Solid Geometry

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Macmillan, 1913 - Geometry, Solid - 107 pages
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Page xxxv - If two triangles have two sides of the one equal to two sides of the...
Page 303 - 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 222 - If two angles not in the same plane have their sides respectively parallel and lying on the same side of the straight line joining their vertices, they are equal, and their planes are parallel. Let the corresponding sides of angles A and A' in the planes MN and PQ be parallel, and lie on the same side of AA'.
Page 287 - THEOREM. Every section of a sphere, made by a plane, is a circle.
Page 224 - Theorem. —A line perpendicular to one of two parallel lines is perpendicular to the other.
Page 226 - V 678. // a straight line is perpendicular to a plane, every plane containing this line is perpendicular to the given plane.
Page 220 - If a line is perpendicular to each of two lines at their point of intersection, it is perpendicular to their plane. Given FB perpendicular at B to each of two straight lines AB and BC of the plane MN. To prove FB perpendicular to the plane MN.
Page 254 - A truncated pyramid is the portion of a pyramid included between the base and a plane not parallel to the base.
Page xlii - The area of a rectangle is equal to the product of its base and altitude. Given R a rectangle with base b and altitude a. To prove R = a X b. Proof. Let U be the unit of surface. .R axb U' Then 1x1 But - is the area of R.
Page 319 - The volumes of two spheres are to each other as the cubes of their radii, or as the cubes of their diameters.

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