The Science of the Shulba: A Study in Early Hindu Geometry c14.14

c14.14

The order in which these two and other closely related propositions is mentioned by different writers is noteworthy. The oldest known Śulbakāra, Baudhāyana, states the second proposition before the first intervened by two other rules in the same connexion. The posterior writers like Āpastamba and Kātyāyana place the second just after the first. This change in the order in stating these propositions may not be entirely without any significance. It shows that by the time of Āpastamba and Kātyāyana the importance and generality of the theorem of the square of the diagonal of a rectangle was recognised fully. So they very naturally stated the corresponding theorem for the particular case of a square as a corollary to it. But from the point of view of the origin and growth of the theorem, Baudhāyana's arrangement is more natural.