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Tantrasaṅgraha of Nīlakantha Somayājī
K. Ramasubramanian, IIT Bombay, Powai, India, and M. S. Sriram, University of Madras, Chennai, India
A publication of Hindustan Book Agency.
 Hindustan Book Agency 2011; 642 pp; hardcover ISBN-10: 93-80250-09-6 ISBN-13: 978-93-80250-09-0 List Price: US$82 Member Price: US$65.60 Order Code: HIN/48 Tantrasaṅgraha, composed in 1500 CE by the renowned Kerala astronomer Nīlakantha Somayājī (c.1444-1545 CE), ranks along with Āryabhatīya of Āryabhata and Siddhāntaśiromani of Bhāskarācārya as a seminal work that significantly influenced further work on astronomy in India. One of the distinguishing features of this text is that it introduces a major revision of the traditional planetary models, leading to a unified theory of planetary latitudes and a better formulation of the equation of center for the interior planets (Mercury and Venus) than was previously available. Several important innovations in mathematical technique are also to be found in Tantrasaṅgraha, especially related to the computation of accurate sine tables, the use of series for evaluating the sine and cosine functions, and a systematic treatment of the problems related to the diurnal motion of the celestial objects. The spherical trigonometry relations presented in the text--applied to a variety of problems such as the computation of eclipses and elevation of Moon's cusps--are also exact. In preparing the translation and explanatory notes, the authors have used authentic Sanskrit editions of Tantrasaṅgraha by Suranad Kunjan Pillai and K. V. Sarma, which includes the commentaries Laghu-vivrti and Yukti-dīpikā by Śaṅkara Vāriyar. The text consists of eight chapters covering mean longitudes, true longitudes, gnomonic shadow, lunar eclipse, solar eclipse, vyatīpāta, reduction to observation and elevation of Moon's cusps. All 432 verses have been translated into English and supplemented with detailed explanations through the use of mathematical equations, tables, and figures. This edition of Tantrasaṅgraha will appeal to historians of astronomy as well as those who are keen to know about the actual computational procedures employed in Indian astronomy. It is a self-contained text with several appendices, enabling the reader to comprehend the subject matter easily. A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels. Readership Anyone interested in the history of Indian astronomy. Reviews "It is truly remarkable that Nīlakantha and Copernicus, contemporaries living 4000 miles apart, should have independently made profound revisions to the classical epicyclic models of the planetary system at the same time. Here, for the first time, Westerners can read Nīlakantha's great work, the Tantrasaṅgraha, and learn the mathematical principles of Indian astronomy in their most developed form. This work has a major place in the canon of the history of science, enlarging our worldwide view of the landmark human discoveries." -- David Mumford Table of Contents Mean longitudes of planets True longitudes of planets Gnomonic shadow Lunar eclipse Solar eclipse Vyatīpāta Reduction to observation Elevation of lunar horns Appendices Representation of numbers Spherical trigonometry Coordinate systems Solution of the ten problems: A couple of examples from Yuktibhāsā Derivation of the maximum declination of the Moon The traditional Indian planetary model and its revision by Nīlakantha Glossary Bibliography Index Index of half-verses
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