Expounding the Mathematical Seed, Volume 1: The Translation A Transl
In the 5th century the Indian mathematician Aryabhata (476-499) wrote a small but famous work on astronomy, the Aryabhatiya. This treatise, written in 118 verses, gives in its second chapter a summary of Hindu mathematics up to that time. Two hundred year
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Agathe Keller
Expounding the Mathematical Seed
Volume 1: The Translation A Translation of Bhaskara I on the Mathematical Chapter of the Aryabhatiya
Birkhäuser Verlag Basel · Boston · Berlin
Author Agathe Keller Rehseis CNRS Centre Javelot 2 place Jussieu 75251 Paris Cedex 05 e-mail: [email protected]
A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbiographie; detailed bibliographic data is available in the internet at http://dnb.ddb.de
ISBN 3-7643-7291-5 Birkhäuser Verlag, Basel – Boston – Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use, permission of the copyright owner must be obtained.
© 2006 Birkhäuser Verlag, P.O.Box 133, CH-4010 Basel, Switzerland Part of Springer Science+Business Media Cover design: Micha Lotrovsky, CH-4106 Therwil, Switzerland Cover illustration: The cover illustration is a free representation of “Rat and Hawk” (made by Mukesh) Printed on acid-free paper produced from chlorine-free pulp. TCF ∞ Printed in Germany Vol. 1/SN 30: Vol. 2/SN 31: Set SN 30/31:
987654321
ISBN 10: 3-7643-7291-5 ISBN 13: 978-3-7643-7291-0 ISBN 10: 3-7643-7292-3 ISBN 13: 978-3-7643-7292-7 ISBN 10: 3-7643-7299-0 ISBN 13: 978-3-7643-7299-6
e-ISBN: 3-7643-7592-2 e-ISBN: 3-7643-7593-0 e-ISBN: 3-7643-7594-9
Contents Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii Abbreviations and Symbols . . . . . . . . . . . . . . . . . . . . . . . . . ix Introduction How to read this book? . . . . . . . . . . . . . . . . . . . . . . A Situating Bh¯ askara’s commentary . . . . . . . . . . . . . . 1 A brief historical account . . . . . . . . . . . . . . 2 Text, Edition and Manuscript . . . . . . . . . . . . B The mathematical matter . . . . . . . . . . . . . . . . . . 1 Bh¯ askara’s arithmetics . . . . . . . . . . . . . . . . 2 Bh¯ askara’s geometry . . . . . . . . . . . . . . . . . 3 Arithmetics and geometry . . . . . . . . . . . . . . 4 Mathematics and astronomy . . . . . . . . . . . . C The commentary and its treatise . . . . . . . . . . . . . . 1 Written texts in an oral traditio
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