The Science of the Shulba: A Study in Early Hindu Geometry c14.18

c14.18

Did the ancient Hindus discover a proof of the theorem of the square of the diagonal? No conclusively satisfactory answer which will be beyond a shadow of doubt can be given to this question. For there is not found any mention, direct or indirect, of such a proof, even if it had existed anywhere in the early literature of the Hindus. So what we shall say on this point will be more or less conjectural, based of course on other matters having positive bearing on the point in question. It may be pointed out that the state of affairs is not much better elsewhere. It has been already stated that though the proposition is now universally associated with the name of the Greek Pythagoras, “no really trustworthy evidence exists that it was actually discovered by him.” The tradition which attributes the theorem to him began five centuries after Pythagoras and was based upon a vague statement which did not specify this or any other great geometrical discovery as due to him. This led some eminent scholars like Hankel¹ and Junge² even to deny to Pythagoras the discovery of the proposition of the theorem of the square of the diagonal. Again the method which is supposed by the modern believers of the Pythagoras hypothesis to have been presumably followed by him to prove the theorem is purely conjectural.³ So in the same way we proceed to discuss how the theorem was proved by the ancient Hindus. It may be noted that Bürk and Hankel are definitely of opinion that the Hindus had a general geometrical proof. So also was, and more pronouncedly, the eminent German philosopher Schopenhauer.