PREFACE. XIII and that the value of each succeeding place is taken to be ten times the value of the immediately preceding place. Although certain words forming the names 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 decima? system of notation is almost invariably followed. If we took the words moon, eye, fire, and sky to represent respectively 1, 2, 3 and 0, as their Sanskrit equivalants are understood in this work, then, for instance," fire-sky-moon-eye would denote the. number 2103, and moon-eye-sky-fire would denote 3021, since these nominal numerals denoting numbers are generally repeater 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 use of such nominal numerals as well as the decimal system of notation Mahavirācārya 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 the 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 Brahmagupta's writings also there is evidence to show that he was acquainted with the use of nominal numerals and the decimal system of notation. Both Aryabhaṭa and Brahmagupta claim that their astronomical works
