History of Hindu Mathematics: A Source Book v2.c17.s18.15

v2.c17.s18.15

Âpastamba also derives from a known right-angled triangle several others by changing the unit of measure of its sides and vice versa.¹ In other words, he recognised the principle that 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 Kâtyâyana in which a is any quantity. It is now known that all rational solutions of x² + y² = z² can be obtained without duplication in this way.