Mathematics in Ancient and Medieval India c6.s4.6

c6.s4.6

No proof of this theorem is given by Baudhāyana and other Śulba writers, since it is beyond their traditions. Zeuthen¹, Cantor², Vogt³, Cajori⁴, and Heath⁵ have expressed the view that the general statement was possibly the result of an induction from a small number of cases of right-angled triangles having sides in rational numbers known to them. But this is not the actual case. Our discussion on rational rectangles and construction of geometrical figures amply justify that the general character of the theorem was rightly understood by the Sulbakāras. This has been discussed by Burk⁶, who concluded that the theorem of square on the diagonal was known and proved in all its generality by the Indians long before the date of Pythāgoras (c-540 B. C ). He went further that so far from Indian Geometry being indebted to the Greek, the much travelled Pythāgoras probably obtained his theory from India.⁷ In this connection a number of conjectures by Bretschneider¹, Gow², Hankel³, Allman⁴, Heath⁵, Dutta⁶ and others as to the way the proof of the theorem could have been arrived at by the Indians are available.