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" The volume of a frustum of a cone is equivalent to the sum of the volumes of three cones 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. "
Elements of Geometry, After Legendre, with a Selection of Geometrical ... - Page 300
by Charles Scott Venable - 1881
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 394 pages
...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 abd, parallel...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 346 pages
...or H. THEOREM. 527. The solidify of the 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 upper base of the frustum, the lower base of the frustum, and a mean proportional between them. T Let...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 394 pages
...PROPOSITION VI. THEOREM. The solidity of the frustum of a cone is equal to the sum of the solidities of three cones whose common altitude is the altitude of the frustum, and whose bases are, the upper base of the frustum, the lower base of the frustum, and a mean proportional between them. Let...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 216 pages
...pyramid or cone is equivalent to the sum of three pyramids or cones, which have for their common altitude the altitude of the frustum, and whose bases are the lower base , of the frustum, its upper base, and a mean proportion.il between therV Demonstration. Let ABCD &c. MNOP&.C. (fig. 171)...
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 268 pages
...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 abcde,...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 894 pages
...PROPOSITION X. THEOREM. The solidity of the frustum of a cone is equal to the sum of the solidities of three cones whose common altitude is the altitude of the frustum, and whose bases are, the upper bases of the frustum, the lower base of the frustum, and a mean proportional between them. Let...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1847 - 204 pages
...pyramid or cone is equivalent to the sum of three pyramids or cones, which have for their common altitude the altitude of the frustum, and whose bases are the lower base of the frustum, its upper base, and a mean proportional between them. Proof. Let ABCD&c. JtfJVOP &c. (fig. 171) be...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

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 prisms...
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Elements of Geometry and Conic Sections

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 the frustum, its upper base, and a mean proportional between them. gon let a regular pyramid be constructed having...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...the frustum of a triangular pyramid is equal to that of 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. THEOEI;M. Similar triangular prisms...
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