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### Contents

 REFERENCES TO PLANE GEOMETRY xi 315 INTRODUCTION 327 THE OCTAHEDRON 333 LINES AND PLANES IN SPACE 339 PERPENDICULAR LINES AND PLANES 351 DIHEDRAL ANGLES 357 CO�RDINATES IN SPACE 368 POLYHEDRONS CYLINDERS CONES 375
 VOLUMES 406 PRISMATOIDS AND SOLIDS OF REVOLUTION 428 THE SPHERE 439 AREA AND VOLUME 458 SPHERICAL POLYGONS AND POLYHEDRAL ANGLES 466 POLAR TRIANGLES 476 SUPPLEMENTARY PROPOSITIONS 487 INDEX 501

### Popular passages

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...