118 with which the least remainder in the odd position of order (in the above-mentioned process of successive division) 18 to be multi- plied; and (then put down) below (this again) this product increased or decreased (as the case may be by the given known number) and then divided (by the last divisor in the above men- tioned process of successive division. Thus the Valliha or the creeper-like chain of figures is obtained. In this) the sum obtained by adding (the lowermost number in the chain) to the product obtained by multiplying the number above it with the number (immediately) above (this upper number, this process of addition being in the same way continued till the whole chain is exhausted,) this sum, is to be divided by the (originally Thus we get the chain or Vallaká noted in the first column of figures in the maigm. Then we multiply the penultimate figune below in the chain, viz, 1, by 4, which is ahove it, and add 8, the last number in the cham, the resulting 12 is wiitten down so as to be in the place corresponding to 4, then multiplying this 12 by 1 which is the figure ahove it in the creeper chain, nd adding 1, the figure similarly below it, we get 13 in the place of 1 proceeding in the same manner 38 and 51 are obtained. in the places of 2 and 1 respectively. This 51 is divided by 23, the divisor in the problem, and the remainder 5 is seen to be the least number of fruits in a bunch. The rationale of the rule will be clear from the following algebraical repre- sentation - Bx + b A 1-51 2-38 1--13 4-12 1 8 GANITASARASANGRAHA. .. = y (an integer) = dpi - 71 , (where r₁ =9p+ Po, where pe=pb Ta the second remainder. 11 Hence, Pipe + b =9sp: + P3, where p = 232 + b third quotient and r3 the thnd remainder. 72 Similarly, paraps-b P3= 1 + p1, where p1 = B-Agi the inst remainder) (B-A₁) + b A
94 P3 P4, where P4
15 P4 + b 74 73 P4+b 14 Thus we have, x=92 P₁ + Pai P113 P + Psi P294 P3 P4, P315 P4 P5. and is the second quotient and 13
96 P4 P5, where Ps
24 P3-b 73 and is the
