The Science of the Shulba: A Study in Early Hindu Geometry c15.121

c15.121

Here it is clear that the altitude (= 188 aṅgulis) of the *vedi* is supposed to be divided into 36 parts, so that one part will be equal to 5 2/9 aṅgulis. On taking this for a new unit of pada or prakrama, in terms of it the altitude of the *Nirūḍhapaśubandha-vedi* will contain 36 padas or prakramas. So the rational rectangle (15, 36, 39) can be applied to construct it, as in the Method I, page 64 (Fig. 28). The spatial magnitudes of the rational rectangle employed will truly be (78⅓, 188, 203⅔) in terms of the usual unit aṅguli. But by supposing the unit to be one of 5 2/9 aṅgulis, Āpastamba represents it as (15, 36, 39). Similarly in constructing several other altars, by a suitable change of the length of the unit of linear measure, Āpastamba always represents the sides and the diagonal of the rational rectangle employed by (15, 36, 39).¹ Actually they are particular cases of the rectangle (a, 5a/12, 13a/12), a being the length of the altitude of the *vedi* under construction.