Culture and History of Mathematics

Tantrasaṅgraha, composed in 1500 CE by the renowned Kerala astronomer Nīlakaṇṭha Somayājī (c.1444–1545 CE) ranks along with Āryabhaṭīya of Āryabhaṭa and Siddhānta-śiromaṇi 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 centre 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, a systematic treatment of the problems related to the diurnal motion of the celestial objects, as well as the computation of eclipses and elevation of Moon's cusps.

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 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