Revising Ptolemy

Astronomy is one of the most widely researched topics in contemporary India, with a large number of institutes and telescopes dotting the landscape, from optical telescope in Hanle in Ladakh to the solar observatory in Kodaikanal in the South. And the tradition of studying astronomy is an old one, as the new title from Hindustan Book Agency reminds us once again...

The Tantrasangraha of Nilakantha Somayaji by K. Ramasubramanian and M. S. Sriram is a new contribution to HBA's Culture and History of Mathematics series. Composed in 1500 CE by the renowned Kerala astronomer Nilakantha Somayaji (c.1444–1545 CE), the Tantrasangraha ranks along with the Aryabhatiya of Aryabhata and the Siddhàntashiromani of Bhàskaràcàrya 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 centre for the interior planets (Mercury and Venus) than was previously available.

Several important innovations in mathematical technique are also to be found in Tantrasangraha, 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 Tantrasangraha by Suranad Kunjan Pillai and K V Sarma. , The text consists of eight chapters covering mean longitudes, true longitudes, gnomonic shadow, lunar eclipse, solar eclipse, vyatãpàta, reduction to observation and elevation of Moon’s cusps. All 432 verses have been translated into English and supplemented with detailed explanations through use of mathematical equations, tables and figures.

This edition of Tantrasangraha 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.

It is truly remarkable that Nilakantha 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 Nilakantha’s great work, the Tantrasangraha 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 world-wide view of the landmark human discoveries... says David Mumford, Professor of Mathematics at Harvard.

In our History of Science and Mathematics sections, in hardcover, 642 pages Rs. 975. ISBN 9789380250090