# Tantrasaṅgraha of Nīlakantha Somayājī

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*K. Ramasubramanian; M. S. Sriram*

A publication of Hindustan Book Agency

Tantrasa&ndot;graha, 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 Tantrasa&ndot;graha, 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 Tantrasa&ndot;graha by Suranad Kunjan
Pillai and K. V. Sarma, which includes the commentaries
Laghu-vivrti and Yukti-dīpikā by
Śa&ndot;kara 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 Tantrasa&ndot;graha 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 & Endorsements

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 Tantrasa&ndot;graha, 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