Indian Mathematics c7.28

c7.28

The complete integral solution is given by a combination (*a*) and (*b*) of which the former only is given by Brahmagupta, while both are given by Bhāskara (five centuries later). The latter designates (*a*) the ‘method by composition’ and (*b*) the ‘cyclic method.’ These solutions are alone sufficient to give to the Indian works an important place in the history of mathematics. Of the ‘cyclic method’ (*i.e.*, the combination of (*a*) and (*b*)) HANKEL says, “It is beyond all praise: it is certainly the finest thing achieved in the theory of numbers before Lagrange.” He attributed its invention to the Indian mathematicians, but the opinions of the best modern authorities (*e.g.*, TANNERY, CANTOR, HEATH) are rather in favour of the hypothesis of ultimate Greek origin.