________________
OHAPTER VI-XIXRD PROBLBX6.
188
confidential language to both the owners of the cocks. He said to one: "If your bird wins, then you give the stake-money to me. If, however, you prove unvictorious, I shall give you two-thirds of that stake-money then.” He went to (the owner of) the other (cock) and promised to give three-fourths (of his stake-lonoy on similar conditions). From both of them the gain to him could live only 12 (gold-pieces in cach case). You tell me, 0 ornament on the forehead of mathematicians, the (values of the stako-inonoy which each of) the cock-owncra had on band.
The rule for separating tho (unknown) dividend number, tho quotient, and the divisor from their combinod sum :
2734. Any (snitable optionally chosen) number (which has to be) subtracted from the (given combinod rum happous to be tho divisor (in question). On dividing, by this (divisor) as increased by one, the remainder left after subtracting the optionally choson number from the given combined sum), tho (required) quotient is arrived at. Tho vory samo remainder (nhove mentionell), as diminished by this quotient becomes the required dividend) number.
An example in illustration thereof. 2745. A certain unknown quantity in divided by a certain (other) unknown quantity. The quotient bere as combined with the divisor and the dividend number is 53. What is that divinor, and what (that) quotient ?
The rulo for arriving at that number, which becomes a squaro either on adding a known number (to the original number), or on subtracting another) given number (from that same original number): -
275). The sum of the quantity to be added and the quantity to be subtracted is multiplied by one as assoointed with whatever may happen to be the excess above the even number (nonrest to
2751. Algebrsically, let be the quantity to be found out, and a, b, the respective quantities to be added to or subtracted from it; then, the forumla to represent the rule will be (a + b)+(1+1)2 -1
+1+a-ti
2
