Solid Geometry

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American Book Company, 1912 - Geometry, Solid - 188 pages
 

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Page 455 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Page 366 - An oblique prism is equivalent to a right prism whose base is a right section of the oblique prism, and whose altitude is equal to a lateral edge of the oblique prism. Hyp. OM is a right section of oblique prism AD', and OM ' a right prism whose altitude is equal to a lateral edge of AD'. To prove AD' =0= GM' . Proof. The lateral edges of GM
Page 355 - The lateral area of a prism is equal to the product of the perimeter of a right section of the prism by a lateral edge. Let AD...
Page 399 - A pyramid is inscribed in a cone when its base is inscribed in the base of the cone and its vertex coincides with the vertex of the cone.
Page 337 - If two face angles and the included dihedral angle of the one are respectively equal to two face angles and the included dihedral angle of the other...
Page 397 - The lateral area of a cylinder is equal to the product of the perimeter of a right section of the cylinder by an element. Hyp. S is the lateral area, P the perimeter of a right .section, and E an element of the cylinder AK; S...
Page 296 - Two triangles which have an angle of one equal to the supplement of an angle of the other are to each other as the products of the sides including the supplementary angles.
Page 314 - If a straight line is parallel to a plane, the intersection of the plane with any plane passed through the given line is parallel to that line. Let...
Page 365 - ... the edge of a cube whose volume is double that of a given cube...
Page 315 - If two angles not in the same plane have their sides parallel and lying in the same direction, these angles will be equal, and their planes will be parallel.

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