LESSON 7. A cabinet-maker had three pieces of plain furniture finished off by the foot; one piece 4 feet 3 inches long, and 3 feet 7 inches wide; a second piece 5 feet 8 inches long, and 4 feet 5 inches 7 seconds wide; and a third piece 6 feet 9 inches 3 seconds long, and 4 feet 6 inches wide: how many superficial square feet did the whole contain? Answer, 71 ft. 0 in. 0′′ 2′′ A plasterer overlaid the walls of a room 21 feet 3 inches long, 14 feet 4 inches wide, and 7 feet 5 inches high; how many square feet were contained in the four superficies, after deducting 14 feet for the fire place? Answer, 513 f. 9 in. 10" How many solid feet in a stick of timber 48 feet 6 inches long, 1 foot 3 inches thick, and 1 foot 9 inches wide? PROOF OF DUODECIMALS. The length of the stick in feet and in. 48 6 Inches in a foot x by 12 divided by 1728, that is, the number of solid inches in a By the last operation we can perceive the utility of Duodecimals: this requires one hundred and nineteen figures, while that immediately under Lesson 9, requires only thirty-three. LESSON 10. A carman undertook to move a bank of earth, 224 feet 7 inches in length, 48 feet 9 inches in breadth, and 7 feet 5 inches in height; how many solid feet in the bank? Multiply the length, Answer, 81200 ft. 10 in. 11" 3" 224 ft. 7 in. 48 9 Multiply by 8 and by 6 for 48 as in Compound Multiplication. Then take aliquot parts arising from 9 inches-Consider first, that the bank contains 48 feet in breadth, and a strip also 9 inches wide; consequently, the breadth must be 48 feet, and of a foot, because 9 inches make of a foot: Now the half of the 224 feet 7 inches, will make a strip a foot wide, and the half of that half, will make a strip of a foot wide; then added to, will make, or a strip 9 inches wide. This superficial content must be multiplied by the height, viz. 7 ft. 5 in. First multiply by 7 feet; then take aliquot parts arising from 5 inches: say, 4 inches are of the mul tiplicand, and 1 inch is the of that third: This opera tion will produce the solid content in cubic feet. How many solid feet in a stick of timber 28 feet long, 1 ft. 6 in. wide, and 1 ft. 3 in. thick? 1. As the stick is 28 feet long, and 1 foot 3 inches thick; so there must be 28 superficial feet, and the fourth of 28 on one side; because a strip 28 feet long, and 3 inches wide, |