The Science of the Shulba: A Study in Early Hindu Geometry c14.s1.1

c14.s1.1

The early history of the theorem of the square of the diagonal, in India, has been very ably treated by Bürk.² We have now discovered a few more corroborative evidence of unquestionable value as regards its ancient character. In the *Śulba*, the theorem is found to have been applied very extensively. Even in the construction of a square, a rectangle or a trapezium, is ordinarily presupposed a knowledge of its converse. We may, however, presume for the sake of the best argument on the adverse that in the anterior times, those simple geometrical figures were used to be constructed by methods which would not depend in any way on that theorem.¹ The proof of the possibility and existence of such methods, we find also in the *Sulba*. But there are certain other geometrical constructions such as (i) the geometrical constructions of √2, √3, etc., and (ii) the transformation of rectangles into squares, for which the theorem of the square of the diagonal is absolutely indispensable. Hence to determine the ancient history of the theorem in India, we shall have to find from the ancient literature of the Hindus the oldest instances of the application of the one or the other of those geometrical constructions. Such instances occur indeed copiously.