Solid Geometry

Cover Solid Geometry
Solid Geometry
Fletcher Durell
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671.
Denote the volumes of the tetrahedrons in P by vi, V2, vs . . . And of those in P f by v'i, 1/2, v's Then Also H f B fi !_!_ 1/1 Art. 674, Ax. 1.
(for each of these ratios^.
Vl jat= : -2L j that is> *1 = L. Art . 312 .
HB Ax. 1. Q. E. D- 400 BOOK VII. SOLID GEOMETRY EXERCISES. CROUP 67 THEOREMS CONCERNING POLYHEDRONS Ex. 1. The lateral faces of a right prism are rectangles.
Ex. 2. A diagonal plane of a prism is parallel to every lateral edge of the prism not contained in the plane.
Ex. 3.
...The diagonals of a parallelepiped bisect each other.
Ex. 4. The square of a diagonal of a rectangular parallelepiped equals the sum of the squares of the three edges meeting at a vertex.
Ex. 5. Each lateral face of a prism is parallel to every lateral edge not contained in the face.
Ex. 6. Every section of a prism made by a plane parallel to a lateral edge is a parallelogram.
Ex. 7. If any two diagonal planes of a prism which are not par- allel to each other are. Perpendicular to the base of the prism, the prism is a right prism.


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