A History of the Kerala School of Hindu Astronomy (in Perspective) c8.s6.10

c8.s6.10

Mādhava’s verses quoted above have been extracted and explained in the *Yuktibhāṣā* (*op. cit.*, pp. 113-16) in the traditional manner and its rationale demonstrated in terms of modern mathematics by C.T. Rajagopal and others.¹ Rajagopal’s demonstration throws up, *inter alia*, certain interesting anticipations of Kerala mathematicians. Thus, after giving the general derivation of Gregory’s series according to the *Yuktibhāṣā* and offering the proof therefor, Rajagopal observes: “There are two points which emerge from a consideration of the mathematical text presented here. In the first place, it employs relations which would appear not to have been noticed in Europe before modern forerunners and followers of the calculus started investigations.........Our second point is not unconnected with the first. The Hindu mathematicians achieved, without the aid of calculus, results which, for us, are treated best by means of the calculus.²