Elements of South-Indian Palæography, from the Fourth to the Seventeenth Century A.D. c6.14.2

c6.14.2

It is thus perfectly clear that the Indians knew of numerals with a value according to position in the sixth century A. D., but the system of Āryabhaṭa which is totally different to the one described, *appears* to render improbable the assumption that he also about 500 A. D. found this system in common use, though he was acquainted with it⁴. He himself uses the successive vowels of the Sanskrit alphabet to express place, and thus his system agrees in principle with the Tamil notation; **a**, **ā** and **i** corresponding in value with the Tamil signs for ‘ten’, ‘hundred’ and ‘thousand.’ Woepcke, however, considers that Āryabhaṭa invented this notation to suit his style of composition in verse, and that the system of notation by words with value according to position was ‘probably anterior to Āryabhaṭa’⁵. If it had been then in common use, would not Āryabhaṭa have used it? Beyond the end of the fifth century there is, therefore, nothing to indicate the use of the cipher; for the high orders of numerals (equivalent to billions, trillions, etc.) first noticed by Profr. Weber⁶ do not necessarily imply anything of the kind. An illustrious French mathematician and a more eminent French philosopher have shown that this invention may have occurred (as was the case) in the middle ages of Europe spontaneously¹);