History of Hindu Mathematics: A Source Book v2.c17.s18.t2.1

v2.c17.s18.t2.1

Mahâvîra also obtained right triangles whose sides multiplied by arbitrary rational numbers have a given sum. Algebraically, the problems require the solution of $.x² + y² = z², / rx + sy + tz = A;$ where r, s, t, A are known rational numbers. His method of solution is the same as that described above. Starting with the general solution of $x'² + y'² = z'²$ we are asked to calculate the value $rx' + sy' + tz' = P, say.$ Then, says Mahâvîra, the required solution is $x = x'A/P, y = y'A/P, z = z'A/P.$