A key to the national arithmetic: exhibiting the operation of the more difficult questions in that work, for the use of teachers only

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R. S. Davis, 1861 - Mathematics - 252 pages
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Page 205 - ... and 3d, 8 small squares, each having its side equal in length to the thickness of the plank. Since the box is twice as wide as it is high, and twice as long as wide, the area of an end is doubled in a side, and quadrupled in the top or bottom. Then an end, a side, and the top or bottom, contain 7 times as many large squares, strips, and small squares as an end; that is, 14 large squares -j...
Page 246 - DA, we have the semi-diameter of the larger circle, 5.7735027 -(- 5 = 10.7735027. By multiplying this last number by 2, we have the diameter of the larger circle, 10.7735027 X 2 = 21.5470054. As the area of a circle may be found by multiplying the square of the diameter by .785398, therefore, by dividing the area by .785398, the quotient will be the square of the diameter. The area of the lady's field is 500 acres = 80000 square rods ; 80000 -=-.785398 = 101859.28 square of the diameter ; V 101859.28...
Page 248 - Find the altitude of an equilateral triangle each side of which is 12 inches.
Page 179 - If now 18 be divided into two parts, one of which shall be twice as great as the other, we have 12 and 6 ; hence, if one note of $200 run 12mo., and the other note of 8200 run 6mo., it will be equivalent to $200 in ISino., or to $400 in 9nio.
Page 205 - These shaded parts represent the thickness of the plank, and form part of the external area of the side and end of the box, but no part of the side and end pieces. If we draw the line AB vertically across the middle of the end of the box, the whole end is divided into 2 equal squares; but, taking away the shaded...
Page 244 - The distance between the rings being 5 feet, it follows that the diameter of the inner ring will be 10 feet, and the diameter of the outer ring 20 feet.
Page 204 - ... 12 strips -\- 8 small squares = the area of the board = 49 sq. ft. = 7146 sq. in. •Notice the difference between the side and side piece, and the end and end piece, of the box. Fig. 2. From this, deduct...
Page 205 - ... side and end of the box, but no part of the side and end pieces. If we draw the line AB vertically across the middle of the end of the box, the whole end is divided into 2 equal squares; but, taking away the shaded portions, it is evident that the end piece. is not divided...
Page 245 - granted" that cones, spheres, and all similar bodies, are to each other as the cubes of their homologous sides...

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