parts, called minutes, and each minute into 60 equal parts, called seconds. 76. The circumference' of the earth is a great circle of 360 de grees. On this circle every minute is reckoned a mile, 60 of which are equal to 1 degree or about 69 statute or common miles. 78. How many single things in 5 dozen? In 1 gross? In 5 score? sheets of paper in 21 quires? quires in 5 reams? 79. How many pounds in 21⁄2 barrels of pork? In of a barrel of shad? In 23 barrels of shad? 1 CIRCUMFERENCE, from circum, L. round, and fero, L. to bring. The distance round the outside. 80. BOOKS. A FOLIO1 is when a sheet is folded in two leaves. A QUARTO2 or 4to., is when a sheet is folded in four leaves. ALIQUOT PARTS. 81. AN ALIQUOT PART is that number which is contained in another an exact number of times: thus 5 is an aliquot part of 15, for it is contained in 15 exactly 3 times; that is, 5 is } of 15. 82. So 50 cents and 25 cents are both aliquot parts of a dollar; for 50 cents (these 2 lines mean equal to) 1⁄2 of 100 cents or 1 dollar, and 25 cents of 1 dollar. 83. Again; every 6 cent piece is an aliquot part of 100 cents or 1 dollar, being exactly of a dollar, for 64 times 16=100. 16 84. Again; every 12 cent piece is an aliquot part of 1 dollar, being exactly of a dollar, for 12 times 8=100. 85. If one 6 cent piece is, then two 6 cent pieces, which make 12 cents, are, and are equal to ; for 8 times are, which are equal to 1 whole; and 8 times equal to 1 whole. 1 8 2 are 18, which are also 1 FOLIO, from the Latin folium a leaf. 2 QUARTO, from the Latin quartus, the fourth. 3 OCTAVO, from the Latin octavus, the eighth. 4 DUODECIMO, Latin duodecimus, the twelfth. 5 An 18mo. from octavus, L. eighth, and decimus, L. tenth, both making eighteen. 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? 4 4 90. Why is or 3 equal to ? or equal to ? A. is equal to, because it means 4 of 16 equal parts, which is of them: and is equal to į, because it means 2 of 8 equal parts, which is also of them. 16 3/ 91. How many cents in of a dollar? in? in? in 3? in in ? in ? in? in 2? 3 Repeat the Table. 92. What will 4 knives cost, at 6 cents apiece? At 12 cents apiece? At 25 cents? At 50 cents? 93. How many yards of cloth may be bought for 1 dollar, at 50 cents a yard? At 25 cents a yard? At 12 cents? At 64 cents? 94. How many yards then would 5 dollars buy at 50 cents a yard? At 25 cents? At 12 cents? At 64 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? 12 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? 8 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 ́ength, 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 awful days for labor in 1 week? in 1 week? in 32 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? 19. How many wholes are 7 2 1, 2 and 3? and ?? [1}] }, 3, 3, 4, § and § ? 2 3 20. When a floor is 4 feet square, how many square feet does it contain? [4 times 4.] 21. What then is the square of 4 [16.] What the square of 5? [5 times 5.] What is the square of 6 of 7 of 8 of 10? of 20? 6? 22. The 4, before it is multiplied by itself, is called the square root of 16;1 what then is the square root of 25, and why? 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 ?3 A. 20. 26. What is the cubic or solid content of a regular cube 10 inches 'ong, 10 inches wide, and 10 inches thick? 27. What is the 10 and 1000 each called? A. The 10 is called he 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? A. 2, because 2 times 30. What is the cube root of 8, and why? 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 con tains 1000 solid or cubic inches? What is the cube of 10? 39. If of a barrel of flour cost 4 dollars; what will of a barrel cost? What will the whole barrel cost []? 3 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 7 first. 41. Henry's age is 14 years, which is of his brother's age. How old is his brother? Find how much is first. 3 42. A man lost 15 dollars, which was of all the money he had; 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? 12 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 te each indorsed; a roll, list, or catalogue; a row of soldiers ranged one behind another from front to rear |