The Science of the Shulba: A Study in Early Hindu Geometry c19.s1.5

c19.s1.5

A further generalisation has been tacitly assumed in some methods employed by Āpastamba for the construction of the *Mahāvedi*. If the sides of a rational right triangle are known, then other rational right triangles can be obtained by multiplying them by any rational integer, or how he puts it, by increasing them by any rational multiples of them. Thus if α, β, γ be a rational solution of x² + y² = z², then other rational solutions of it will be given by la, lβ, lγ where l is any rational number. This is clearly in evidence in the formula of Kātyāyana. It is now known that all rational solutions of (A) can be obtained without duplication in this way.