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if it confifts of pounds, ounces, &c. it will be most convenient to reduce the pounds to ounces, and proceed by Rule 2.

What is the value of 361 of gold, at £64 per ft?

36×64 = £2304 Anf. PROB. 2. To afcertain the value of any given quantity of gold in Spanish milled Dollars.

THEOREM 2. pwt. of gold = 5s. 1 dol. = 6s.
And 5, therefore,

RULE -Reduce the given quantity of gold to pennyweights; then, as the denominator is to the given quantity, fo is the numerator to the answer in dollars.

Or,

Divide by the denominator, and multiply the quotient by the numerator.

Or,

Divide by the denominator, and fubtract the quotient from the dividend; in either cafe you will have the anfwer.

1. What is the value of 6oz. 6prut. of gold, in Spanish

dollars?

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PROB. 3. To ascertain the weight of gold equivalent to any

given fum, currency.

RULE 1.If the given fum be in pence, reverfe Rule 1, Theor. 1, that is; As the numerator 8 is to the given fum in pence; fo is the denominator 3 to the weight required in grains.

What

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RULE 2.-If the given fum be in pounds, Shillings and pence; As 5 is equal to ; therefore divide the given fum by 8, and that quotient by 2; add the two quotients together, double the laft denomination, and you will have the answer.

What quantity of gold is equivalent £45 135. 4d.?

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PROB. 4. To find the weight of gold equivalent to any giv en number of dollars.

RULE. Divide the dollars by the numerator 8, add the quotient to the dividend, and the fum is pennyweights.

Required the weight of gold equal to 76 dollars?

76+89% and 76+91 85% pwt. Anf.

RULE OF THREE DIRECT, IN DECIMALS.

RULE. Having reduced your fractions to decimals, and ftated your queftion as in whole numbers, multiply the fecond and third together; divide by the first, and the quotient will be the answer.

1. If of a yard coft of a pound; what will 97

yards come to?

ΤΣ

{≈,625,7% =,583+ and 3,666+ rd. £. Yd.

As ,625,583 :: 9,666

9583

28998

77328

48330

,625)5,635278(9,0164+ = £9 os. 34d. Anf. 2. If 10%. of filver coft 6s. 8d. what is the price of a bowl, which weighs 1ft 70z. 13gr. ?

Anf. £6 6s. 10d. 3. If 9 yards cost £3 75. 6. ; what will

to?

yard come Anf. 35. 54d. 4. There is a ciftern which has three cocks, the first will empty it in 4 of an hour, the second in 4, and the third in 1 hour; In what time will it be emptied, if all three run together?

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5. A conduit has a cock, which, running into a ciftern will fill it in 12 minutes: This ciftern has 3 cocks ; the first will empty it in 1 hour, the fecond in 37 minutes, and the third in an hour; In what time will the ciftern be filled, if all four run together?

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Cift. h. Cift. h.

b. m.

Then, as,6: 1 :: 1 : 1,66+ = 1 40 Ans.

The following Questions are in the Coin of the United States. 6. If 19 yards cost 25dol. 7d. 5c.; what will 435% yards come to?

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D. d. c.m.

7.

19)11214,125(590,2 1 73 Anf.

If 345 yards of tape coft 5dol. id. 7c. 5m. ; what will one yard cost?

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8. If I give 12dol. 8d. 2c. 5m. for 675 tops; how many tops will 19 mills buy?

D. d. c. m. T.

d. c. m.

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RECIPROCAL PROPORTION,

OR,

RULE OF THREE INVERSE,

Teaches, by having three numbers given, to find a fourth, which fhall have the fame proportion to the fecond, as the firft has to the third.

Therefore, the greater the third term is, in respect to the first, the lefs will the fourth term be in refpect to the fecond; or, the lefs the third term is in proportion to the first, the greater the fourth must be in proportion to the fecond; and this is called reciprocal, inverted or indi rect Proportion.

The principal difficulty, that will embarrass the learner, will be, to diftinguish when the proportion is direct, and when indirect.--This is done by an attentive confideration of the fenfe and tenor of the queftion propofed: For if thereby it appears, that when the third term of the flating is less than the first, the answer must be lefs than the fecond; or when the third is greater than the first, the answer must be greater than the fecond; then the proportion is direct: But, if the third be lefs than the firft, and yet the fenfe of the queftion requires the fourh to be greater than the fecond; or if the third being greater than the first, the answer must be lefs than the fecond, the proportion is inverse,

RULE. State and reduce the terms as in the Rule of Three direct; then, multiply the first and fecond

terms

If 4 men can do a piece of work in 12 days; in what time will 8 men do it?

As 4 men: 12 days: 8 men :

4 X 12
8

=6 days, the answer.

And here the product of the first and fecond terms, that is 4 times 12, or 48, is evidently the time in which one man would perform the work; therefore, 8 men will do it in one eighth part of the time, or 6 days.

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