Elements of geometry and trigonometry . ecjual, without b(;ing caj)able of sujxMpositiiJii, andare called solid angles equal hy symmetry, or symmetrical solidangles. Among piano figures, equality by symmetry docs not pro-perly exist, all figures which might take; this nam<î being abso-lutely erjual, or <(|ual bv su|)crposition ; the rcas(»n of which is,that a plane figure may be inverted, aful the; upper |)art takenindiscriminately lor the under. This is not the ease with solids ;in which the thinl dimf risiijn may be taken in two dilVercnldirections. 142 GEOMETRY. BOOK VII. POLYEDRONS.
Elements of geometry and trigonometry . ecjual, without b(;ing caj)able of sujxMpositiiJii, andare called solid angles equal hy symmetry, or symmetrical solidangles. Among piano figures, equality by symmetry docs not pro-perly exist, all figures which might take; this nam<î being abso-lutely erjual, or <(|ual bv su|)crposition ; the rcas(»n of which is,that a plane figure may be inverted, aful the; upper |)art takenindiscriminately lor the under. This is not the ease with solids ;in which the thinl dimf risiijn may be taken in two dilVercnldirections. 142 GEOMETRY. BOOK VII. POLYEDRONS. Definitions. 1. The name solid polyedron, or simple pohjedron, is givento every solid terminated by planes or plane faces; whichplanes, it is evident, will themselves be terminated by straightlines. 2. The common intersection of two adjacent faces of apolyedron is called the side, or edge of the poiyedron. 3. The prism is a solid bounded by several parallelograms,which are terminated at both ends by equal and parallelpolygons. IC Tc. B & à c To construct this solid, let ABCDE be any polygon ; thenif in a plane parallel to ABCDE, the lines FG, GH, HI, &c. bedrawn equal and parallel to the sides AB, BC, CD, &c. thusforming the polygon FGHIK equal to ABCDE ; if in the nextplace, the vertices of the angles in the one plane be joined withthe homologous vertices in the other, by straight lines, AF, BG,CH, &c. the faces ABGF, BCHG, «fee. will be parallelograms,and ABCDE-K, the solid so formed, will be a prism. 4. The equal and parallel polygons ABCDE, FGHIK, arecalled Û\e bases of the prism; the parallelograms taken togetherconstitute the lateral or convex surface of the prism ; the equalstraight lines AF, BG, CH, &c. are called the sides, or edges ofthe prism, 5. The altitude of a prism is the distance between its twobases, or the perpendicular drawn from a point in the upperbase to the plane of the lower base. BOOK VIL 143 6. A prism is right, when the sides AF, BG, CII, «fcc.
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