 | Elias Loomis - Conic sections - 1877 - 458 pages
...equal to the volume of the cone. But, whatever be the number effaces of the pyramid, its volume is equal to one third of the product of its base by its altitude ; hence the volume of the cone is equal to one third of the product of its base by its altitude.... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...to oue third the product of its base by its altitude. THEOREM XVII. 69. The volume of any pyramid is equal to one third of the product of its base by its altitude. Let A-BCDEF be any pyramid; its volume is equal to one third the product of its base BCDEF... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 170 pages
...is, a triangular pyramid is one third, etc. Cor. 1.—Hence, the volume of a triangular pyramid is equal to one third of the product of its base by its altitude (Theo. XXI). Cor. 2.—The volume of any pyramid whatever, is equal to one third the product... | |
 | Charles Davies - Geometry - 1886 - 352 pages
...solidity of a sphere is equal to one third of the product if BOOK VI. Of the Sphere. This polyedron may be considered as formed of pyramids, each having...the solidity of each pyramid, will be equal to one th1rd of the product of its base by its altitude (Th. xvii). But if we suppose the faces of the polyedron... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 246 pages
...S-ABC =0= S'-A'B'C'. § 284 314 PROPOSITION XVIII. THEOREM. 651. The volume of a triangular pyramid is equal to one third of the product of its base by its altitude. Let V denote the volume, B the base, and H the altitude, of the triangular pyramid S-ABC.... | |
 | George Albert Wentworth - Geometry - 1899 - 496 pages
...S-ABC =0= S'-A'B'C'. §284 314 PROPOSITION XVIII. THEOREM. 651. The volume of a triangular pyramid is equal to one third of the product of its base by its altitude. Let V denote the volume, B the base, and H the altitude, of the triangular pyramid S-ABC.... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...greater than pyramid V. .: V= V. PROPOSITION XVII. THEOREM 593. The volume of a triangular pyramid is equal to one third of the product of its base by its altitude. Hyp. V is the volume, B the base, and a the altitude of the triangular pyramid E-ABC. To... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...O'-A'B'C'. .'. O-ABC ^O'-A'B'C'. PROPOSITION XVII. THEOREM 593. The volume of a triangular pyramid is equal to one third of the product of its base by its altitude. 7i II PYRAMIDS To prove. V=\B x a. Proof. On ABC construct the prism ABC-DEF, having its... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...O'-A'B'C'. .'. 0-ABC ^O'-A'B'C'. PROPOSITION XVII. THEOREM 593. The volume of a triangular pyramid is equal to one third of the product of its base by its altitude. DFD To prove. V= \ B x a. Proof. On ABC construct the prism ABC-DEF, having its lateral edges... | |
 | George Albert Wentworth - Geometry, Solid - 1902 - 246 pages
...Hence, S-ABC ^ S'-A'B'C'. §284 PROPOSITION XVIII. THEOREM. 651. The volume of a triangular pyramid is equal to one third of the product of its base by its altitude. Let V denote the volume, B the base, and H the altitude, of the triangular pyramid S-ABC.... | |
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This pulyedrun may be considered as formed of pyramids, each having for its vertex the centre of the sphere, and for its base one of the faces of the polyedron. 
