Plane and solid geometry . Fio. Fig. 2. Given two similar polyhedrons XM and E^C\ To prove that XM and £C may be radially placed. APPENDIX 479 Outline of Proof 1. Take any point O within polyhedron E^cf and constructpolyhedron EC so that it is radially placed with respect to E^Cand so that OA^ : OA = OB : OB = ••. = ab : KL. 2. Then polyhedron EC ^ polyhedron Ec. § 1025, 3. Prove that the dihedral A of polyhedron EC are equal,respectively, to the dihedral A of polyhedron XM, each beingequal, respectively, to the dihedral A of polyhedron Ec. 4. Prove that the faces of polyhedron EC are equa
Plane and solid geometry . Fio. Fig. 2. Given two similar polyhedrons XM and E^C\ To prove that XM and £C may be radially placed. APPENDIX 479 Outline of Proof 1. Take any point O within polyhedron E^cf and constructpolyhedron EC so that it is radially placed with respect to E^Cand so that OA^ : OA = OB : OB = ••. = ab : KL. 2. Then polyhedron EC ^ polyhedron Ec. § 1025, 3. Prove that the dihedral A of polyhedron EC are equal,respectively, to the dihedral A of polyhedron XM, each beingequal, respectively, to the dihedral A of polyhedron Ec. 4. Prove that the faces of polyhedron EC are equal, respec-tively, to the faces of polyhedron XM. 6. Prove, by superposition, that polyhedron EC = XM. 6. .-. polyhedron JTJ/may be placed in the position of EC. 7. But EC and Ec are radially placed. 8. .*. XM and Ec may be radially placed. Propositiox V. Theorem 1027. If a pyramid is cut by a plane parallel to its base: I. The pyramid cut off is similar to the given pyi^a-mid. II. Tlie two pyramids are to each other as
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