Solid Geometry

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Page 439 - The axis of a circle of a sphere is the diameter of the sphere which is perpendicular to the plane of the circle. The ends of the axis are called the poles of the circle.
Page 439 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Page 319 - ... the third side of the first is greater than the third side of the second.
Page 362 - If two intersecting planes are each perpendicular to a third plane, their intersection is perpendicular to that plane.
Page 495 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.
Page 322 - If two triangles have an angle of one equal to an angle of the other, and...
Page 479 - If two triangles on the same sphere, or on equal spheres, are mutually equiangular, they will also be mutually equilateral. Let A and B be the two given triangles; P and Q their polar triangles. Since the angles are equal in the triangles A and B, the sides will be equal in.
Page 361 - If two planes are perpendicular to each other, a line drawn in one of them perpendicular to their intersection is perpendicular to the other.
Page 338 - The sum of the face angles of any polyhedron is equal to four right angles taken as many times, less two, as the polyhedron has vertices.
Page 480 - 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...

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