The Religion and Philosophy of the Veda and Upanishads v2.c41.43

v2.c41.43

The effort to show that the Pythagorean theorem and the problem of the square root of the number two are older in India than in Pythagoras, is based on a mistake: the error was certainly in great measure favoured by Cantor, who declared that the Indian versions of these matters must be based on those of Greece, and it was, therefore, easy for von Schroeder to argue that the relation must be the other way, that the Indian versions occurred in works which were much older than the versions recorded in Greece. The fact is that the Çulba Sūtras which contain the earliest mentions of these matters are of uncertain date: they are nominally parts of the ritual Sūtras, in the sense that they bear the name of the school, and it is urged that further they are so essentially connected with the structure of the sacred altars that they must be held to be early. The arguments for their age cannot be taken as at all conclusive:¹ the Sūtras of the schools were works without internal connexion of such a kind as to render it in the slightest degree difficult to interpolate, and that the Çulba Sūtras may not have been added long after the Çrauta Sūtras were composed it would be absurd to contend. The existing Sūtras have no appearance of great antiquity in any way: they have new technical terms, but little or none of the irregularities of construction and the archaic phraseology which justify us in placing some of the Çrauta Sūtras about the fourth century b. c., and even then of course the date assigned to them would be too late to prove borrowing by Pythagoras. We may legitimately assume that they were composed at the close of the Sūtra period, when interest in their subject-matter had developed. What is more important, and what, it may be added, tells against borrowing by India in this regard from Greece, is that examination of the Sūtras² has shown that complete generality of the theorem of Pythagoras was never attained and was not even striven after. The practical form of the problem was known to the Egyptians and Babylonians, long before it was known to the Sūtras.³ The same remark applies to the alleged knowledge of the theorem of the irrational—the mere approximate calculation of the root of two, which is all the Sūtras attained, is far from being equivalent to the discovery of the solution of an irrational. The real period when these questions came to be discussed in India was doubtless at a date considerably later than Pythagoras—not before the third century B.C. in all likelihood, when the ingenuity of the Brahmans began to deal with the questions of the signification of the exact details of the measurements of the sacrificial ground. The Brāhmaṇas themselves are guiltless of any knowledge of the discussions of numbers, and this is proof positive that the speculations found in the Çulba Sūtras are of later origin.