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 449 - The area of a zone is equal to the product of its altitude by the circumference of a great circle.
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 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 469 - The altitude of a regular triangular pyramid, each side of whose base is 4 ft., is 12 ft. Find the area of a section made by a plane parallel to the base and 4 ft. from the vertex. Ex.
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 328 - If from the foot of a perpendicular to a plane a straight line is drawn at right angles to any line in the plane, the line drawn from its intersection with the line in the plane to any point of the perpendicular is perpendicular to the line of the plane.
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...

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