Ganitasara Sangraha of Mahavira

Author(s): Rangacharya
Publisher: Rangacharya

Page 21

PRBLADE.
tions with the sero cannot be carried on-not to any cannot be even thought of easily--without a symbol of some sort to represent it. Mahävirācārya gives, in the very first chapter of his Ganita-sära-sangraha, the results of the operations of addition, subtraction, multiplication and division carried on in relation to the zero quantity; and although he is wrong in saying that a quantity, when divided by zero, remains unaltered, and should have said, like Bhaskarācārya, that the quotient in such a case is infinity, still the very mention of operations in relation to zero is enough to show that Mahaviracårya must have been aware of some symbolic representation of the zero quantity. Since Brahmagupta, who must have lived at least 150 years beforo Mahāvīrācārya, mentions in his work the results of operations in relation to the zero quantity, it is not unreasonable to suppose that before his time the zero must have had a gymbol to represent it in written calculations. That even Aryabhata knew guch a symbol is not at all inprobable. It is worthy of note in this connection that in enumerating the norr.inal numerals in the first chapter of his work, . Mahavirácarya mentions the namos donoting the nine
figures from 1 to 9, and then gives in the end the names denoting zero, calling all the ton by the naine of sankhya: and from this fact also, the inferenco,may well bo drawn that the zero had a symbol, and that it wns well known that with the aid of the ten digits and the decimal Ayrtom of notation namerical quantities of all values may be definitely and accurately expressed. What this known sero-symbol was, is, however, a different question.
The labour and attention bestowed upon the study and translation and annotation of the Ganila-sära-sangraba