 The frustum of a triangular 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 two bases of the frustum.  Elements of Geometry - Page 315by Andrew Wheeler Phillips, Irving Fisher - 1896 - 540 pagesFull view - About this book
 | George Albert Wentworth - Geometry - 1882 - 442 pages
...%HX(B+b + VZTxl). 580. COR. 2. The frustuт of any pyramid is equivalent to the sum of three pyramids whose common altitude is the altitude of the frustum,...bases are the lower base, the upper base, and a mean proport'onal between the bases of the frustum. For the frustum of any pyramid is equivalent to the... | |
 | George Albert Wentworth - Geometry - 1884 - 422 pages
...PROPOSITION XXXVIII. THEOREM. 667. A frustum of any cone is equivalent to the sum of three cones ivhose common altitude is the altitude of the frustum and...mean proportional between the bases of the frustum. le Let V denote the volume of the frustum, B its lower base, b its upper base, and H its altitude.... | |
 | 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... | |
 | 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... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...altitude. PROPOSITION XIX. A frustum of a triangular pyramid is equivalent to the sum of three pyramids whose common altitude is the altitude of the frustum,...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... | |
 | William Chauvenet - Geometry - 1887 - 346 pages
...PROPOSITION XIX.— THEOREM. 50. A frustum of a triangular pyramid is equivalent to the sum of three pyramids whose common altitude is the altitude of the frustum,...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... | |
 | William Chauvenet - Geometry - 1888 - 826 pages
...equivalent to the sum of three cones whose common altitude is the altitude of the frustum, and whose basec are the lower base, the upper base, and a mean proportional between the bases of the frustum. Let V denote the volume of the frustum, B its lower base, b its upper base, and h its altitude. Let... | |
 | William Chauvenet - Geometry - 1888 - 346 pages
...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. Suggestion. Let ABCDE-F be a frustum of any pyramid S-ABCDE. Construct a triangular pyramid, S'-A'B'C',... | |
 | Benjamin Franklin Finkel - Mathematics - 1888 - 518 pages
...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... | |
 | 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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