...perceive that the volume of the frustum of a cone w equal to the. sum of the volumes of three cones, whose common altitude is the altitude of the frustum,...lower base, the upper base, and a mean proportional to the two. From the above formula wo also derive the following _ , r , RULE. •So the sum of the...

...Therefore, etcTHEOREM XVIThe volume of a frustum of a triangular 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 the lower base of the frustum, the upper base of the frustum, and a mean proportional between the two basesLet ABC...

...etc. THEOREM XVI. TJte volume of a frustum of a triangular 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 the lower base of the frustum, the upper base of the frustum, and a mean proportional between the two bases. Let ABC—F...

...AC' X " V~ v PROPOSITION XXI.— THEOREM. ; /\<v 58. J. frustum of a triangular pyramid is equivalent to the sum of three pyramids whose common altitude...mean proportional between the bases, of the frustum. Let ABG-D be a frustum of a triangular pyramid, formed by a plane . DEF parallel to the base ABC. Through...

...i& X b + $h X VB^Tb, >r F=t* (B + 6 + i/5~X~3). 59. 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. For, let ABCDE-F be a frustum of any pyramid S-ABCDE. Let S'-A'B'C' be a triangular pyramid, having...

...V= iA X -B + iA X b + i& X F=|A (B + b + 59. Corollary A frustum of any pyramid is equivalent to ike sum of three pyramids whose common altitude is the...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...

...truncated by a section parallel to the base, the volume of the frustum 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, those of the frustum and a geometric mean between them. Let ABCDEF (Fig. 148) be a triangular...

...its altitude: then will its volume be 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...

...sum of the volumes of three pyramids whose common altitude is that of the frustum, and whose bases re the lower base, the upper base, and a mean proportional between the two (B. VII., P. XVIII.), whatever may be the number of lateral faces. But when the numbe1 of faces...

...sum of the volumes of three pyramids whose common altitude is that of the frustum, and whose bases re the lower base, the upper base, and a mean proportional between the two (B. VII., P. XVIII.), whatever may be the number of lateral faces. But when the numbe1 of faces...