...of the radii of their bases. EXERCISE. i Theorem.—A frustum of any cone is equivalent to the sum of three cones whose common altitude is the altitude...mean proportional between the bases of the frustum, (v. VII., Proposition XIX., Corollary.) THE SPHERE. 31. Definition. A spherical segment is a portion...

...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...

...sum of three cones, having for their common altitude the altitude of the frustum, and for their bases the lower base, the upper base, and a mean proportional...the bases of the frustum. Let V denote the volume, B the area of the lower base, 6 the area of the upper base, and H the altitude of the frustum of the...

...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',...

...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...

...base 12 inches. Proposition 8. Theorem. 781. The volume of a frustum of any cone is equal to the siim of the volumes of three cones, whose common altitude...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...

...inches. Ans. 1206.37 sq. ins. Proposition 8. Theorem. 781. The volume of a frustum of any cone is equal to the sum of the volumes of three cones, whose common...the upper base, and a mean proportional between the baxes of the frustum. Hyp. Let V, B, b, H denote the volume of the frustum, its bases, and its altitude,...

...inches. Proposition 8. Theorem. 781. The volume of a frustum of any cone is equal to the sum of (he volumes of three cones, whose common altitude is the...the upper base, and a mean proportional between the banes of the frustum. Hyp. Let V, B, b, H denote the volume of the frustum, its bases, and its altitude,...

...of the frustum. 51. COROLLARY. A frustum 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 preportional between the bases, of the frustum. Suggestion. Let ABCDE-F be a frustum of any pyramid...

...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...