________________
186
GAŅITABĀRASANGRAHA.
The rule for arriving at the required increase or decrease in relation to a given multiplicand and a given multiplier (80 as to arrive at a given product): -
284. The difference between the required product and the resulting product (of the given multiplicand and the multiplier) is written down in two places. To (one of the factors (of the resulting product) one is added, and (to the other) the required product is added. That (difference written above in two positions as desirod) is (severally) divided in the inverse order by the gums (resulting thus). These give rise to the quantities that are to be added (respectively to the givon multiplicand and the multiplier) or (to the quantities that are to be respectively) subtracted (from thom).
E.camples in illustration thereof. 285. The product of 3 and 5 is 15; and the required product is 18; and it is also it. What are the quantities to be added (rospectively to the multiplicand and the multiplier) here, or what to be subtracted from them)?
The rule for arriving at the required result hy) the procese of working baokwards:
286. To divide where there has been a multiplioation, to multiply where there has beon a division, to subtract where thero has been an addition, to get at the square root where there has been a squaring, to get at the squaring where the root has been given--this is the process of working backwards.
An example in illustration thereof. 287. What is that quantity which when divided by 7, (then) multiplied by 3, (then) squared, (then) increased by 5, (then)
284. The quantition !o be added or subtracted sre--
d~ad and -46.
d+ b
a
+i
For (a + b
) (0+ 4+ )=d, where a sad b aro the given factors,
where a and b are the given factors,
and a the required multiple,
