BRAHMAGUPTA AS AN ALGERRAIST If the multiplier be negative, it must be made positive; and the additive must be made negative and then the method of the pulveriser should be employed. Pṛthudaka Svāmi, however, does not indicate how to derive the solution of the equation. by=-ax+c 240 from that of the equation by=ax-c ...(2) The method, however, seems to have been this : Let x-a, y-3 be the minimum solution of (2). Then we get bB=a a-c b(a-B)= a(a-b)+c Hence x-a-by-a-3 is the minimum solution of (1). This rule is very clearly indicated by Bhaskara II and others. or We shall give two examples from Bhaskara II (Bijaganita) to illustrate the rule: Example I. ...(1) 13y=-60x +3 By the method described before, we find that the minimum solution of 13y=60x+3 is x 11, y 51. Subtracting these values from their respective abraders, namely 13 and 60, we get 2 and 90. Then by the maxim: "In the case of the dividend and divisor being of differ- ent signs, the results from the operation of division should be known to be so", making the quotient negative we get the solu- tion of 13y=-60x+3 as x=2, p=-9. Subtracting these values again from their respec- tive abraders (13. 60), we get the solution of 13y=-60x-3 as x 11, p=-51. Example II. 11p=18x+10
