 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 346by George Albert Wentworth - 1877 - 398 pagesFull view - About this book
 | William Chauvenet - Geometry - 1875 - 390 pages
...proposition is expressed by the formula a 59. Corollary A frustum of any pyramid is equivalent to the mm of three pyramids whose common altitude is the altitude...mean proportional between the bases, of the frustum. For, let ABCDE-F be a frustum of any pyramid S-ABCDE. Let S'-A'B'C' be a triangular pyramid, having... | |
 | William Guy Peck - Conic sections - 1876 - 376 pages
...of any two homologous edges. PROPOSITION XVIII. THEOREM. A frustum of a triangular pyramid is equal to the sum of three pyramids whose common altitude...of the frustum and whose bases are the lower base of the frustum, the upper base of the frustum, and a mean proportional Let ACD-PQR be a frustum of... | |
 | William Guy Peck - Conic sections - 1876 - 412 pages
...of any two homologous edges. PROPOSITION XVIII. THEOREM. A frustum of a triangular pyramid is equal to the sum of three pyramids whose common altitude is the altitude of the frustum and whose banes are the lower base of the frustum, the upper base of the frustum, and a mean proportional between... | |
 | William Frothingham Bradbury - Geometry - 1877 - 262 pages
...triangular pyramid, we have V=^aXB + ^aXb + ^a^BXb THEOREM XIX. 74. 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 tlie two bases of the frustum and a mean proportional between them. Let AB-CD be a frustum of a pyramid... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...by its altitude (III., 7 Cor.). XV. Theorem. A. frustum of any pyramid is equal to three pyramids, whose bases are the lower base, the upper base, and a mean proportional between the two bases, of the frustum, and whose altitude is the altitude of the frustum. HYPOTH. B is the lower... | |
 | Isaac Sharpless - Geometry - 1879 - 282 pages
...pyramids. Proposition 19. Theorem. — The volume of a frustum of a pyramid is equal to the volume of three pyramids, whose common altitude is the altitude of the frustum, and whose bases are the two bases of the frustum and a mean proportional between them. 1. Consider the triangular frustum ABC-DEF.... | |
 | William Chauvenet - Geometry - 1879 - 380 pages
...equivalent to the sum of three cones whose common altitude is the altitude of the frustum, and whose baset are the lower base, the upper base, and a mean proportional between the bases of the frustum. Let F denote the volume of the frustum, B its lower base, 6 its upper base, and h its altitude. Let... | |
 | Cornell University - 1880 - 868 pages
...and the included angle of the other. 4. A frustum of any cone is equivalent to the sum of three cones whose common altitude is the altitude of the frustum,...mean proportional between the bases of the frustum. 5. To find two straight lines in the ratio of the volumes of two given cubes. 6. A perpendicular from... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...from each pyramid, the frustum A B- CD is equivalent to the frustum KLM-GrHI, that is, is equivalent to the sum of three pyramids whose common altitude...the altitude of the frustum, and whose bases are the two bases of the frustum and a mean proportional between them. 75i Corollary. As a cone is a pyramid... | |
 | Charles Scott Venable - 1881 - 380 pages
...and for its altitude the altitude of the frustum. Hence, the frustum of a pyramid is equivalent to three pyramids whose common altitude is the altitude of the frustum, and whose bases are respectively the lower and upper bases of the frustum, and a mean proportional between these two bases.... | |
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