Solid Geometry

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American Book Company, 1912 - Geometry, Solid - 188 pages
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Page 317 - A straight line perpendicular to one of two parallel planes is perpendicular to the other also.
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 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 387 - Every section of a cylinder made by a plane passing through an element is a parallelogram.
Page 361 - COR. 2. The volume of a rectangular parallelopiped is equal to the product of its base by its altitude.
Page 321 - The acute angle that a straight line makes with its own projection upon a plane is the least angle that it makes with any line passing through its foot in the plane.
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 316 - Two lines perpendicular to the same plane are parallel. 6. If two lines are parallel, every plane containing one of the lines and only one is parallel to the other.
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 365 - ... the edge of a cube whose volume is double that of a given cube.

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