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" 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 346
by George Albert Wentworth - 1877 - 398 pages
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Syllabus of Geometry

George Albert Wentworth - Mathematics - 1896 - 68 pages
...of the three edges of these trihedral angles. 608. The frustum of a triangular pyramid is equivalent to the sum of three pyramids whose common altitude...the upper base, and a mean proportional between the two bases of the frustum. 609. Cor. If the volume of the frustum of a triangular pyramid is denoted...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...frustum of a cone is equivalent to the sum of three cones whose common altitude is tlie dl fit licit- of the frustum and whose bases are the lower base,...mean proportional between the bases of the frustum. GIVEN — a frustum of a cone. Denote its bases by B and b, its altitude by k, and its volume by V....
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 376 pages
...lateral edges by the area of a right section. 696. Exercise. — A frustum of any pyramid is equivalent to the sum of three pyramids whose common altitude...mean proportional between the bases of the frustum. Hint. — To find the volume of the frustum, subtract the volume of the small pyramid from the volume...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 574 pages
...PROPOSITION XXVI. THEOREM 713. A frustum of any pyramid is equivalent to the sum of three pyram1ds whose common altitude is the altitude of the frustum...mean proportional between the bases of the frustum. GIVEN the frustum AC of the pyramid V-ABCD. Denote its lower and upper bases by B and b respectively,...
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The Elements of Geometry

Henry W. Keigwin - Geometry - 1897 - 254 pages
...parallel to the base. PROPOSITION X. THEOREM. 486. A 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 bases of the frustum. Pass a plane through EF parallel to AD. Draw...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1898 - 376 pages
...i& X or 7=iA (B + b + i/5~X~J). 59. Corollary A frustum of any pyramid is equivalent to the sum 6j 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...
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Elements of Geometry: Geometry of space

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1898 - 324 pages
...its bases. PROPOSITION VIII. THEOREM 969. A frustum of a cone is equivalent to the sum of three cones whose common altitude is the altitude of the frustum...lower base, the upper base, and a mean proportional bctween the bases of the frustum. 428 GIVEN — a frustum of a cone. Denote its bases by B and b, its...
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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...that: A frustum of any pyramid is equivalent to the sum of three pyramids, having the same altitude as the frustum, and whose bases are the lower base, the...mean proportional between the bases, of the frustum. the upper base, and a mean proportional between the bases of the frustum. If R and R' denote the radii...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 424 pages
...its longest side as an axis. (§324.) 78. A frustum of a circular cone is equivalent to three cones, whose common altitude is the altitude of the frustum,...mean proportional between the bases of the frustum. (§ 660.) 79. The volume of a cone of revolution is equal to the area of its generating triangle, multiplied...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 450 pages
...its longest side as an axis. (§ 324.) 78. A frustum of a circular cone is equivalent to three cones, whose common altitude is the altitude of the frustum,...mean proportional between the bases of the frustum. (§ 660.) 79. The volume of a cone of revolution is equal to the area of its generating triangle, multiplied...
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