Solid Geometry

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Lyons & Carnahan, 1916 - Geometry, Solid - 162 pages
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Page 253 - Conversely, when two sides of a triangle are equal respectively to two sides of another, but the third side of the first is greater than the third side of the second...
Page 254 - If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.
Page 301 - Any 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. Let ABCDE-A' be the oblique prism. At any point F in the edge AA', pass a plane perpendicular to AA' and forming the right section FGHIK Produce AA...
Page 253 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Page 389 - COR. 2. The volume of any truncated triangular prism is equal to the product of its right section by one third the sum of its lateral edges.
Page 373 - 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 347 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Page 396 - If two spherical triangles on the same sphere, or equal spheres, have two sides and the included angle of one equal, respectively, to two sides and the included angle of the other, I.
Page 254 - In any proportion the terms are in proportion by division; that is, the difference of the first two terms is to the second term as the difference of the last two terms is to the fourth.
Page 254 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.

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