The Science of the Shulba: A Study in Early Hindu Geometry c20.s3.36

c20.s3.36

Thus it is evident that according to the interpretation of the commentators Kapardisvāmī and Karavindasvāmī, the term *saviśeṣa* for the diagonal of a square implies intrinsically a knowledge of the following: (1) The value of the diagonal as calculated by the rule stated for the purpose is only an approximate one; (2) that value of the diagonal has a small quantity in excess over the true value of the diagonal; or in other words, the square of that value exceeds by some quantity twice the area of the given square; (3) that excess cannot be completely eliminated in calculating the value of the diagonal arithmetically. If the validity of this interpretation be accepted, then there will remain nothing to doubt that the ancient Hindus were aware of the incommensurability of the diagonal of a square with its sides.