The rule for arriving at the required increase or decrease in relation to a given multiplicand and a given multiplier (so as to arrive at a given product):-
284.[1] 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 desired) is (severally) divided in the inverse order by the sums (resulting thus). These give rise to the quantities that are to be added (respectively to the given multiplicand and the, multiplier) or (to the quantities that are) to be (respectively) subtracted (from them).
Examples in illustration thereof.
285. The product of 3 and 5 is 15; and the required product is 18; and it is also 14. What are the quantities to be added (respectively to the multiplicand and the multiplier) here, or what to be subtracted (from then)?
The rule for arriving at (the required result by the process of working backwards:-
286. To divide where there has been a multiplication, to multiply where there has been a division, to subtract where there 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, (them) squared, (then) increased by 5, (then)
284.^ The quantities o be added or subtracted are:- .
For , where a and b are the given factors, and d the required multiple.
