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 which is identical with the linga-çarīra of the Sānkhya system. Finally, the many heavens of the Gnostics are evidently derived from the fantastic cosmogony of later Buddhism.

With regard to the present century, the influence of Indian thought on the pessimistic philosophy of Schopenhauer and Von Hartmann is well known. How great an impression the Upanishads produced on the former, even in a second-hand Latin translation, may be inferred from his writing that they were his consolation in life and would be so in death.

In Science, too, the debt of Europe to India has been considerable. There is, in the first place, the great fact that the Indians invented the numerical figures used all over the world. The influence which the decimal system of reckoning dependent on those figures has had not only on mathematics, but on the progress of civilisation in general, can hardly be over-estimated. During the eighth and ninth centuries the Indians became the teachers in arithmetic and algebra of the Arabs, and through them of the nations of the West. Thus, though we call the latter science by an Arabic name, it is a gift we owe to India.

In Geometry the points of contact between the Çulva Sūtras and the work of the Greeks are so considerable, that, according to Cantor, the historian of mathematics, borrowing must have taken place on one side or the other. In the opinion of that authority, the Çulva Sūtras were influenced by the Alexandrian geometry of Hero (215 B.C.), which, he thinks, came to India after 100 B.C. The Çulva Sūtras are, however, probably far earlier than that date, for they form an integral portion of the Çrauta Sūtras, and their geometry is a part of the Brahmanical theology, having taken its rise in India from practical