Elements of geometry and trigonometry . teral sur-face. 11. If from the pyramid S-ABCDE,the pyramid S-abcde be cut off by aplane parallel to the base, the remainingsolid ABCDE-^, is called a truncatedpyramid, or the frustum of a j)yramid. 12. The altitude of a pyramid is theperpendicular let fall from the vertex upon the plane of thebase, produced if necessary. 13. A pyramid is triangular, quadrangular, &c. accordingas its base is a triangle, a quadrilateral, vfec. 11. A pyramid is regular, when its base is a regular poly-gon, and when, at ihit same time, the peri)endicular let fallfrom the ve
Elements of geometry and trigonometry . teral sur-face. 11. If from the pyramid S-ABCDE,the pyramid S-abcde be cut off by aplane parallel to the base, the remainingsolid ABCDE-^, is called a truncatedpyramid, or the frustum of a j)yramid. 12. The altitude of a pyramid is theperpendicular let fall from the vertex upon the plane of thebase, produced if necessary. 13. A pyramid is triangular, quadrangular, &c. accordingas its base is a triangle, a quadrilateral, vfec. 11. A pyramid is regular, when its base is a regular poly-gon, and when, at ihit same time, the peri)endicular let fallfrom the vertex on the j)lane of the base ))asses through thecentre of the base. That perpendicular is then called the axisof the pyramid. ir>. Any line, as SF, drawn from the vertex S of a regularpyramid, pfT[)endicuIar to either side of the polygon whichfonns its base, is called the slant height of the pyramid. 10. The diagonal (){ a [)olyedn)n is a straight line joinmgthe vcrticeg of two solid angles which are not adjacent to 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 theirbases.
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