Jyotihshastra: Astral and Mathematical Literature c4.s5.19

c4.s5.19

But the most important school of astronomers from south India was founded by its most brilliant member, Mādhava²⁴⁶ of Saṅgamagrāma (near Cochin in Kerala), in the late fourteenth century. His most ingenious work was done in the investigation of the series that express the value of π and of other trigonometric functions used in astronomy; this achievement is discussed more fully in the chapter on mathematics. The surviving astronomical works of Mādhava are for the most part concerned with refinements of the vākya system. They include, on the lunar vākyas, the Sphuṭacandrāpti;²⁴⁷ its elaboration, the Veṇvāroha,²⁴⁸ whose epoch is 1403; and a new set of Candravākyāni²⁴⁹ giving daily longitudes of the Moon correct to the second sexagesimal place instead of to the first as in the Candravākyāni of Vararuci. The idea of the Sphuṭacandrāpti and the Veṇvāroha is to utilize the cyclic nature of the lunar vākyas, in which nine anomalistic months equal 248 days, to determine easily the lunar longitude at nine equally distant times in one day. A Malayalam commentary was written on the Veṇvāroha by Acyuta Piṣāraṭi²⁵⁰ in the early seventeenth century. On the computation of the longitudes of the planets Mādhava wrote a Madhyamānayanaprakāra and an Agaṇitagrahacāra, the latter apparently in 1418. He also composed a Lagnaprakaraṇa on computing the ascendant. None of these has yet been published.