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" A frustum of any pyramid is equivalent to the sum 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. For, let ABCDE-F be... "
Elements of Plane and Solid Geometry - Page 346
by George Albert Wentworth - 1877 - 398 pages
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 367 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...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 316 pages
...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 - 359 pages
...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....
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 237 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...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 894 pages
...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 - 150 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....
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...THEOEEM. The solidity 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 lower base of the frustum, the upper base of the frustum, and a mean proportional between them. Let AEB-CD be...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...THEOREM. The solidity 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 lower base of the frustum, the upper base of the frustum, and a mean proportional between them. Let AEB•CD be...
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre ...

Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 444 pages
...THEOREM. The solidity 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 lower base of the frustum, the upper base of the frustum, and a mean proportional betiueen them. Let AEB•CD...
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