 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
 | George Albert Wentworth - Geometry - 1899 - 500 pages
...length of one edge. PROPOSITION XX. THEOREM. 655. The frustum of a triangular pyramid is equivalent to the sum of three pyramids whose common altitude...whose bases are the lower base, the upper base, and the mean proportional between the two bases of the frustum. Let B and b denote the lower and upper... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...VII. SOLID GEOMETRY. PROPOSITION XX. THEOREM. 655. The frustum of a triangular pyramid is equivalent to the sum of three pyramids whose common altitude...whose bases are the lower base, the upper base, and the mean proportional between the two bases of the frustum. D Let B and b denote the lewer and upper... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 246 pages
...PROPOSITION XXI. THEOREM. 657. The volume of the frustum of any pyramid is equal to the sum of the volumes of three pyramids whose common altitude is the altitude...whose bases are the lower base, the upper base, and the mean proportional between the bases of the frustum. tu, '• Let B and b denote the lower and upper... | |
 | George Albert Wentworth - Geometry - 1899 - 498 pages
...VII. SOLID GEOMETRY. PROPOSITION XX. THEOREM. 655. The frustum of a triangular pyramid is equivalent to the sum of three pyramids whose common altitude...the altitude of the frustum and whose bases are the loiver base, the upper base, and the mean proportional between the two bases of the frustum. Let B... | |
 | Webster Wells - Geometry - 1899 - 180 pages
...of three pyramids, having for their common altitude the altitude of the frustum, and for their bases the lower base, the upper base, and a mean proportional between the bases, of the frustum. (§ 524.) 53. The upper base of a truncated parallelepiped is a parallelogram. (Let planes AC' and... | |
 | George Albert Wentworth - Geometry - 1899 - 496 pages
...VII. SOLID GEOMETRY. PROPOSITION XX. THEOREM. 655. The frustum of a triangular pyramid is equivalent to the sum of three pyramids whose common altitude is the altitude oŁ the frustum and whose bases are the lower base, the upper base, and the mean proportional between... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...— The volume of a frustum of a circular cone is equivalent to the sum of the volumes of three cones whose common altitude is the altitude of the frustum,...whose bases are the lower base, the upper base, and the mean proportional between the bases of the frustum. For, the value of V may be written, MISCELLANEOUS... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...— The volume of a frustum of a circular cone is equivalent to the sum of the volumes of three cones whose common altitude is the altitude of the frustum,...whose bases are the lower base, the upper base, and the mean proportional between the bases of the frustum. For, the value of V may be written, \U y.B+... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...— The volume of a frustum of a circular cone is equivalent to the sum of the volumes of three cones whose common altitude is the altitude of the frustum,...whose bases are the lower base, the upper base, and the mean proportional between the bases of the frustum. For, the value of V may be written, MISCELLANEOUS... | |
 | James Howard Gore - Geometry - 1902 - 266 pages
...471. COR. 2. The volume of a frustum of any cone is equal to the sum of the volumes of three cones, whose common altitude is the altitude of the frustum,...mean proportional between the bases of the frustum. If R and R' denote the radii of the lower and upper bases of the frustum, and h the altitude, then... | |
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