The Science of the Shulba: A Study in Early Hindu Geometry c14.101

c14.101

Another plausible hypothesis will be that the ancient Hindus were led to the discovery of the general proof of the theorem of the square of the diagonal in the following way: Let *ABCD* be a given square. Draw the diagonal *AC* and cut off *AE* equal to *AC*. Construct the square *AEFG* on *AE*. Join *DE* and on it construct the square *DHME*. Complete the construction as indicated in Fig. 69. Now the square *DHME* is seen to be comprised of four right-angled triangles each equal to *DAE* and the small square *ANPQ*. This square will be easily recognised to be equal to the square *CRFS* and triangles equal to the rectangles *AERD* and *ABSG*. Therefore the square *DHME* is equal to the sum of the squares *ABCD* and *AEFG*. Hence the theorem. Constructions like this are necessary in the usual course in the *Śulba*.¹