The Science of the Shulba: A Study in Early Hindu Geometry c14.87

c14.87

We thus find from the *Śulba* how by successive stages the ancient Hindus developed, as is highly probable, a general proof of the theorem of the square of the diagonal. As confirmatory to this hypothesis, we may refer to the method of Āpastamba for the enlargement of a square. If it be required to construct a square whose side will exceed a side b of a given square by a, add, says Āpastamba,¹ on the two sides of the given square two rectangles whose lengths are equal to b and breadths to a; then add on the corner a square whose sides are equal to the increment a. Thus will be obtained a square with a side equal to a+b (Fig. 68). A similar method is taught by Baudhāyana.² Now we can divide the added rectangles by their diagonals and place the four resulting triangles of sides a, b, c around another square of the same size as the enlarged square, in the manner shown in Fig. 67.