# Elements of Geometry: Geometry of space

Harper & Brothers, 1898 - Geometry
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### Contents

 BOOK VI 235 PARALLEL LINES AND PLANES 249 DIEDRAL ANGLES AND PROJECTIONS 257 POLYEDRAL ANGLES 270 PROJECTIONS 282 PRISMS AND PARALLELOPIPEDS 288 PYRAMIDS 308 SIMILAR POLYEDRONS 326
 MEASUREMENT OF SPHERICAL FIGURES 398 PROBLEMS OF DEMONSTRATION 408 THE CONE 420 THE SPHERE 430 PROBLEMS FOR COMPUTATION 445 EXERCISES 463 BOOK III 469 BOOK IX 488

 REGULAR POLYEDRONS 335 GENERAL THEOREMS ON POLYEDRONS 345 PROBLEMS FOR COMPUTATION 351 THE CONE 360 THE SPHERE 366 SPHERICAL ANGLES 378 POLAR TRIANGLES 390
 HARMONIC SECTION 495 THE STEREOGRAPHIC PROJECTION 508 PERSPECTIVE 515 INVOLUTION 523 TABLE OF WEIGHTS AND MEASURES 533 RULES OF MENSURATION 539 Copyright

### Popular passages

Page 325 - The frustum of a triangular pyramid is equivalent to the sum of three pyramids whose common altitude is the altitude of the frustum and whose bases are the lower base, the upper base, and a mean proportional between the two bases of the frustum.
Page 309 - A regular pyramid is a pyramid whose base is a regular polygon, and whose vertex lies in the perpendicular erected at the centre of the base.
Page 390 - 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 334 - If a pyramid is cut by a plane parallel to its base, the...
Page 392 - In two polar triangles, each angle of one is measured by the supplement of the side lying opposite to it in the other. Let ABC and A'B'C' be two polar triangles. Let the sides AB and AC, produced if necessary, meet the side B'C
Page 426 - The lateral area of a frustum of a cone of revolution is equal to the circumference of a section equidistant from its bases multiplied by its slant height.
Page 268 - The acute angle which a straight line makes with its projection upon a plane is the least angle which it makes with any line of the plane.
Page 476 - The area of a regular hexagon inscribed in a circle is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Page 247 - If a straight line is parallel to a plane, the intersection of the plane with a plane passed through the line is parallel to the line.
Page 527 - The sum of the angles of a triangle is less than two right angles, and the propositions of the last chapter hold without restriction.