78 GANITASĀRASANGRAHA. at last 12 ascetics were seen (to remain without being included among those mentioned before) O (you) excellent ascetic, of what numerical value was (this) collection of ascetics? 46 Five and one-fourth times the square root (of a herd) of. clephants are sporting on a mountain slope; of the remainder sport on the top of the mountain; five times the square root of the remainder (after deducting this) sport in a forest of lotuses; and there are 6 elephants then (left) on the bank of a river How many are (all) the elephants here? Here ends the Sesamula variety (of miscellaneous problems on fractions). The rule relating to the Sisamula variety involving two known (quantities constituting the) remainders :- 47 The (coefficient of the) square root (of the unk own collective quantity), and the (final) quantity known (to remain), should (hoth) be divided by the product of the fractional (proportional) quantities, as subtracted from one (in each case); then the first known quantity should be added to the (other) known quantity (treated as above) Thereafter the operation relating to the Sesamula variety (of miscellaneous problems on fractions is to be adopted) 47 Algebraically, this lla rule enables us to anive at the expressions +a, which are required to be substituted for c and a respectively in the formala for samüla, which is and (1-0₁) (18) x &c. (1-b₁) (1-b)x &c. ) 2 √( ) ² + +aj In applying this formula the value of b becomes zero, as the mila or square root involved in the duraya-samüla is that of the total collective quantity and not of a fractional part of that quantity. Substitating as desired, we get = C -{za- L2 (1-6₁) (1-₂) x &c + N 21 = 0 may casily be obtained from the equation -a₁-b₁ (α₁) b₂x1₁-b₁ x-bx= ak a 72 -b₁) (1 bs) x &c. + (1-₁) (16₂) × &c. + a₁). This result (2-₁)}- -c-a₂=0, where b, b, &c., are, the various fractional parts of the successive remainders, and a, aud ag are the first known quantity and the final known quantity respectively.
