 | Adrien Marie Legendre - 1822 - 394 σελίδες
...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... | |
 | Adrien Marie Legendre - 1828 - 346 σελίδες
...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... | |
 | Adrien Marie Legendre - 1836 - 394 σελίδες
...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... | |
 | Benjamin Peirce - 1837 - 216 σελίδες
...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)... | |
 | James Bates Thomson - 1844 - 268 σελίδες
...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,... | |
 | Nathan Scholfield - 1845 - 894 σελίδες
...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... | |
 | Benjamin Peirce - 1847 - 204 σελίδες
...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... | |
 | Charles Davies - 1849 - 372 σελίδες
...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... | |
 | Elias Loomis - 1849 - 252 σελίδες
...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... | |
 | Adrien Marie Legendre - 1852 - 436 σελίδες
...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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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. 
