...AG = FG XAF ' ; the area of BH=GHXBG; of (7/=///XCH ; and so on. But the edges AF, BG, CH, &c. K / are equal to each other and to the altitude of the...perimeter of its base multiplied by its altitude. 1,>. Corollary. As a cylinder is a right prism (12), this demonstration includes the cylinder. If,...

...rectangle AG=. FG X AF; the area of BH=GHXBG; of CI — HI X CII; and so on. But the edges AF, BG, GII, &c. are equal to each other and to the altitude of...the altitude of a cylinder, the convex surface = 2 IT RA. THEOREM II. 16. The sections of a prism made by parallel planes are equal polygons. Let the...

...cylinder. The prism will be inscribed in the convex surface of the cylinder. The convex surface of this prism is equal to the perimeter of its base multiplied by its altitude, AG (Theo. IX. Bk. V.). Conceive now the arcs subtending the sides of the polygon to be continually...

...is common to both proportions, we have AE: EB: : CF : F D. THEOREM IX. 289. The convex surface of a right prism is equal to the perimeter of its base multiplied by its altitude. Let ABCDE-KbQa. right prism ; then will its convex surface be equal to the perimeter of its base, AB...

...of the same altitude are equal to one another. Proposition 10. Theorem.—The lateral surface of a right prism is equal to the perimeter of its base multiplied by its altitude. Because the prism is a right prism (Def. 3) the angle ABC is a right angle. Hence the figur^ AC is...

...Therefore the convex surface = (B 0+ CD + DH + EF + IB) XAG H 21 • Cor. 1. The convex surface of a right prism is equal to the perimeter of its base multiplied by its altitude. 22. Cor. 2. As a cylinder is a prism (14), this demonstration includes the cylinder. In a circular...

...is the perpendicular distance between the planes of its bases. THEOREM XX. The convex surface of a right prism is equal to the perimeter of its base multiplied by its height. Let ABE be a right prism. Since its principal edges are, by definition, perpendicular to the...

...altitude. For, inscribe in the cylinder a prism whose base is a regular polygon. The convex surface of this prism is equal to the perimeter of its base multiplied by its altitude (B. VTI., PI), whatever may be the number of sides of its base. But, when the number of sides is infinite...

...the distance be J ween the parallel planes which form its bases THEOREM I. The convex surface of a right prism is equal to the perimeter of its base multiplied by its altitude. Let ABCDE—K be a right prism : then will its convex surface be equal to (AB.) BC+CD+DE+EA)xAF. For,...

...Whence by § 195, S = PxE. 704. COROLLARY I. The lateral area of a cylinder of revolution (§ 597) is equal to the perimeter of its base multiplied by its altitude. 705. COROLLARY II. If S denotes the lateral area, H the altitude, and R the radius of the base of a...