Bodleian Li
brary, Oxford, and the Bibliotheque Nationale, Paris. Corpus Christi Col
lege, Cambridge, appointed me to a Visiting Fellowship in Trinity Term,
1988, which allowed me to make good use of the rich resources of both
the University Library, Cambridge, and the Bodleian Library. I am also
grateful to the Curators of the latter institution for supplying photographs
of manuscripts in the library. Brown University has been generous in its
continuing support of my work. I am grateful to Springer-Verlag for {he
interest and care which it has devoted to this project. I thank Prof. A.
Aaboe, Dr. J. Hamadanizadeh, Dr. J.P. Hogendijk, my former pupil Dr. J.
Sesiano, Dr. J. van Maanen, and especially Prof. Dr. Fuat Sezgin, for their
help in obtaining reproductions of books and mss. which were rare or dif
ficult of access.
The typesetting of the whole book, with the exception of the make
up of the pages containing the figures, was done by me, using Macintosh
and IBM XT personal computers. In overcoming the numerous difficulties
arising from this I was aided by a number of experts. I wish particularly to
thank Jonathan Sachs, and my former pupil Dr. Alexander Jones, who
wrote the computer program "Euclid", which I used, in a modified form,
to draw the figures.
viii Preface
I wish to acknowledge a particular debt of gratitude to my former col
league, J.P. Hogendijk. He read the whole book in draft form, corrected a
number of errors, made several suggestions for improvement, and offered
some original contributions, which I have gladly incorporated. I need
hardly say that all remaining imperfections are solely my responsibility.
Above all, lowe more than I can say to my beloved wife, Janet Sachs
Toomer. Not only did she improve the book by her expert proof-reading,
but it is due to her unfailing enthusiasm, support and encouragement
that the whole project was begun and finished. I dedicate it to her as an
inadequate expression of my feelings.
Table of Contents
Volume!
Part 1
Introduction
§ 1 Apollonius: Life ....................................................................................... xi
§2 Works other than the Conics ................................................................ xii
§3 The Conics ............................................................................................ xiv
a. Composition and contents ............................................................. xiv
b. History after Apollonius ................................................................ xvi
i. In antiquity ............................................................................. xvi
ii. In the Islamic world ............................................................. xvii
iii. In the medieval west ........................................................... xix
iv. In the Renaissance ................................................................. xx
c. Recovery of the later books in Europe .......................................... xxi
d. Modern editions and translations of the Conics .......................... xxv
§4 Mathematical Summary ................................................................... xxviii
a. Generation of conic sections before Apollonius ....................... xxviii
b. Apollonius' method of generating the sections .......................... xxix
c. Propositions from Conics I and II used in Books V-VII .............. xxxi
d. Book V ....................................................................................... xxxviii
e. Book VI. ............................................................................................ lxi
f. Book VII .......................................................................................... lxix
§5 The Ancient Mathematical Background .......................................... lxxxi
a. "Geometrical algebra" ............................................................... lxxxii
b. Ratios ........................................................................................ lxxxiv
c. Analysis, synthesis and determination .................................... lxxxiv
§6 Descriptions of Manuscripts ............................................................ lxxxv
§7 Editorial Principles ................................................................................. xc
a. The text. ............................................................................................ xc
b. The translation ................................................................................ xci
c. The figures ..................................................................................... xciv
d. The notes ....................................................................................... xciv
e. The appendices ............................................................................... xcv
f. The indexes ..................................................................................... xcv
x Table of Contents
Part 2
Conics: Text and Translation
Book V .......................................................................................................... 2
Book VI ..................................................................................................... 262
Book VII .................................................................................................... 382
Volume!!
Part 3
Notes on theText and Translation
Notes on Book V ........................................................................................ 551
Notes on Book VI ....................................................................................... 576
Notes on Book VII ...................................................................................... 595
Part 4
Appendices
Appendix A: Preface to the Conics of the Banu Musa ............................. 619
Appendix B: Premisses of the Banu Mus:! ................................................ 631
Appendix C: Premisses of aI-Shirazi ......................................................... 651
Appendix D: Huygens' solution of the problem of Pappus IV 30 ............ 659
Part 5
Figures
Figures to the Introduction ........................................................................ 665
Figures to Book V ....................................................................................... 680
Figures to Book VI ...................................................................................... 746
Figures to Book VII ..................................................................................... 779
Figures to the Appendices ......................................................................... 835
Part 6
Bibliography and Indexes
Bibliography .............................................................................................. 847
I: Index of Technical Terms ...................................................................... 859
II: General Index ......................................................................................... 882