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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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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...and OC its altitude : then is its volume equal to the sum of three cones whose common altitude is OC, and whose bases are the lower base, the upper base, and a mean proportional between them. For, inscribe a frustum of a right pyramid in the given frustum. The volume of this frustum is...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 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 o JLet AF be a frustum of a_ triangular pyramid. Let AF be a frustum of any pyramid 0-ABC. Denote the...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...mean proportional between the bases of the frustum. Corollary. A frustum of any pyramid is equivalent to the sum of three pyramids whose common altitude...mean proportional between the bases of the frustum. PROPOSITION XX. A truncated triangular prism is equivalent to the sum of three pyramids whose common...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1887 - 346 pages
...point taken within it. PROPOSITION XIX.— THEOREM. 50. A 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 basts, of the frustum. Let ABC-D be a frustum of a triangular pyramid, the plane DEF being parallel...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1888 - 826 pages
...proposition is expressed by the formula or 69. Corollary A frustum of any pyramid is equivalent to the sum oj 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. Ijet S'—A'B'C' be a triangular pyramid, having...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1888 - 346 pages
...proportional between the bases of the frustum. v 51. COROLLARY. 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....
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A Mathematical Solution Book Containing Systematic Solutions to Many of the ...

Benjamin Franklin Finkel - Mathematics - 1888 - 518 pages
...two parallel planes are equal polygons. 4. The frustum of a triangular pyramid is equal in volume to 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. 5. To draw a plane tangent to a cylindar...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 414 pages
...Theorem. 781. The volume of a frustum of any cone is equal to the siim of the volumes of three cones, whose common altitude is the altitude of the frustum,...mean proportional between the bases of the frustum. Hgp. Let V, B, b, H denote the volume of the frustum, its bases, and its altitude, respectively. To...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 418 pages
...Theorem. 781. 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,...the upper base, and a mean proportional between the bates of the frustum. Hgp. Let V, B, b, H denote the volume of the frustum, its bases, and its altitude,...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 420 pages
...frustum of a triangular 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. Hyp. Let B denote the lower base, b the upper base, h the altitude, and V the volume of the frustum...
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