 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
 | William Chauvenet - Geometry - 1891 - 336 pages
...proportional between the bases of the frustum. 51. COROLLARY. A frustum of any pyramid is equivalent to the sum of three pyramids whose common altitude...bases are the lower base, the upper base, and a mean preportional between the bases, of the frustum. Suggestion. Let ABCDE-F be a frustum of any pyramid... | |
 | Seth Thayer Stewart - Geometry, Modern - 1891 - 428 pages
...frustum of any triangular pyramid. The volume of the frustum equals the volume of three pyramids whose altitude is the altitude of the frustum, and whose bases are the bases of the frustum and a mean proportional between them. Construction : Draw BH, BF, and A F. thus... | |
 | George Albert Wentworth - Geometry - 1892 - 468 pages
...SD'C'). §605 §374 §319 PROPOSITION XX. THEOREM. 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. Let B and b denote the lower and upper bases of the frustum ABC-DEF, and... | |
 | William Chauvenet - 1893 - 340 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...and whose bases are the lower base, the upper base, aud a mean proportional between the bases of the frustum. PROPOSITION XX. A truncated triangular prism... | |
 | Arthur Latham Baker - Geometry, Solid - 1893 - 150 pages
...192. COR. The volume of the frustum of a pyramid (cone) is equal to the sum of three pyramids (cones) whose common altitude is the altitude of the frustum and whose bases are respectively the upper base, the lower base, and a mean proportional between them. Notation. Let e^... | |
 | Webster Wells - Geometry - 1894 - 400 pages
...were taken out in its construction ? 80. 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. (§ 677.) 81. The volume of a cone of revolution is equal to the area of its generating triangle, multiplied... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 416 pages
...frustum. PROPOSITION XX. 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 of the frustum and whose bases are respectively the upper base of the frustum, the lower base of the frustum, and a mean proportional... | |
 | George Albert Wentworth - Geometry - 1894 - 456 pages
...GEOMETRY. — BOOK VII. PROPOSITION XX. THEOREM. 608. The frustum of a triangular pyramid is equivalent to the sum of three pyramids whose common altitude is the altitude of tJie frustum and- iv7iosc bases are the lower base, the upper base, and a mean proportional between... | |
 | George Albert Wentworth - Geometry - 1895 - 468 pages
...volume of the frustum of any pyramid is equal to the sum, of the volumes of three pyramids whose connnon altitude is the altitude of the frustum, and whose...mean proportional between the bases of the frustum. Let B and b denote the lower and upper bases, H the altitude, and V the volume of AbCD-EFGI. To prove... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...planes of its bases. PROPOSITION XXV. THEOREM 711. A frustum of a triangular pyramid is equivalent to the sum of three pyramids whose common altitude...mean proportional between the bases of the frustum. GIVEN — the frustum ABC—DEFoi a triangular pyramid. To PROVE — it is equivalent to the sum of... | |
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