will do the same work in a shorter time than six men, it is plain that the fourth term must be less than the third: therefore 30 men, the greater of the remaining numbers, is written in the first term. Besides, it is plain that the fourth term must be just so many times less than 40, as 6 is less than 30.

Ex. 5. If 25 yards of cloth cost £2 3s 4d, what will 5 yards cost at the same rate?

When we come to divide the product of the 2d and 3d terms by the first, it is found the £10 does not contain 25. We then reduce to the next lower denomination and divide as in division of denominate numbers.

Ex. 6. If 3cwt. of sugar cost £9 2s Od, what will 4cwt. 3gr. 26lb. cost at the same rate?

£9 2s Od

20

182

12

2184

33676. 55876 :: 2184d: answer

110. If the product of the two mean terms be divided by either of them, the quotient will be the other. But the product of the two extremes is equal to the product of the two means § 107, therefore, we have the following

RULE.

Divide the product of the first and fourth terms by the second term, and if the work is right the quotient will be equal to the third term.

QUESTIONS.

§ 104. If 1 yard of cloth cost $2, what will 6 yards cost? How many numbers are considered in this question? What are they called? How many were known, or given? Name the terms. How many times does the 2d term contain the first? How many times does the fourth contain the third? How many times is the 2d term greater than the first?

§ 105. When are four numbers in geometrical proportion? How are they written? What terms of a proportion expresa quantities of the same kind?

106. How do you find the 4th term of a proportion?

107. What are the first and fourth terms called? What are the second and third terms called? What is the product of the two extremes equal to ?

108. From what does the Rule of Three take its name? 109. What is the first thing to be done in stating a ques tion? Which number do you make the third term? How do you determine which to put in the first? After stating the question, how do you find the 4th term? What will be its denomination ?

§ 110. How do you prove the Rule of Three ?

APPLICATIONS.

1. If 4 hats cost $12, what will 55 cost at the same rate?

Ans. $165. 2. What is the value of 2cwt. of sugar at 5d. per pound?

Ans. £4 13s 4d. 3. If 40 yards of cloth cost $170, what will 325 yards cost?

Ans. $1381,25. 4. If 240 sheep yield 66026. of wool, how many pounds will be obtained from 1200 ?

Ans. 3300lb. 5. If 2 gallons of molasses cost 65 cents, what will 3 hogsheads cost?

Ans. $61, 42.

6. If a man travels at the rate of 210 miles in 6 days, how far will he travel in a year supposing him not to travel on Sundays?

Ans. 10955 miles. 7. If 1 yard of cloth cost $3,25, what will be the cost of 3 pieces each containing 25 yards? Ans. $243,75. 8. If 30 barrels of flour will support 100 men for 40 days, how long would it subsist 25 men? Ans. 160 days.

9. If 30 barrels of flour will support 100 men for 40 days, how long would it subsist 400 men? Ans. 10 days.

10. A owes B £679 6s., but compounds with him by paying 3s. 4d. on the pound: how much does B receive of his debt?

Ans. £113 4s. 4d.

11. If 90 bushels of oats will feed 40 horses for 6 days, how long would 450 bushels last them? Ans. 30 days. 12. If 5cwt. 3qr. 14lb. of sugar cost £6 1s. 8d., what will 35cwt. 28lb. cost?

'Ans. £36 10s. 13. What is the cost of 3cwt. of coffee at 15d. per pound?

Ans. £21. 14. If 3 quarters of a yard of velvet cost 7s. 3d., how many yards can be bought for £13 15s. 6d. ? Ans. 28yd. 2qr. 15. If an ingot of gold weighing 97b. 9oz. 12pwt. be worth £470 8s., what is that per grain?

Ans. 2d. 16. Bought 4 bales of cloth, each containing 6 pieces, and each piece 27 yards, at £16 4s. per piece : what is the value of the whole, and the cost per yard?

Ans. £388, 16s. at 12s. per yard. 17. What will be the cost of 72 yards of cloth, at the rate of £5 12s. for 9 yards?

Ans. £44 16s. 18. A person's annual income is £146: how much is that per day?

Ans. 8s.

If 3 paces, or common steps of a person, be yards, how many yards will 160 paces

Ans. 106yd. 2ft.

20. What length must be cut off from a board that is 9 inches wide, to make a square foot, that is, as much as is contained in 12 inches in length and 12 in breadth?

Ans. 16 inches."

21. If 750 men require 22500 rations of bread for a month, how many rations will a garrison of 1200 men require?

Ans. 36000. 22. If 7cwt. 1gr. of sugar cost $64,96, what will be the price of 4cwt. 2qr.?

Ans. $40,32. 23. The clothing of a regiment of foot of 750 men amounts to £2831 5s.: what will it cost to clothe a body of 3500 men?

Ans. £13212 10s. 24. How many yards of carpeting, that is 3 feet wide, will cover a floor that is 27 feet long and 20 feet broad?

Ans. 60 yards. 25. What is the cost of 6 bushels of coal at the rate of £1 14s. 6d. the chaldron ?

Ans. 5s. 9d. 26. If 6352 stones of 3 feet long will complete a certain quantity of wall, how many stones of 2 feet long will raise the like quantity?

Ans. 9528. 27. If a person can count 300 in 2 minutes, how many can he count in a day?

Ans. 216000. 28. A garrison of 536 men have provisions for 365 days: how long will those provisions last if the garrison be increased to 1124 men?

Ans. 174 days and $4 29. What will be the tax upon £763 15

rate of 3s. 6d. per pound sterling?

Ans. £133