87. What is meant by an aliquot part? 81. Why is 5 an aliquot part of 15 81.

88. What aliquot part of a dollar is 64 cents? is 50 cents? is 25 cents? 12 cents? Why is each an aliquot part?

89. Why is equal to ? See 85. 90. Why is or equal to ? A. is equal to, because it means 4 of 16 equal parts, which is of them and is equal to 4, because it means 2 of 8 equal parts, which is also of them.

91. How many cents in of a dollar? in? in? in 3? in

in ? in 1? in? in? Repeat the Table.

92. What will 4 knives cost, at 6 cents apiece? At 12 cents apiece? At 25 cents? At 50 cents?

bought for 1 dollar, at 50 cents? At 6 cents?

93. How many yards of cloth may be cents a yard? At 25 cents a yard? At 12 94. How many yards then would 5 dollars buy at 50 cents a yard? At 25 cents? At 12 cents? At 6 cents?

95. Mary, having purchased 29 yards of ribbon for 61 cents a yard, gave the merchant a 2 dollar bill; how much change ought she to have received?

MISCELLANEOUS

QUESTIONS.

VIII. 1. A man bought 12 bushels of wheat for 30 dollars, and sold 9 bushels for 25 dollars. How many bushels had he left, and what did they cost him?

2. Suppose a stage goes 120 miles in 12 hours, and a railroad car 3 times as fast, how far does each go in an hour? How far would they be apart in 2 hours after they had started?

3. How many times 12 in 27? 2 times 12 are how many? How many times 11 in 30? 2 times 11 are how many?

4. How many inches in 8 nails? yards in 10 rods? cents in 5 dollars? shillings in 2 pounds 2 shillings?

5. When a coat costs 2 pounds 2 shillings in London, how many guineas, at 21 shillings each, will pay for it?

6. If 1 quart of rum is enough to make one man act like a fool; how many at that rate may be made fools by 10 gallons?

7. What would a narrow strip of board only 4 inches wide and 3 feet or 36 inches long cost, at 2 cents a square foot? How many square rods make 1 acre? [4 times 40.]

8. When a piece of land is 40 rods long, how wide must it be to make 1 acre? A. 4 rods, [for 40 in 160=4 times.] How wide to make 2 acres? When a piece is 80 rods long, how wide must it be to make 1 acre ?-to make 2 acres?

9. How many solid feet in a block whose three dimensions, viz length, breadth and thickness, are each 2 inches? How many when each dimension is 3 inches? is 4 inches? is 5 inches?

10. How many cord feet in a small pile of wood, 4 feet long, 2 feet wide and 2 feet deep? How many in a pile 8 feet long, 2 feet wide and 2 feet high? In one 8 feet long, 4 feet wide and 4 feet high? 11. If a man earns 1 dollar a day, how much will he earn in the lawful days for labor in 1 week? in 1 week? in 3 weeks?

12. At 1 dollar a day, how many weeks' labor may be hired for 13 dollars? [2.] for 22 dollars? for 20 dollars? for 32 dollars?

13. What will 16 pounds of butter cost at 12 cents a pound? What will 24 pounds cost? 25 pounds cost?

14. What is the cost of 4 bushels of potatoes at 25 cents a bushel? of 20 bushels? 40 bushels? 41 bushels?

15. When 3 bushels of dried apples sell for 6 dollars, what are they a bushel? What would 2 bushels cost? 8 cost? 20 cost?

16. If 5 yards of broadcloth sell for 20 dollars, what will 8 yards sell for at the same rate? Find the price of 1 yard first. What would be the price of 9 yards? 11 yards? 12 yards? 20 yards?

17. If 8 pounds of sugar cost 1 dollar, what will 3 pounds cost? How many pounds may be bought for 4 dollars? for 5 dollars? for 10 dollars?

18. When 4 bushels of oats cost 2 dollars, how many bushels may be bought for 2 dollars 50 cents? for 3 dollars 50 cents? for 5 dollars for 8 dollars 50 cents?

