RESIDUES OF TWO OR MORE PLANETS GIVEN 45 Example 3. "Some number of days is (severally) divided by the (abraded) civil days for the Sun and for Mars. The (resulting) quotients are unknown to me; the residues, too, are not seen by me. The quotients obtain- ed by multiplying those residues by the respective (abraded) revolution- numbers and then dividing (the products) by the respective (abraded) civil days are also biown away by the wind. The remainders of the two (divisions) now exist. The remainder for the Sun is 38472, and that for Mars is 77180625. From these remainders severally calculate, O mathema- tician, the aharganas for the Sun and Mars and also the ahargana conforming to the two residues and state them in proper order."¹, The abraded revolution-number and the. abraded civil days for the Sun are 576 and 210389 respectively; the same for Mars are 191402 and 131493125 respectively. Let A be the number of days (i.e., the ahargana conforming to the two residues). Then suppose that and A 210389 A 131493125 576 a 210389 191402 b 131493125 = x + = y + =B+
+ a 210389 The equations (2) reduce to b 131493125 38472 210389 131493125 77180625 131493125 where A, x, y, a, b, B, and λ are all unknown quantities. The problem is to find a and b and therefrom A. 576a38472 210389 191402 b-77180625 = B, (1) ¹ Bhāskara I's example, occurring in his comm. Also see MBh, viii. 24-24*. (3) on A, ii. 32-33.
