The Shulbasutras of Baudhayana, Apastamba, Katyayana and Manava: With Text, English Translation and Commentary c5.s3.13

c5.s3.13

The above-mentioned squared relationships are followed or preceded by the general statement that the diagonal of a rectangle produces by itself both (the areas) produced separately by its two sides. This is the so-called theorem known after Pythagoras. A question has often been asked whether such a definition resulted from empirical guess work or was based on a proof of some kind. Such questions are of course to be expected from scholars firmly entrenched in the Euclidean tradition in geometry. As is well known, mathematics, including geometry, in ancient India did not follow the Euclidean tradition, and usually gave the rules, leaving their proofs to be explained by the teachers to the pupils of their respective schools. Several scholars who discussed this issue of proof have shown that such proof is implicit in the very operations with rectilinear figures; we have discussed the matter in detail in our commentaries in connection with the rule and further elaboration here is unnecessary. George Sarton, while considering the question of Hindu influence on Pythagorean derivation of the theorem of squares, referred to Gaston Milhaud's claim that Pythagorean geometry may have been partly inspired by Hindu models. This argument was based on the high antiquity of Baudhāyana and Āpastamba. But Sarton, presumably on the basis of Keith's views on the dates of the *śulbakāras*, pleaded inability to accept such high antiquity and observed: 'It is highly probable that the *śulbasūtras* date from a period posterior to 500 B.C. and pre-Christian. They are probably post-Pythagorean'.a