2

19. How many wholes are,, and? and ? [1], 3, 3, 4, 20. When a floor is 4 feet square, contain? [4 times 4.]

and 3? 2, 3, 4, 5 and ૧ and ?

how

many square feet does it

21. What then is the square of 4?
[5 times 5.] What is the square of 6?
22. The 4, before it is multiplied
root of 16;' what then is the square root of 25, and why?

[16.] What the square of 5?
of 7? of 8? of 10? of 20?
by itself, is called the square

A. 5, because 5 times 5 are 25

23. What is the square root of 4 of 9? 16? of 36? of 64? of 100 of 144? of 400? of 10000.

1 ROOT. That part of a plant which penetrates the ground and supports the plant; the first ancestors; the original cause of any thing. To take root means to become firmly fixed. The square root of any number is so called because it is the first number that is repeated or multiplied.

24. In a square room which is calculated to accommodate 100 boys, how many must sit on a single bench?

25. Suppose 400 scholars should wish to form themselves into a solid phalanx,' or square body, how many must stand in each rank❜ and file 13 A. 20.

26. What is the cubic or solid content of a regular cube 10 inches long, 10 inches wide, and 10 inches thick?

27. What is the 10 and 1000 each called? A. The 10 is called the cube root of the 1000, and the 1000 the cube of 10.

28. What then is the cube of 2, and why? A. 8, because 2 times 2 are 4, and 2 times 4 are 8.

29. What is the cube of 3? What is the cube of 4?

30. What is the cube root of 8, and why? A. 2, because 2 times 2 are 4, and 2 times 4 are 8.

31. What is the cube root of 27 of 125? of 1000?

32. What is the length of each side of a cubical block which contains 1000 solid or cubic inches? What is the cube of 10?

of what number?

of what number?

33. 6 is of what number? 10 is 34. 12 is of what number? 11 is 35. What is that number of which is 9? of which is 8? of which is 10?of which is 12? of which is 11? 36. What number is that of which is 10? must be 5. 4. 15. 37. What number is that of which is 24? Find first. A. 32. 38. What number is that of which is 16?- of which is 30? of which is 635 of which is 60? of which is 72?

39. If of a barrel of flour cost 4 dollars; what will of a bar

rel cost? What will the whole barrel cost []?

40. A man bought of a load of hay for 6 dollars, what was the whole load worth at that rate? Find the value of

first. of his brother's age. is first.

of all the money he had;

41. Henry's age is 14 years, which is How old is his brother? Find how much 42. A man lost 15 dollars, which was how much had he? How much had he left? 43. A man, who owed a certain sum of money paid 12 dollars, which was of the debt; how much remained unpaid?

44. A man, who lent a certain sum of money, could collect only 8 dollars, which was of it; how much did he lose?

45. If a man, having a quantity of flour on hand, sells 20 barrels, which is of it; how much will he have left?

46. Suppose a man sells of a barrel of flour, for 14 dollars, what will the remainder of the barrel bring at that rate?

1 PHALANX. A square battalion or body of soldiers, formed in ranks and files close and deep; any body of troops or men formed in close array, or any combination of people distinguished for their intrepidity and union.

2 RANK. A row or line; men standing side by side in a line; a line of things; degree; class; order; degree of dignity.

3 FILE. A thread, string or line; a bundle of papers tied together with the title to each indorsed; a roll, list, or catalogue; a row of soldiers ranged one behind another from front to rear.

47. A boy having a stick, broke it into two parts, one of which was 2 feet long, or of the length of both parts; what was the length of the stick before it was broken?

48. If and of a number are 16; what is that number?

NOTE-Say and are which is 16; then is of 16, which is 4, and is 5 times 4, which is 20. A. 20.

49. If and of a number are 10; what is that number?

what is that number?

50 If and of a number are 70; 51. There is a pole erected so that stands in the mud, in the water, and the rest which is 10 feet above water; what is the entire length of the pole?

