Indian Science and Technology in the Eighteenth Century: Some Contemporary European Accounts c13.45

c13.45

As to the progress which the Hindus had made in the analytic art, it will be seen, that they possessed well the arithmetic of surd roots;68 that they were aware of the infinite quotient resulting from the division of finite quantity by cipher;69 that they knew the general resolution of equations of the second degree; and had touched upon those of higher denomination; resolving them in the simplest cases, and in those in which the solution happens to be practicable by the method which serves for quadratics;70 that they had attained a general solution of indeterminate problems of the first degree;71 that they had arrived at a method for deriving a multitude of solutions of answers to problems of the second degree from a single answer found tentatively;72 which is as near an approach to a general solution of such problems, as was made until the days of La Grange, who first demonstrated that the problem, on which the solutions of all questions of this nature depend, is always resolvable in whole numbers.73 The Hindus had likewise attempted problems of this higher order by the application of the method which suffices for those of the first degree;74 with indeed very scanty success, as might be expected.