 | Euclid, Dionysius Lardner - 1828 - 542 σελίδες
...pyramid. PROPOSITION XXVI. (144) The volume of a solid included by two planes intersecting the sides of a triangular prism, is equal to the sum of the volumes of three pyramids whose common base is either of the sections, and whose vertices are the vertices of the angles of the other section. If... | |
 | James Hayward - 1829 - 218 σελίδες
...plane DEF were inclined to the base, we should say — A truncated triangular prism is equivalent to three pyramids whose common base is the base of the prism, and whose heights are respectively equal to the distances of the opposite vertices from the base. 255. As all... | |
 | Dionysius Lardner - 1840 - 386 σελίδες
...formed by the section of a prism by a plane not parallel to its base is called a truncated prism. (343.) The volume of a truncated triangular prism is equal to the sum of volumes of three pyramids •whose base is one of the hases of the truncated prism, and whose vertices... | |
 | William Chauvenet - 1871 - 380 σελίδες
...PRISM. x _<"'* v PROPOSITION XXII.— THEOREM. 60. A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section. Let ABC-DEF be a truncated triangular prism whose base is ABC... | |
 | Edward Olney - 1872 - 102 σελίδες
..._^J^--. 12 732. DBF. — A Truncated Prism is one whose upper and lower bases are not parallel. 733. The volume of a truncated triangular prism is equal...volumes of three pyramids whose common base is the lower base of the prism, and whose vertices are the angles of the upper base. SUo's. — Let 6D, cD',... | |
 | Edward Olney - 1872 - 96 σελίδες
...732. DEF. — A Truncated JPrism is one whose upper and lower bases are not parallel. 733. The yolume of a truncated triangular prism is equal to the sum...volumes of three pyramids whose common base is the lower base of the prism, and whose vertices are the angles of the upper base. SUG'S.— Let bD, cD',... | |
 | William Chauvenet - 1872 - 382 σελίδες
...TRIANGULAR PRISM. PROPOSITION XXII.—THEOREM. 'GO. A truncated triangular prism, is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section. Let ABC-DEF be a truncated triangular * prism whose base is... | |
 | André Darré - 1872 - 226 σελίδες
...THEOREM. 173. A pyramid being truncated by a section parallel to the base, the volume of the frustum is equal to the sum of the volumes of three pyramids whose common altitude is the altitude of the frustum and whose bases are, respectively, those of the frustum and... | |
 | Charles Davies - 1872 - 464 σελίδες
...between them. For, inscribe a frustum of a right pyramid in the given frustum. The volume of this frustum is equal to the sum of the volumes of three pyramids whose common altitude is that of the frustum, and whose bases re the lower base, the upper base, and a mean proportional... | |
 | James Maurice Wilson - 1872 - 160 σελίδες
...PYRAMIDS; 35 COR. 1. This may be expressed as follows; The volume of the frustum of a triangular pyramid is equal to the sum of the volumes of three pyramids, whose height is the height of the frustum, and whose bases are respectively the parallel faces of the frustum,... | |
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A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism and whose vertices are the three... 
