# The Elements of Geometry

Leach, Shewell, and Sanborn, 1886 - Geometry - 371 pages
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### Contents

 DEFINITIONS AND GENERAL PRINCIPLES 227 DEFINITIONS 242 PAGE 260 DEFINITIONS 261 QUADRILATERALS 265 PYRAMIDS 279 PROPORTIONAL LINES 281 EXERCISES 291
 THE CONE 312 THE CIRCLE 316 DEFINITIONS AND GENERAL PRINCIPLES 322 SPHERICAL ANGLES 323 ON MEASUREMENT 338 LINES AND PLANES IN SPACE DIEDRAL 341 MEASUREMENT OF THE CYLINDER CONE 346 207 353

 SIMILAR POLYEDRONS 295 REGULAR POLYGONS 300 MISCELLANEOUS THEOREMS 306
 THE SPHERE 361 PAGE 369

### Popular passages

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.