52. There is a pole, above water, in the water; and 8 feet in. the mud; what is the entire length of the pole?

53. Four men A, B, C, and D purchased a sloop together. A took of it, B., C. and D, the rest, which cost him 100 dollars. What was D's part? What did the other parts severally cost? What did the whole sloop cost?

54. The fifth part of an army was killed; of it taken prisoners, and 1000 fled; how many were there in the army? How many were killed? How many were taken prisoners?

55. In an orchard of fruit trees, of them bear apples, bear plums: 8 bear peaches, and 2 bear cherries: how many trees of each sort are there in the orchard? How many trees does the orchard contain? 8 trees and 2 trees are 10 trees which are }.

56. In a certain school of the pupils study Arithmetic, study Grammar and 10 only read and spell: what is the number of scholars in the school? What is the number in Arithmetic? What is the number in Grammar?

57. A man having 16 oranges would divide them so that his own son Samuel may have 4 more than his neighbor's son George; How many must he give to each?

NOTE Give 4 to Samuel first then divide the rest equally between the two? A. George 6, and Samuel 10. 58. A gentleman bought a horse and carriage for 240 dollars, paying 40 dollars more for the horse than for the carriage; what did each cost?

59. A man and a boy were both hired for 20 dollars a month, the man receiving 4 dollars a month more than the boy; what would the wages of each amount to in a year?

60. A man, woman, and boy were hired a week for 21 dollars; the woman to receive 5 dollars more than the boy, and the man 5 dollars more than the woman; at that rate what would the wages of each amount to in one month.

3

ARITHMETIC.

PART SECOND.

AS CONSISTING BOTH IN THEORY2 AND PRACTICE3

QUANTITY AND NUMBER.

IX. 1. QUANTITY' is any thing that may be increased or diminished; as, a sum of money, a line, weight.

2. A QUANTITY is ascertained to be great or small, much or little, only in comparison with a known quantity of the same kind, which is either greater or smaller.

3. For example, ten thousand hogsheads of water is a great quantity, compared with one gill of water, but quite a small quantity, compared with the water in the ocean.

4. A UNIT," which represents a single thing; as, 1 hat, 1 ounce, &c. is fixed upon as the criterion' or known quantity by which to measure all other quantities of that kind.

5. Thus 2 would express a quantity 2 times as great as 1, that is, 2 units; 3, 3 times as great, or 3 units, and so on.

6. QUANTITIES then of every kind are properly expressed by NumBERS; as 5 bushels of rye, oranges, &c.

7. A CONCRETE NUMBER has reference to some particular object or objects; as, 1 man, 2 dollars, 3 benches.

8. AN ABSTRACT NUMBER has no reference to any object whatever; as 1, 2, 3.

IX. Q. What is Quantity? 1. How is a quantity ascertained to be great or small? 2. Give an example? 3. What is the criterion for estimating different quantities? 4. Illustrate it? 5. How are quantities expressed? 6. What is a Concrete Number? 7. An Abstract Number? 8.

1 ARITHMETIC, [G. Arithmetike.] Reckoning by numbers; calculating.

2 THEORY, [F. theorie. L. theoria.] Speculation; a system, plan, scheme; opposed to practice.

3 PRACTICE, [F. pratique.] Habit, use, dexterity, method.

4 QUANTITY, [Quantitas.] Any thing that may be increased or diminished; bigness; bulk, weight; measure.

5 UNIT, [L. unus.] One; a word denoting a single thing.

6 REPRESENT. To show; to exhibit; to describe.

7 CRITERION, [G. kriterion.] A standard of judging; a distinguishing mark.

8 CONCRETE, [L. concretus.] United in one mass; a compound; a term involving both the thing and its quality; as, a white fence; 2 mellons; 1 cent.

9 ABSTRACT, [L. abstractus.] Separate; distinct; expressing only quality or num ber; as, whiteness; 1, 2, 3, &c.