George Rusby Kaye

“ The S'ulvasūtras are not primarily mathematical but are rules ancillary to religious ritual—they have not a mathematical but a religious aim. No proofs or demonstrations are given and indeed in the presentation there is nothing mathematical beyond the bare facts. ”

“ In connection with (1) and (2) the Pythagorean theorem is stated quite generally. It is illustrated by a number of examples which may be summarised thus:
Kātyāyana gives no such rational examples but gives (with Āpastamba and Baudhāyana) the hypotenuse corresponding to sides equal to the side and diagonal of a square, i.e., the triangle , and he alone gives , and . There is no indication that the S'ulvasūtra rational examples were obtained from any general rule. Incidentally is given an arithmetical value of the diagonal of a square which may be represented by ”

“ Neither the value itself nor this form of fraction occurs in any later Indian work.
There is one other point connected with the Pythagorean theorem to be noted, viz., the occurrence of an indication of the formation of a square by the successive addition of gnomons. The text relating to this is as follows:
"Two hundred and twenty-five of these bricks constitute the sevenfold agni with aratni and pradesa."
"To these sixty-four more are to be added. With these bricks a square is formed. The side of the square consists of sixteen bricks. ”