History of Hindu Mathematics: A Source Book v1.c8.s15.1

v1.c8.s15.1

It has been shown that the zero was invented in India about the beginning of the Christian era to help the writing of numbers in the decimal scale. The Hindu mind did not rest satisfied till it evolved the complete arithmetic of zero. The Hindus included zero among the numbers (*saṅkhyā*), and it was used in their arithmetic at the time when the original of the Bakhshâlî Manuscript was written, about the third century A.D. The operation of addition and subtraction of zero are incidentally mentioned in the *Pañcasiddhântikâ* of Varâhamihira (505). The complete decimal arithmetic is found in the commentary of Bhâskara I (*c.* 525) on the *Âryabhaṭîya*. The results of operations by zero are found stated in the work of Brahmagupta (628) and in all later mathematical treatises. The treatment of zero in the arithmetic of the Hindus is different from that found in their algebra. In order, therefore, to bring out this difference clearly, we give separately the results found in *pâṭîgaṇita* (arithmetic) and in *bîjagaṇita* (algebra).