The Elements of Geometry

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Leach, Shewell, and Sanborn, 1886 - Geometry - 371 pages
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Page 323 - A spherical angle is measured by the arc of a great circle described from its vertex as a pole, and included between its sides, produced if necessary.
Page 315 - A Sphere is a solid bounded by a curved surface all points of which are equally distant from a point within called the centre.
Page 324 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The...
Page 349 - The lateral or total areas of two similar cones of revolution are to each other as the squares of their slant heights...
Page 252 - The projection of a point on a plane is the foot of the perpendicular from the point to the plane.
Page 330 - Two triangles are congruent if (a) two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other...
Page 326 - If from the vertices of a spherical triangle as poles arcs of great circles are described, another spherical triangle is formed which is called the polar triangle of the first.
Page 334 - ADC ; the last two are therefore right angles ; hence the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is perpendicular to the base, and bisects the vertical angle.
Page 244 - If two planes are perpendicular to each other, a straight line drawn in one of them, perpendicular to their intersection, is perpendicular to the other.
Page 279 - DEF. The slant height of a regular pyramid is the altitude of any one of the lateral faces.

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