Ganitasara Sangraha of Mahavira

Author(s): Rangacharya
Publisher: Rangacharya

Page 19

PRBPACE.
and that the value of each succeeding place is taken to be ten times the value of the immediately precediug place. Although certain words forming the namos of certain things are utilized in this work to represent various numerical figures, still in the numeration of numbers with the aid of such words the decimal system of notation is almost invariably followed. If we took the words moun, eye, fire, and sky to represent respectively 1, 2, 3 and 0. as their Sanskrit oquivalants are understood in this work, then, for instance, fire-sky-mrun-eye would denote the pomber 2103, and noon-eye-sky.fire would denoto 3021, since these nominal numerals denoting numbers are generally repeateil in order from the units place upwards. This combination of nominal numerals and the decimal system of notation has been adopted obviously for the sake of securing metrical convenience and avoiding at the same time cumbrous ways of mentioning numerical expressions ; and it may well be taken for granted that for the age of such nominal numerals as well as the decimal system of notation Mahavirácārya was indebted to his
predecessors. The decimal system of notation is distinctly . described by Aryabhata, and there is evidence in his writings
to show that he was familiar with nominal numerals. Even in his brief mnemonic method of reperesenting numbers by certain combinations of tho consonants and vowels found in the Sanskrit language, the decimal system of notation is taken for granted; and ordinarily 19 notational places are provided for therein. Similarly in Brabmagupta's writings also there is evidence to show that he was acquaintod with the use of nominal pomeruls and the decimal system of notation. Both Aryabbata and Brahmagupta claim that their astronomical works