Apollonius: Conics Books V to VII: The Arabic Translation of the Lost Greek Original in the Version of the Banū Mūsā PDF
Preview Apollonius: Conics Books V to VII: The Arabic Translation of the Lost Greek Original in the Version of the Banū Mūsā
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 sion of the publisher (Springer-Verlag, 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trade matks, etc. in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks 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
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