 | George Roberts Perkins - Geometry - 1856 - 460 pages
...slant height. IX. A triangular pyramid, having in all four triangular faces, is called a Tetraedron. X. If a pyramid is cut by a plane parallel to its base it will be divided into two portions, one of which will be a second pyramid having the same vertex... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...the perpendicular let fall from the vertex to either side of the polygon which forms the base. 13. If a pyramid is cut by a plane parallel to its base, forming a second base, the part lying between the bases, is called a truncated pyramid, or frustum... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...slant height. IX. A triangular pyramid, having in all four triangular faces, is called a Tetraedron. X. If a pyramid is cut by a plane parallel to its base it will be divided into two portions, one of which will be a second pyramid having the same vertex... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...one of these trapezoids is the slant height of the frustum. , vvt PROPOSITION XIV.— THEOREM. 43. If a pyramid is cut by a plane parallel to its base : 1st, the edges and the altitude are divided proportionally ; 2d, the section is a polygon similar... | |
 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...pyramid is the perpendicular distance between the parallel edges of the bases ; as GO. THEOREM VII. 39. If a pyramid is cut by a plane parallel to its base, 1st. The edges and altitude are divided proportionally ; 2d. The section is a polygon similar to the... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...of any one of these trapezoids is the slant height of the frustum. PROPOSITION XIV.— THEOREM. 43. If a pyramid is cut by a plane parallel to its base : 1st, the edges and the altitude are divided proportionally ; 2d, the section is a polygon similar... | |
 | William Frothingham Bradbury - Geometry - 1872 - 262 pages
...pyramid is the perpendicular distance between the parallel edges of the: bases; as GC. THEOREM VII. 39. If a pyramid is cut by a plane parallel to its base, 1st. The edges and altitude are divided proportionally ; 2d. The section is a polygon similar to the... | |
 | William Guy Peck - Conic sections - 1876 - 412 pages
...squares of any two homologous edges, and their altitudes are to each other as those edges; hence, the pyramids are to each other as the cubes of any two homologous edges. PROPOSITION XVIII. THEOREM. A frustum of a triangular pyramid is equal to the sum of three pyramids... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...pyramid is the perpendicular distance between the parallel edges of the bases; as G C. THEOREM XI. 57. If a pyramid is cut by a plane parallel to its base, 1st. The edges and altitude are divided proportionally; 2d. The section is a polygon similar to the... | |
 | William Chauvenet - Geometry - 1887 - 346 pages
...section and the base are similar. 1 -7. '•' BOOK VII. H- - T>^ '• 1C ' - - /> 241 40. COROLLARY I. If a pyramid is cut by a plane parallel to its base, the area of the section is to the area of the base as the square of its distance from the vertex is to... | |
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If a pyramid is cut by a plane parallel to its base, the... 
