The Science of the Shulba: A Study in Early Hindu Geometry c12.46

c12.46

Why Dvārakanātha Yajvā explains the method at a place other than what is proper for it seems very probably to be this. The process as defined in the rules of Baudhāyana and Āpastamba does not begin, as has been already pointed out by Bürk, with the construction of a greater rectangle (*EFCD* in Fig. 47) as required in the above explanations of the commentators. But it begins very clearly to cut off from the given square a smaller rectangle (*ABFE* in Fig. 48). Or in other words the explanation of the commentators has in view the case in which the given length is greater than a side of the given square, whereas the rule of the Śulbakāras has in view the case in which the given length is smaller than a side of the given square. So Dvārakanātha Yajvā was not wrong in calling the method described by him to be a different one. This case was treated under the unsatisfactory rule of Baudhāyana undoubtedly as a sort of modification and improvement of it. The case of the Śulbakāra has been explained by him in its proper place under the succeeding rule.