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 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 449 - The area of a zone is equal to the product of its altitude by the circumference of a great circle.
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 353 - If two pyramids have equal altitudes and equivalent bases, sections made by planes parallel to the bases, and at equal distances from the vertices, are equivalent.
Page 387 - Every section of a cylinder made by a plane passing through an element is a parallelogram.
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 364 - Two rectangular parallelopipeds have equal altitudes and bases whose dimensions are 4 and 7, and 5 and 9 respectively. Find the ratio of their volumes.
Page 369 - The plane passed through two diagonally opposite edges of a parallelopiped divides it into two equivalent triangular prisms.

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