Elements of South-Indian Palæography, from the Fourth to the Seventeenth Century A.D. c6.14.1

c6.14.1

It therefore appears that, neglecting all possibilities, in favour of which evidence does not exist, (such as the simultaneous existence of the more modern system of notation with the older in the fifth century A. D. or even earlier), the only possible conclusion is that, the great improvement of using numerals with a value according to position, and consequently the use of the cipher, first occurred in Central India about 500 A. D. Now though the inscriptions fail us as yet for this period, the acuteness of Woepcke detected some evidence in the works of the astronomers who lived in India during the fifth and following centuries. These are: Āryabhaṭa who himself tells us that he was born in 476 A. D.¹, Varāha Mihira who died in 587 A. D.², Brahmagupta who lived about 600, and Bhaṭṭotpala who lived about 1000 also of our era. All these writers composed their treatises in metre, and to suit the exigencies of the strict limits thus imposed on them, the three last were obliged to express the terms of their calculations by words, and these not the usual ones, but by symbolical words denoting natural objects, and in a conventional way, (as here used) also numerals. This peculiar system (which will be fully explained further on in this chapter) implies value by position, and also has words which express *indirectly* the cipher³. This same system is also used in the Sūryasiddhānta which is of very uncertain date in its actual form.