terms together, and divide the product by the third; the quotient will be the anfwer, in the fame denomination as the middle term was reduced into.

If there be fractions in your question, they must be ftated as before directed; and if they be vulgar, invert the third term Then multiply the three terms con. tinually together, and the product will be the answer.

EXAMPLES.

I. How much shalloon, that is 4 yard wide, will line 6 yards of cloth, which is 1 yard wide?

Yd. yds. qr.

As 1 6

3

The fame by Decimal Fractions.

1=1,25,616,75, and 3grs.=,75, then

yds. yd.

yd. As 1,25

75)8,4375(11,25 yds. Anf.

12 :: 71⁄2 : 19} Ans.

3.

How many yards of carpet, 2 feet wide, will cover a floor, which is 18 feet long and 16 feet wide?

Note, I multiply 24 by 3, becaufe 3 feet1 yd. 4. Suppofe I lend a friend £350 for 5 months, he promifing the like kindness; but, when requefted, can fpare but £125; how long may I keep it to balance the favour?

E. Mo. £. Mo.

As 350 5 125: 14 Anf.

5. Suppofe 450 men are in a garrifon, and their pro. vifions are calculated to laft but 5 months; how many muft leave the garrifon, that the fame provifions may be fufficient for thofe who remain, 9 months?

Mo. Men. Mo. Men. Men.

As 5

450:9: 250, & 450-250-200 Men. Anf. 6. If a man performs a journey in 15 days, when the day is 12 hours long; in how many will he do it, when the day is but 10 hours?

b. d. As 12

b. d.

15: 10: 18 Anfwer.

7. If a piece of land, 40 rods in length, and 4 in breadth, make an acre; how wide muft it be, when it is but 19 rods long to make an acre ?

Leng. Br. Leng. Br. ft. in.

As 40 4: 19: 8 6 1

Anf.

8. If, when wheat is 6s. per bufhel, the two penny loaf weighs 9,60%. what ought it to weigh, when wheat is 7s. 6d. per bushel?

S. 0%. s. d. oz. pwt. gr.

As 6: 9,67 6:7 13 14,4 Answer.

9. If a piece of board be 30 inches in length; what breadth will make 11⁄2 square foot?

Sq.f. in. in. in.

As 1,5: 1 :: 30: 7,2 Answer.

IO. If 9 men can build a house in 5 months, by working 14 hours per day; in what time will the fame number of men do it, when they work only 10 hours per day?

II. A wall which was to be built 24 feet high, was raised 8 feet by 6 men, in 12 days; how many men must be employed to finish the wall in 4 days?

ft. men. ft. men.

As 86 24-8: 12 to finish it in 12 days. And days. men. days. men.

As 12 12 4: 36 to finish it in 4 days.

12. There is a ciftern having a pipe, which will empty it in 6 hours; how many pipes, of the fame capacity, will empty it in 20 minutes?

ho. pi. min. pi.

As 6: 1 :: 20: 18 Anfwer.

13. What number of men must be employed, to finish in 9 days, what 15 men would be 30 days about? da. men. da. men.

14.

As 30: 159: 50 Answer.

If a field will feed 6 cows 91 days; how long will it feed 21 cows?

cows. d. cows. d.

As 6 91: 21 : 26 Anfwer.

15. How much in length, that is 8 inches broad, will make a foot square?

in. in. in. in.

As 144 8: 16

Anfwer.

16. How much in length, that is 13 poles in breadth, will make a fquare-acre ?

17. A regiment of foldiers, confifting of 745 men, is to be clothed, each suit to contain 3 yards of cloth, which is 1 yard wide, and lined with shalloon yard wide ; how many yards of shalloon will line them?

As 745 X3 14 :: 7 : 4097 yds. Anf.

18. If a fuit of clothes can be made of 4 yards of cloth, 1 yard wide; how many yards of coating, of a yard wide, will it require for the fame person?

yd. yds. yd. yds. qr. n.

As 1 4

7 6 1 34 Answer.

ABBREVIATIONS.

To know whether a fraction, when abbreviated, be equivalent in all refpeals to the original given fraction.

RULE. As the numerator of the fraction, in its lowest terms, is to its denominator; fo will the nume. rator of the original fraction be to its own denomi

nator.

Or, as one numerator is to the other; fo will one denominator be to the other, &c.

A owes B 75 13s. 6d. now £100 of A's money is equal to 140 of B's; what muft A pay to fatisfy the faid debt?

Now, to prove whether & be equal to 100

Num. Den. Num. Den.

Num. Num. Den. Den.

As 5: 7 :: 100: 140-Or, as 5: 100 :: 7 : 140.

COMPOUND

COMPOUND PROPORTION,

OR,

DOUBLE RULE OF THREE,

Teaches to refolve fuch queftions as require two, or more ftatings, by fimple proportion; and that, whether direct, or inverse :-It is compofed (commonly) of 5 numbers to find a fixth, which, if the proportion be direct, must bear fuch proportion to the 4th and 5th, as the 3d bears to the 1ft and 2d: But if inverse, the 6th number muft bear fuch proportion to the 4th and 5th, as the 1ft bears to the 2d and 3d.

Always place the three conditional terms in this order: That number, which is the principal cause of gain, lofs or action, poffeffes the firft place; that which denotes the space of time or diftance of place, the fecond; and that, which is the gain, lofs or action, the third; this being done, place the other two terms, which move the queftion, under those of the same name, and if the blank place, or term fought, fall under the third place, then the question is in direct proportion; therefore,

RULE 1.-Multiply the three laft terms together, for a dividend, and the two firft for a divifor :- -But if the blank fall under the first or fecond place; then, the proportion is inverfe; therefore,

RULE 2.-Multiply the first, second and laft terms together for a dividend, and the other two for a divifor, and the quotient will be the anfwer.

I.

If foo gain £6 in a year; what will £400 gain in 9 months?

L.P. Mo..Int.

100 : 12 :: 6 Terms in the supposition, or conditional terms. 400 : 9 Terms which move the question.

Here, the blank falling under the third place, the queftion is in direct proportion, and the anfwer must be found by the firft rule; therefore,