The Science of the Shulba: A Study in Early Hindu Geometry c19.s1.4

c19.s1.4

A still more general solution of (A) which includes the solution (I) as a particular case, is furnished by the method of transformation of a rectangle into a square. It is this: $(√mn)² + ((m-n)/2)² = ((m+n)/2)²,$ where m, n are any two arbitrary numbers. Substituting p², q² for m, n respectively, in order to eliminate the irrational quantities, we get $p² q² + ((p²-q²)/2)² = ((p²+q²)/2)². (II)$