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Clemency Montelle Kim Plofker Sanskrit Astronomical Tables Sources and Studies in the History of Mathematics and Physical Sciences Sources and Studies in the History of Mathematics and Physical Sciences Clemency Montelle Kim Plofker Sanskrit Astronomical Tables Sources and Studies in the History of Mathematics and Physical Sciences Managing Editor Jed Z. Buchwald Associate Editors A. Jones J. Lützen J. Renn Advisory Board C. Fraser T. Sauer A. Shapiro Sources and Studies in the History of Mathematics and Physical Sciences was inaugurated as two series in 1975 with the publication in Studies of Otto Neugebauer’s seminal three-volume History of Ancient Mathematical Astronomy, which remains the central history of the subject. This publication was followed the next year in Sources by Gerald Toomer’s transcription, translation (from the Arabic), and commentary of Diocles on Burning Mirrors. The two series were eventually amalgamated under a single editorial board led originally by Martin Klein (d. 2009) and Gerald Toomer, respectively two of the foremost historians of modern and ancient physical science. The goal of the joint series, as of its two predecessors, is to publish probing histories and thorough editions of technical developments in mathematics and physics, broadly construed. Its scope covers all relevant work from pre-classical antiquity through the last century, ranging from Babylonian mathematics to the scientific correspondence of H. A. Lorentz. Books in this series will interest scholars in the history of mathematics and physics, mathematicians, physicists, engineers, and anyone who seeks to understand the historical underpinnings of the modern physical sciences. More information about this series at http://www.springer.com/series/4142 Clemency Montelle • Kim Plofker Sanskrit Astronomical Tables 123 Clemency Montelle Kim Plofker Department of Mathematics & Statistics Department of Mathematics University of Canterbury Union College Christchurch, Canterbury, New Zealand Schenectady, NY, USA ISSN 2196-8810 ISSN 2196-8829 (electronic) Sources and Studies in the History of Mathematics and Physical Sciences ISBN 978-3-319-97036-3 ISBN 978-3-319-97037-0 (eBook) https://doi.org/10.1007/978-3-319-97037-0 Library of Congress Control Number: 2018952064 © Springer Nature Switzerland AG 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland To our graduate students, past and present, and to Lily, who was born into this book! Contents 1 Introduction .................................................................. 1 1.1 Overview of pre-modern astronomy .................................. 4 1.1.1 Mesopotamian and Egyptian ................................ 4 1.1.2 Hellenistic: Greek-primary discourse ....................... 8 1.1.3 East Asian: Chinese-primary discourse ..................... 11 1.1.4 South Asian: Sanskrit-primary discourse ................... 13 1.1.5 Islamicate: Arabic-primary discourse ....................... 16 1.2 Overview of classical Indian mathematical astronomy ............. 18 1.2.1 Astronomy and mathematics ................................ 19 1.2.2 The topics of astronomical computation .................... 19 1.2.3 The paks. as or parameter schools ............................ 23 1.3 Astrological aspects of jyotis. a ........................................ 24 1.3.1 Divination from omens or sam. hita¯ .......................... 24 1.3.2 Celestial forecasting and horoscopes........................ 25 1.3.3 Fundamental astrological concepts ......................... 25 1.4 Text genres in classical jyotis. a ........................................ 27 1.4.1 The comprehensive treatise or siddhanta¯ ................... 28 1.4.2 The astronomical handbook or karan. a...................... 29 1.4.3 The annual calendar or pañca¯nga˙ ........................... 29 1.4.4 Astrological and miscellaneous works ...................... 31 1.4.5 The astronomical table text .................................. 32 1.5 Tables and Sanskrit astral sciences in the second millennium ....... 32 1.5.1 Origins and development of Sanskrit tables ................ 32 1.5.2 The influence of Islamic tables .............................. 34 1.5.3 Concurrent developments in jyotis. a......................... 35 2 Content and classification of table texts .................................. 37 2.1 Computing astronomical quantities ................................... 37 2.1.1 Mean motions ............................................... 37 2.1.2 True motions: manda longitude/velocity corrections ...... 38 2.1.3 True motions: s´¯ıghra longitude/velocity corrections ....... 41 vii viii Contents 2.1.4 Synodic phenomena.......................................... 43 2.1.5 Times, ascensions, and shadows ............................ 46 2.1.6 Eclipses ....................................................... 51 2.1.7 The mahap¯ atas¯ or luni-solar symmetries ................... 54 2.1.8 Trigonometry ................................................. 57 2.2 Approximation of numerical values in table entries ................. 58 2.2.1 Interpolation procedures ..................................... 59 2.2.2 Precision of data values ...................................... 61 2.3 Classification schemata for table texts ............................... 65 2.3.1 Classification by table type or paks. a ........................ 66 2.3.2 Classification by computational structure................... 67 3 Table-text manuscripts ...................................................... 71 3.1 Table texts in Sanskrit scientific manuscript collections ............. 71 3.1.1 General surveys in SATIUS and SATE ...................... 73 3.1.2 Smith Indic and Smith Sanskrit Collections, Columbia University ......................................... 74 3.1.3 Gaekwad Collection, India Office Library .................. 76 3.1.4 Wellcome Library ............................................ 76 3.1.5 Chandra Shum Shere Collection, Bodleian Library ........ 77 3.1.6 Mahar¯ aja¯ Man Singh II Museum, Jaipur.................... 78 3.1.7 Some miscellaneous collections in north India ............. 79 3.1.8 Collections in Kerala and Tamil Nadu ...................... 81 3.2 Spatial and graphical characteristics of table-text manuscripts...... 83 3.2.1 Notation and layout conventions ............................ 83 3.2.2 Scribal errors, emendations and markup .................... 87 4 Elements of table texts....................................................... 95 4.1 Mean longitudinal displacement ...................................... 95 4.2 True longitudes and velocities ........................................ 105 4.2.1 Correcting longitude and velocity for manda-inequality... 105 4.2.2 Correcting longitude and velocity for s´¯ıghra-inequality ... 109 4.2.3 True longitude and velocity in mean-to-true table texts.... 113 4.2.4 True longitude and velocity in cyclic table texts ........... 113 4.3 Synodic phenomena of planets........................................ 116 4.4 Terrestrial latitude and longitude...................................... 117 4.5 Ascensions and ascendant ............................................. 119 4.6 Mean time correction functions ....................................... 131 4.7 Ecliptic declination .................................................... 137 4.8 Tables specific to eclipses ............................................. 139 4.8.1 Lunar-nodal elongation ...................................... 140 4.8.2 Lunar latitude ................................................ 142 4.8.3 Apparent diameters of sun, moon, and shadow............. 142 4.8.4 Duration of eclipse stages ................................... 144 4.8.5 Eclipse deflection (valana) .................................. 146 4.8.6 Lunar parallax ................................................ 152 Contents ix 4.9 Lunar latitude .......................................................... 156 4.10 Calendric tables ........................................................ 160 4.11 The mahap¯ atas¯ ......................................................... 175 4.11.1 Patas¯ aran¯ . ¯ı of Gan.esa´ ........................................ 175 4.12 Trigonometric functions ............................................... 176 4.13 Astrological tables ..................................................... 181 5 The evolution of the table-text
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