Operations corresponding to the Rule of Three have already been taught, in Relations of Numbers, Chap. VI. To show the correspondence, suppose it to be asked-If 3 yards of cloth cost 4 dollars, what will 9 yards cost?

In Relations of Numbers,

1

In the Rule of Three, the question stands thus

3:94: what number?

3:94: A

9

3)36

12 Ans.

12 Ans.

1. If I buy 871 yards of cotton cloth for 78 dollars 39 cents, what is the price of 29 yards of the same?

2. If 13 yard of cotton cloth cost 42 cents, what will 87 yards cost, at the same price per yard?

1.75 87.5= .42 : A

3. If I can buy 1

yard of cotton cloth for 6 pence, how many yards can I buy for £10 6s. 8d.?

6d. 1qr.

10 6s. 8d. lyd. 1qr.: A

4. If I buy 54 barrels of flour for 297 dollars, what must I give for 73 barrels, at the same rate?

5. If 7 workmen can do a piece of work in 12 days, how many can do the same work in 3 days?

6. If 20 horses eat 70 bushels of oats in 3 weeks, how many bushels will 6 horses eat in the same time?

7. If a piece of cloth containing 76 yards cost 136 dollars 80 cents, what is that per ell English?

8. If a staff 4 feet long cast a shadow 7 feet in length, on level ground, what is the height of a steeple, whose shadow at the same time measures 198 feet?

9. How many yards of paper, 2 feet wide, will hang a room, that is 20 yards in circuit, and 9 feet high?

10. A certain work having been accomplished in 12 days, by working 4 hours a day, in what time might it have been done by working 6 hours a day?

11. If 12 gallons of wine are worth 30 dollars, what is the value of a cask of wine, containing 31 gallons?

12. If 83 yards of cloth cost 4 dollars 20 cents, what will 13 yards cost, at the same rate?

13. How many yards of cloth yard wide, are equal to 30 yards 14 yard wide?

14. If 7 pounds of sugar cost 75 cents, how many pounds can I buy for 6 dollars?

15. If 2 pounds of sugar cost 25 cents, and 8 pounds of sugar are worth 5 pounds of coffee, what will 100 pounds of coffee cost?

16. A merchant owning of a vessel, sold of his share, (,) for 957 dollars. What was the vessel

worth, at that rate?

17. A merchant failing in trade, owes 62936 dollars 39 cents; but his property amounts to only 38793 dollars 96 cents, which his creditors agreed to accept, and discharge him. How much does the creditor receive, to whom he owes 2778 dollars 63 cents?

18. Bought 3 tons of oil, for 503 dollars 25 cents; 85 gallons of which having leaked out. I wish to know at what price per gallon I must sell the residue, that I may neither gain nor lose by the bargain.

19. If, when the price of wheat is 6s. 3d. a bushel, the penny loaf weighs 9 oz., what ought it to weigh, when wheat is at 8s. 21 d. a bushel?

20. If 15 yards of cloth 2 yard wide cost 6 dollars 25 cents, what will 40 yards, being yard wide, cost?

21. Borrowed of a friend 250 dollars for 7 months; and then, to repay him for his kindness, I loaned him 300 dollars. How long must he keep the 300 dollars, to balance the previous favor?

22. If 4 cwt. be carried 36 miles for $51, how many pounds can be sent 20 miles for the same money ?

23. A person owning of a coal mine, sells of his 394 share for 570 dollars. What is the whole mine worth? 24. If the discount on $106, for a year, be $6, what is the discount on $477, for the same time?

XI.

MEASUREMENT

OF SURFACES, SOLIDS AND CAPACITIES.

It has already been taught, that surfaces are measured in squares, and, that solid bodies are measured in cubes. A SQUARE is a figure, that has four equal sides, and four equal angles. Its angles are called right angles: angles more pointed are called acute angles; and those less pointed, obtuse angles. To find the area of a square, in smaller squares-Multiply one side into itself.

