 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, Solid - 1902 - 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. Let B and b denote the lower and upper bases,... | |
 | George Albert Wentworth - Geometry, Solid - 1902 - 248 pages
...729. 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 and whose bases are the latver base, the upper base, and the mean proportional between the bases of the frustum. Let V denote... | |
 | Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...VII. SOLID GEOMETRY O PROPOSITION XX. THEOREM 655. 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. tr < DIF Given ABC-DEF the frustum of a triangular pyramid, having the area... | |
 | Jacob Henry Minick, Clement Carrington Gaines - Business mathematics - 1904 - 412 pages
...shown by geometry that the frustum of a pyramid or cone is equal to the sum of three pyramids or cones whose common altitude is the altitude of the frustum,...mean proportional between the bases of the frustum. Hence, RULE. — To the sum of the areas of the two ends add the square root of their product, and... | |
 | Fletcher Durell - Geometry - 1911 - 553 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 of the frustum, and wliose bases are the lower base 'the upper base, and a mean proportional between the two bases of the... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...729. 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 and whose bases are the lawer base, the upper base, and the mean proportional between the bases of the frustum. Let V denote... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...SOLID GEOMETRY — BOOK VII PROPOSITION XX. THEOREM 672 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. HYPOTHESIS. , ABC-DEF is a frustum of a triangular... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...SOLID GEOMETRY — BOOK VII PROPOSITION XX. THEOREM 672 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. HYPOTHESIS. ABC DBF is a frustum of a triangular... | |
 | David Sands Wright - Geometry - 1906 - 104 pages
...The volume of a frustum of a cone is equal to onethird of the product of the altitude by the sum of the lower base, the upper base, and a mean proportional between the bases. Formula: -J IT A (R2 + r2 + Rr~). 1. Given a frustum of a right cone, the radius of its lower base... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...of a triangular pyramid is equivalent, to the sum of three pyramids whose altitudes are the same as the altitude of the frustum and whose bases are the...mean proportional between the bases of the frustum. SOLID GEOMETRY 631. THEOREM. The volume of the frustum of any pyramid is equal to one third the altitude... | |
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