A History of Sanskrit Literature c35.s5.1

c35.s5.1

The relation of India to Greek mathematics in this period is one of complexity and difficulty, and it cannot be disposed of by insisting on the indebtedness of India to Greece in respect either of astronomy or astrology, for in both cases the exact extent of that influence is obscure.² The question is obscured also by the fact that we have lost the works of Hypatia, murdered in 415 by the Alexandrian mob, and therefore cannot trace the progress of mathematics after Diophantos (*c.* 260). The visit of the philosophers expelled from the schools of Philosophy in Athens in 530 to the court of Chosrau of Persia in 532 was brief, and it is not much use speculating on its possibilities, though Damaskios and Simplikios, who had some repute in mathematics, were among those involved. The facts are that, as regards indeterminate equations, the Greeks by the fourth century had achieved rational solutions, not necessarily integral, of equations of the first and second degree and of some cases of the third degree. The Indian records go distinctly beyond this. Brahmagupta shows a complete grasp of the integral solution of ax ± by = c, and he indicates one method, called by Bhāskara the method by composition, of the solution of Du² + 1 = t². Bhāskara adds the cyclic method, as he calls it, and the combination of these two methods, which gives integral solutions, has been styled by Hankel the finest thing achieved in the theory of numbers before Lagrange. To find an ultimate Greek origin for these discoveries seems due rather to a *parti pris* than to justice.