Instantaneous Motion(ta-tka-likagati) and the “Derivative” of the Sine Function in Bh¯askara-II’s Siddha-nta´siroman.

By : M. S. Sriram

Page No: 37-52

Abstract
It was well known even before Bha-skara-ca -rya that the daily motion of a planet would vary from day to day. In his Siddha-nta´siroman. i, Bha-skara-II observes that the rate of motion would vary even during the course of a day, and discusses the concept of an instantaneous rate of motion, which involves the derivative of the sine function. We discuss how Bha-skara could have arrived at the correct expression for this, and also how it was applied to find the ‘apogee’ of a planet.