Elements of geometry and trigonometry . 144 GEOMETRY. 17. Two polyedrons are similar when they are containedby the same number of similar planes, similarly situated, andbavins: like inclinations with each other. PROPOSITION I. THEOREM. The convex swfuce of a right prism is equal to the perimeter ofits base multiplied by its altitude. Let ABCDE-K be a right prism : thenwill its convex surface be equal to(AB + BC + CI) + DE + EA) x AF. For, the convex surface is equal to thesum of all the rectangles AG, BH, CI,DK, EF, which compose it. Now, thealtitudes AF, BG, CH, &c. of the rect-angles, are eq
Elements of geometry and trigonometry . 144 GEOMETRY. 17. Two polyedrons are similar when they are containedby the same number of similar planes, similarly situated, andbavins: like inclinations with each other. PROPOSITION I. THEOREM. The convex swfuce of a right prism is equal to the perimeter ofits base multiplied by its altitude. Let ABCDE-K be a right prism : thenwill its convex surface be equal to(AB + BC + CI) + DE + EA) x AF. For, the convex surface is equal to thesum of all the rectangles AG, BH, CI,DK, EF, which compose it. Now, thealtitudes AF, BG, CH, &c. of the rect-angles, are equal to the altitude of theprism. Hence, the sum of these rectan-gles, or the convex surface of the prism,isequalto(AB4-BC + CD4-DE + EA)xAF ; that is, to the perimeter of the base of the prism multi-plied by its altitude. Cor. If tw^o right prisms have the same altitude, their con-vex surfaces will be to each other as the perimeters of PROPOSITION II. THEOREM. In every prism, the sections formed by parallel planes, are equal polygons. Let the prism AH be intersected bythe parallel planes NF, SV ; then are thepolygons NOPQR, STVXY equal. For, the sides ST, NO, are parallel,being the intersections of two parallelplanes with a third plane ABGF ; thesesame sides, ST, NO, are included betweenthe parallels NS, OT, which are sides ofthe prism: hence NO is equal to like reasons, the sides OP, PQ, QR,&c. of the section NOPQR, are equalto the sides TV, VX, XY, &:c. of the sec-tion STVXY, each to each. And since
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Keywords: ., bo, bookcentury1800, booksubjectgeometry, booksubjecttrigonometry
