Indian Mathematics c5.14

c5.14

The questions (*a*) whether the Indians of this period had completely realised the generality of the PYTHAGOREAN theorem, and (*b*) whether they had a sound notion of the irrational have been much discussed; but the ritualists who composed the *S'ulvasūtras* were not interested in the PYTHAGOREAN theorem beyond their own actual wants, and it is quite certain that even as late as the 12th century no Indian mathematician gives evidence of a complete understanding of the irrational. Further, at no period did the Indians develop any real theory of geometry, and a comparatively modern Indian work denies the possibility of any proof of the PYTHAGOREAN theorem other than experience.