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 Out of the similar pairs, joined with the middle term, form so many simple questions, in each of which you find the divisor by Rule II.; then place the divisors on the left hand, and the other extremes on the right, as directed in Rule III. and multiply and divide, as follows.

Joint operation.

Men. days. men.

This compound question is resolved into three simple ones, as follows.

30 : 6 ::  15 : 3 156 :  3 :: 520 : 10 10 : 10 ::  12 : 12 days. Anf

Eamp. If 100 lb. of Venice weigh 70 lb. of Lyons, and 120 lb. of Lyons weigh 100 lb. of Roan, and 80 lb. of Roan weigh 100 b. of Tolouse, and 100 lb. of Toloude weigh 74 lb of Geneva, he many pounds of Geneva will 100 lb. of Venice weigh?

This question belongs to the rule of nine; and because pounds of Geneva is the number sought, the given pounds of Geneva, viz. 74, must be the middle term: the remaining terms are extremes; which may be classed into similar pairs, and stated as follows.

But the question becomes more simple, and is wrought with greater ease and advantage, by being stated in the fractional form, as follows.

We shall conclude by observing, that every compound question, whether in the rule of five, seven, nine, or eleven, &c. properly speaking, consists but of three given terms. For the first term, or divisor, is to be considered as one compound term made up, or produced, by the continual multiplication of the extremes on the left hand, as so many component parts. In like manner, the third term is to be considered as one compound term, made up by the continual multiplication of the extremes on the right, as component parts. Suppose the question to be,

If L. 100 in 12 months gain L. 5 interest, what will L. 75 gain in 19 months?

Here it is obvious, that it is neither the L. 100 prin- cipal, nor the 12 months of time, taken separately, that gains the L. 5 interest, but both contribute their share; that is, they conspire, as joint causes, to produce one effect; and therefore their product, viz. the first term, is to be considered as the cause producing the effect; that is, the first term, viz. 100 X 12, causeth, produceth, or gains L. 5 of interest. And in like manner, the product of the extremes on the right hand, or the third term, viz. 75 X 9, is to be esteemed the cause that produceth a similar effect; that is, gains a like sum of interest, namely, the fourth term, or answer. In reference to this way of considering the first and third terms, the question might be stated as under.

If 100 X 12:51: 75X9

CHAP. VIII. FELLOWSHIP.

FELLOWSHIP, called also Company, or Partnership, is when two or more persons join their stocks, and trade together, dividing the gain or loss proportionally among the partners.

Fellowship is either without or with time, called also Single or Double.

1. Fellowship without time.

Questions in fellowship without time are wrought by the following proportion.

As the total stock

To the total gain or loss,

So each man's particular stock

To his share of the gain or loss.

Quest. A und B make a joint stock: A puts in 12l. and B 8l.; they gain 5l.: What is each man's share? L.