Elements of geometry and trigonometry . PROPOSITION X. THEOREM. Any parallelopipedon may he changed into an equivalent rectan-gular parallelopipedon having the same altitude and anequivalent hase. BOOK VII. 153. Let AG be the par-allelopipedon ©m the points A, B, C,D,drawAl,BK,CL,DM,perpendiculartothe planeof tiie base ; you will thusform the parallelopipe-don AL equivalent toAG, and having its late-ral faces AK, BL, & Hence if thebase ABCD is a rectan-gle, AL will be a rectan-gular parallelopipedon equivalent to AG, and consequently,the parallelopipedon required. But i
Elements of geometry and trigonometry . PROPOSITION X. THEOREM. Any parallelopipedon may he changed into an equivalent rectan-gular parallelopipedon having the same altitude and anequivalent hase. BOOK VII. 153. Let AG be the par-allelopipedon ©m the points A, B, C,D,drawAl,BK,CL,DM,perpendiculartothe planeof tiie base ; you will thusform the parallelopipe-don AL equivalent toAG, and having its late-ral faces AK, BL, & Hence if thebase ABCD is a rectan-gle, AL will be a rectan-gular parallelopipedon equivalent to AG, and consequently,the parallelopipedon required. But if ABCD is not a rectangle,draw AO and BN perpendicular to CI), and mQ IiP OQ and NP perpendicular to the base ; youwill then have the solid ABNO-IKPQ, w hichwill be a rectangular parallelopipedon : forby construction, the bases ABNO, and IKPQare rectangles ; so also are the lateral faces,the edges AI, OQ, &:c. being perpendicularto the plane of the base ; hence the solid APis a rectangular parallelopipedon. But thetwo parallelopipedons AP, AL may be con-ceived as having the same base ABKI andthe same altitude AO : hence the parallelopipedon AG, whichwas at first changed into an equivalent parall
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