The Science of the Shulba: A Study in Early Hindu Geometry c17.62

c17.62

Here two methods are to be discerned. According to one, it is required to construct a *vedi* 14 times as much while according to the other 14 3/7 times as much.³ The operations implied are doubtless as follows :⁴ The altarbuilder should at first construct a square of sides 36 prakramas each. Fourteen such squares should be combined into a large square. A side of the resulting square, which is clearly equal to 36√14 prakramas, is taken for the east-west line. Or otherwise a smaller square should be divided into the 7 equal rectangular portions by drawing lines parallel to a side of the square; the rectangle comprising three of these strips should be transformed into a square and then combined with the former larger square. A side of the resulting square, which will be easily recognised to be equal to 36√(14 3/7) prakramas, is taken for the east-west line of the enlarged *vedi* to be constructed. By the same kind of operations, the face of the new *vedi* is obtained to be 24√(14 3/7) prakramas and its base 30√(14 3/7). So that the size of the new *vedi* will be 14 3/7 times that of the *Mahāvedi* and its shape similar to that of the latter.