 | Adrien Marie Legendre - Geometry - 1822 - 394 pages
...frustum that remains when the little pyramid is taken away, is equal to the sum of three pyramids having for their common altitude the altitude of the frustum,...and whose bases are the lower base of the frustum, the upper one, and a mean proportional between the two bases. Let ABCDE be a pyramid cut by the plane... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...Hence the frustum of a triangular pyramid is equivalent to three pyramids whose common altitude is that of the frustum and whose bases are the lower base of the frustum, the upper base, and a mean proportional between the two bases. PROPOSITION XIX. THEOREM. Similar triangular... | |
 | James Bates Thomson - Geometry - 1844 - 268 pages
...frustum that remains when the small pyramid is taken away, is equal to the sum of three pyramids having for their common altitude the altitude of the frustum,...and whose bases are the lower base of the frustum, the upper one, and a mean proportional between the two bases. Let SABCDE be a pyramid cut by the plane... | |
 | Nathan Scholfield - 1845 - 894 pages
...faces, minus those faces which form the solid angle whence the planes of division proceed. is that of the frustum, and whose bases are the lower base of the frustum, the upper base, and a mean proportonal between the two bases. PROPOSITION XXIX. THEOREM. The frustum... | |
 | Benjamin Peirce - Geometry - 1847 - 204 pages
...surface described is the convex surface of the frustum of a right cone ; and its area is as, in f5 397, the product of the revolving line by the circumference...base, and a mean proportional between them. Proof. Let ABCD&c. JtfJVOP &c. (fig. 171) be the given frustum. Denote the area of the lower base ABCD &c. by... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...THEOREM. A frustum of a cone is equivalent to the sum of three cones, having the same altitude with the frustum, and whose bases are the lower base of...upper base, and a mean proportional between them. gon let a regular pyramid be constructed having its vertex in A. Then will ECDEFG-bcdefg be a frustum... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...Hence the frustum of a triangular pyramid is equivalent to three pyramids whose common altitude is that of the frustum and whose bases are the lower base of the frustum, the upper base, and a mean proportional between the two bases. PROPOSITION XIX. THEOREM. Similar triangular... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...frustum of a cone is equivalent to the sum of the solidities of three cones whose common altitude is the altitude of the frustum, and whose bases are, the lower base of the frustum, the upper base of the frustum, and a mean proportional between them. Let AEB-CD be the frustum of a... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...frustum of a cone is equivalent to the sum of the solidities of three cones whose common altitude is the altitude of the frustum, and whose bases are, the lower base of the frustum, the upper base of the frustum, and a mean proportional between them. Let AEB•CD be the frustum of... | |
 | Education - 1857 - 894 pages
...ANALYTICALLY. The solidity of the frustum of a pyramid ts equal to the sum of three pyramids having for bases the lower base of the frustum, its upper base, and a mean proportional between these two bases, and for a common altitude that of the frustum. Let B be the base and A the altitude... | |
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The volume of the frustum of any pyramid is equal to the sum of the volumes of three pyramids whose common altitude is the altitude of the frustum, and whose bases are the lower base, the upper base, and a mean proportional between the bases of the frustum. 
