Mathematics in Ancient and Medieval India c8.210

c8.210

The formulae (1) and (2) and the values for Jyā of 30⁰, 45⁰, 60⁰, 90⁰ were given by Bhāskara² II (1150 A. D.). Somayaji made the observation that it was probably by this method of Bhāskara II that Āryabhaṭa I and his predecessors constructed the sine table. Srinivasiengar pointed out that Somayaji however gave no evidence in support of his observation. Before discussing the problem, it may be pointed out that the calculation is further simplified if the formulae Jyā A/2 = ½(Jyā² A + Utkramajyā² A)½ is replaced by Jyā² A = ½(R - Kojyā² 2A) (3)