234 BRAHMAGUPTA AS AN ALGEBRAIST Putting Q-2, we get x-40 and y-24, which is the least solution. Assuming now that the residues of the revolution (manda- laja-teşa) of Saturn and Mars are 24 and 40 respectively, we have to obtain the ahargana (which means the number of mean civil days elapsed since the beginning of Kaliyuga, or, in fact, any epoch). The revolution-number of Saturn is 146564 and the number of civil days in a puga is 1,577.917.500. In the present problem, these are respectively the dividend and the divisor. Their H.C.F. is 4, so that dividing them out by 4 we get 36641 and 394,479,375 as the abraded dividend and abraded divisor respectively. We have, therefore, to solve the pulveriser 36641x-24. 394479375 =y where x and y denote the ahar gana and the revolutions respecti- vely made by Saturn. Mutually dividing 36641 and 394479375, we get 36641) 394479375 (10766 394477006 2369) 36641 (15 35535 1106) 2369 (2 157) 1106 (7 1099 7) 157 (22 154 3)7 (2 6 1x27-24-3)3(1 3. 0 We have chosen here the number 27 as the optional number (mati). In fact, mati may be chosen at any stage after an even number of quotients are obtained.
