 | George Washington Hull - Geometry - 1807 - 408 pages
...§457 §431 Therefore vol. P = axbx c. QED 459. COH. 1. — Since a X b is the area of the base, Then the volume of a rectangular parallelepiped is equal to the product of its base and altitude. 4CO. COR. 2. — The volume of a cube is equal to the cube of its edge. For,... | |
 | John Hind - 1856 - 346 pages
...supposed first to be numerically exhibited. 209. The numerical representative of the solid Content or Volume of a rectangular parallelepiped is equal to the product of the magnitudes representing its length, breadth and thickness. Let ABFM represent a rectangular parallelepiped... | |
 | Eli Todd Tappan - Geometry - 1868 - 432 pages
...square whose side is of that length is the measure of area. VOLUME OF PARALLELOPIPEDS. 691. Theorem — The volume of a rectangular parallelepiped is equal to the product of its length, breadth, and altitude. In the measure of the rectangle, the product of one line by another... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...2ffRH, is the area of the convex surface of the cylinder. Flo. 2fl6. PROPOSITION X. 483. Theorem. — The volume of a rectangular parallelepiped is equal to the product of the three edges of one of its triedrah. DEM.— Let H-CBFE be a rectangular parallelopiped. 1st. Suppose... | |
 | Edward Olney - 1872 - 270 pages
...2*RH, is the area of the convex surface of the cylinder. PROPOSITION X. Fio. 298. 482. Theorem.—The volume of a rectangular parallelepiped is equal to the product of the three edges of one of its triedrals. DEM.—Let H-CBFE be a rectangular parallelopiped. 1st. Suppose... | |
 | David Munn - 1873 - 160 pages
...with Q, we have P and -sr = —. Q mn Multiplying these ratios, we have P_ abc Q mnp' PROP. IV.— The volume of a rectangular parallelepiped is equal to the product of its three dimensions, the unit of volume being the cube whose edge is the linear unit. Let a, b, and... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...of its edge. 540. -Сок. II. The product a X b represents the base when с is the altitude; hence: The volume of a rectangular parallelepiped is equal to the product of us base by its altitude. 541. SCHOLIUM. When the three dimensions of the rectangular parallelopiped... | |
 | Edward Olney - Geometry - 1883 - 352 pages
...n, p, q, r, and s, we have A. BC P » * i * t Ax Q abe TXTXT 111 PROPOSITION XI. 588. Theorem. — The volume of a rectangular parallelepiped is equal to the product of its three adjacent edges. DEMONSTRATION. Let P be any rectangular parallelopiped whose adjacent edges... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 342 pages
...multiplying these ratios together, Q p \ \ J x •. \ X N i i p. I \ \ i PROPOSITION X.— THEOREM. 29. The volume of a rectangular parallelepiped is equal to the product of its three dimensions, the unit of volume being the cube whose edge is the linear unit. Let a, b, c,... | |
 | Edward Albert Bowser - Geometry - 1890 - 418 pages
...parallelopipeds whose dimensions are 4, 7, 9, and 6, 14, 15, respectively. Proposition 1 1 . Theorem. 606. The volume of a rectangular parallelepiped is equal to the product of its three dimensions. Hyp. Let P be the rectangular parallelepiped, a, b, and c its dimensions, and... | |
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The volume of a rectangular parallelepiped is equal to the product of its three dimensions. 
