History of Hindu Mathematics: A Source Book v2.c17.s2.16

v2.c17.s2.16

**Origin of Minus Sign.** The origin of · or ° as the minus sign seems to be connected with the Hindu symbol for the zero, 0. It is found to have been used as the sign of emptiness or omission in the early Bakhshâlî treatise as well as in the later treatises on arithmetic (*vide infra*).³ It is placed over the number affected in order to distinguish it from its use in a purely numerical significance when it is placed beside the number. The origin of the Bakhshâlî minus sign (+) has been the subject of much conjecture. Thibaut suggested its possible connection with the supposed Diophantine negative sign ⋔ (reversed ψ, tachygraphic abbreviation for λειψις meaning wanting). Kaye believes it. The Greek sign for minus, however, is not ⋔, but ↑. It is even doubtful if Diophantus did actually use it; or whether it is as old as the Bakhshâlî cross.⁴ Hoernle⁵ presumed the Bakhshâlî minus sign to be the abbreviation *ka* of the Sanskrit word *kanita*, or *nu* (or *nû*) of *nyûna*, both of which mean diminished and both of which abbreviations in the Brâhmî characters would be denoted by a cross. Hoernle was right, thinks Datta,⁶ so far as he sought for the origin of + in a tachygraphic abbreviation of some Sanskrit word. But as neither the word *kanita* nor *nyûna* is found to have been used in the Bakhshâlî work in connection with the subtractive operation, Datta finally rejects the theory of Hoernle and believes it to be the abbreviation *kṣa*, from *kṣaya* (decrease) which occurs several times, indeed, more than any other word indicative of subtraction. The sign for *kṣa*, whether in the Brâhmî characters or in Bakhshâlî characters, differs from the simple cross (+) only in having a little flourish at the lower end of the vertical line. The flourish seems to have been dropped subsequently for convenient simplification.