 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 and inclined...  Chauvenet's Treatise on Elementary Geometry - Page 251by William Chauvenet, William Elwood Byerly - 1887 - 322 pagesFull view - About this book
 | William Chauvenet - 1893 - 340 pages
...lower base, the upper base, aud a mean proportional between the bases of the frustum. PROPOSITION XX. A truncated triangular prism is equivalent to the sum...vertices are the three vertices of the inclined section. BOOK VIII. THEOREMS. PROPOSITION I. Every section of a cylinder made by a plane passing through an... | |
 | Arthur Latham Baker - Geometry, Solid - 1893 - 150 pages
...polyhedron evidently has as many faces as its primitive has vertices. PROPOSITION XXI. THEOREM. 210. A truncated triangular prism is equivalent to the sum...prism and whose vertices are the three vertices of the upper base. Notation. Let P be a truncated triangular prism and R, S 2 and T x three pyramids having... | |
 | Arthur Latham Baker - Geometry, Solid - 1893 - 154 pages
...truncated triangular prism is equivalent to the sum of three pyramids who e common base is the ba e of the prism and whose vertices are the three vertices of the upper base. Notation. Let P be a truncated triangular prism and E, S 2 and T t three pyramids having... | |
 | George Albert Wentworth - Geometry - 1894 - 456 pages
...base of the prism. and whose vertices are the fhret vertices of the inclined section. 7 jLetABC-DEF be a truncated triangular prism whose base is ABC,...prism into the three pyramids E-ABC, E-ACD, and E-CDF. To prove ABC- DEF equivalent to the sum of the three pyramids, E-ABC, D-ABC, and F-ABC. Proof. E-ABC... | |
 | George Clinton Shutts - Geometry - 1894 - 412 pages
...height is 5'. Ex. 352. The volume of a truncated triangular prism is equal to the sum of the volumes of three pyramids whose common base is the base of the prism and whose vertices are, respectively, the vertices of the inclined sections. Let AB CD EF represent a truncated triangular... | |
 | William Chauvenet - Geometry - 1894 - 380 pages
...TRIANGULAB PRISM. PROPOSITION XXIL—THEOREM. 60. A truncated triangular prism is equivalent to {he sum of three pyramids whose common base is the base of the prism, and whose verticet are the three vertices of the inclined section. Let ABC-DEF be a truncated triangular prism... | |
 | George Albert Wentworth - Geometry - 1895 - 468 pages
...a plane parallel to their bases and 6 feet from their vertices. PROPOSITION XXII. THEOREM. 611. -A truncated triangular prism is equivalent to the sum...prism into the three pyramids E-ABC, E-ACD, and E-CDF. To prove ABC-DEF equivalent to the sum of the three pyramids, E-ABC, D-ABC, and F-ABC. Proof. E-ABClaa&... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...are the lower base, the upper base, and a mean proportional between the bases of the frustum. 611. A truncated triangular prism is equivalent to the sum...vertices are the three vertices of the inclined section. 612. Cor. 1. The volume of a truncated right triangular prism is equal to the product of its base by... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...and whose vertex is at the centre of the cube, is one-sixth part of the cube. ,753. Exercise. — A truncated triangular prism is equivalent to the sum of three pyramids whose common base is «ither base of the truncated prism, and whose vertices are the three vertices of the other base. Hint.... | |
 | Henry W. Keigwin - Geometry - 1897 - 254 pages
...COR. 2. Any pyramid is equal to one-third the product of its base and altitude. Vol. = 484. THEOREM. A truncated triangular prism is equivalent to the sum...prism and whose vertices are the three vertices of the section. 485. DEF. A frustum of a pyramid is the part of a pyramid between the base and a section parallel... | |
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