1. How many square feet are there in a table that measures 4 feet on every side? How many square inches? A PARALLELOGRAM is a four-sided

figure, having opposite sides equal, and having four right angles. To find the area of a parallelogram-Multiply the length into the breadth.

sof

2. How many square rods in a garden measuring 4 rods in length, and 3 in breadth? How many square feet? A TRIANGLE is a figure, that has three sides and three angles. A triangle, which has one right angle, is called a RIGHT-ANGLED TRIANGLE. To find the area of a right-angled triangle-Multiply the base by half the perpendicular.

BASE Biedrbay 3. How many square rods are there in a right-angled triangular field, measuring 98 rods on the base, and 75 rods on the perpendicular? How many acres?

A CIRCLE is a plane surface, bounded by one curve line, called the circumference. The diameter being known, to find the circumference-Multiply the diameter by 3.14159. Then, to find the area-Multiply half the circumference by half the diameter.

4. How many square inches are there in the head of a barrel, the diameter of which measures 17 inches? A CUBE is a regular solid body, having six equal, square sides. To find its contents in smaller cubes-Multiply the breadth of a side twice into itself. The product of the length, breadth, and thickness is the contents of any thing, whose opposite sides are equal.

5. How many cubic inches are there in a box measuring 34 inches in length, 26 in width, and 18 in depth? A CYLINDER is a round body, with equal, circular ends. To find its cubical contents-Find the area of one end, and multiply this by the length.

6. How many cubic inches are there in a drum measuring 16 inches across the head, and 18 inches in length?

PLASTERING AND PAVING are charged by the square yard. Their surface is first found in square feet, and then reduced to square yards.

7. How many square yards of plastering in the ceiling and four sides of a room, that is 15 feet long, 12 feet wide, and 10 feet high; deducting two doors, 7 by 4 feet each, and four windows, 5 by 3 feet each ?

6

8. How many bricks are required to pave a cellar, that is 48 feet long and 30 feet wide; allowing each brick to be 8 inches long, and 3.8 inches wide? Here find the area of the cellar in square inches, and divide it by the inches in the area of a brick.

square

SHINGLES AND CLAPBOARDS are of various dimensions. Therefore, to know how many are requisite to cover

a building, we find the number of square inches in the roof or side to be covered, and divide this number by the number of square inches, that one shingle or clapboard will cover.

9. If shingles 4 inches in width be laid so that 6 inches of their length, is exposed to the weather, how many are required to cover a roof 45 by 32 feet?

10. How many clapboards, each covering 46 by 4 inches, are sufficient for the side of a house 45 by 22 feet?

BOARDS are sold by the thousand square feet, and each board is measured thus-Multiply the length in feet by the width in inches, and divide the product by 12; the quotient will be square feet.

11. How many square feet are there in 17 boards, each board being 21 feet long, and 18.5 inches wide?

12. How many square feet of boards will floor a room 14 by 18 feet, allowing of the stuff for waste?

PLANK AND JOIST are measured by finding how many square feet of boards, one inch in thickness, they are equal to. Therefore-Multiply the length in feet by the width in inches, and this product by the depth in inches; then divide the last product by 12, for the square feet.

13. How many square feet in a plank that is 9 feet in length, 14 inches in width, and 2.4 inches in depth?

14. How many square feet in a joist that is 13 feet long, 4 inches wide, and 8.2 inches deep?

TIMBER is sold by the cubic ton. To measure hewn timber-Multiply the length in feet by the width in inches, and this product by the depth in inches; divide by 144, for the cubic feet, and then by 50 for the tons.

To measure round timber-Take the circumference in inches, by girding the log, one-third of the way from the but to the top; then multiply the length in feet, by the square of of the circumference; divide by 144 for the cubic feet, and then by 40 for the tons.

15. How much hewn timber in a stick measuring 25 feet in length, 19 inches in width, and 20 inches in depth? 16. How much round timber in a log, 30 feet long, and 55 inches in circumference?