Expounding the Mathematical Seed Volume 2: The Supplements A Transla
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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Science Networks
Agathe Keller
Expounding the Mathematical Seed Volume 2: The Supplements A Translation of Bha- skara I on the Mathematical Chapter of the Aryabhatı–ya
B i r k h ä u s e r
Science Networks · Historical Studies Founded by Erwin Hiebert and Hans Wußing Volume 31
Edited by Eberhard Knobloch and Erhard Scholz Editorial Board: K. Andersen, Aarhus D. Buchwald, Pasadena H.J.M. Bos, Utrecht U. Bottazzini, Roma J.Z. Buchwald, Cambridge, Mass. K. Chemla, Paris S.S. Demidov, Moskva E.A. Fellmann, Basel M. Folkerts, München P. Galison, Cambridge, Mass. I. Grattan-Guinness, London J. Gray, Milton Keynes
R. Halleux, Liège S. Hildebrandt, Bonn Ch. Meinel, Regensburg J. Peiffer, Paris W. Purkert, Leipzig D. Rowe, Mainz A.I. Sabra, Cambridge, Mass. Ch. Sasaki, Tokyo R.H. Stuewer, Minneapolis H. Wußing, Leipzig V.P. Vizgin, Moskva
Agathe Keller
Expounding the Mathematical Seed
Volume 2: The Supplements 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 3-7643-7292-3 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 List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xii
How to read this book? . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Abbreviations and Symbols . . . . . . . . . . . . . . . . . . . . . . . . . xiii Supplements A
B
C
D
E
1
BAB.2.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
A.1
Arithmetical squaring and its geometrical interpretation . .
2
A.2
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