# Elements of Geometry

American Book Company, 1896 - Geometry - 540 pages
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### Contents

 INTRODUCTION 3 PARALLEL LINES AND SYMMETRICAL FIGURES 15 TRIANGLES 32 PARALLELOGRAMS 60 PROBLEMS 66 BOOK II 73 MEASUREMENT 87 PROBLEMS OF DEMONSTRATION 106
 THE SPHERE 366 SPHERICAL ANGLES 378 POLAR TRIANGLES 390 MEASUREMENT OF SPHERICAL FIGURES 398 PROBLEMS OF DEMONSTRATION 408 THE CONE 420 THE SPHERE 430 PROBLEMS OF DEMONSTRATION 444

 PROBLEMS OF CONSTRUCTION 108 PROBLEMS OF DEMONSTRATION 154 PROBLEMS FOR COMPUTATION 160 BOOK IV 170 PROBLEMS OF DEMONSTRATION 193 BOOK V 202 PROBLEMS OF DEMONSTRATION 229 BOOK VI 235 PARALLEL LINES AND PLANES 246 DIEDRAL ANGLES AND PROJECTIONS 257 BOOK VII 287 PYRAMIDS 318 REGULAR POLYEDRONS 335 PROBLEMS OF DEMONSTRATION 348 THE CONE 360
 MAXIMA AND MINIMA OF PLANE FIGURES 456 EXERCISES 463 BOOK III 469 BOOK V 476 BOOK VIII 485 MAXIMA AND MINIMA 491 SOME PROPERTIES OF CIRCLES 497 RADICAL AXIS AND COAXAL CIRCLES 504 POLES AND POLARS 511 PERSPECTIVE 515 INVOLUTION 523 TABLE OF WEIGHTS AND MEASURES 529 CONSTRUCTIONS 538 Copyright

### Popular passages

Page 36 - If two triangles have two sides and the included angle of one, equal respectively to two sides and the included angle of the other, the triangles are equal. C...
Page 472 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Page 321 - 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 211 - The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or as the squares of their apothems.
Page 42 - ... greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Page 385 - 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 144 - ... twice the product of one of these sides and the projection of the other side upon it.
Page 63 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Page 141 - If from a point without a circle a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and its external segment.
Page 153 - The product of two sides of a triangle is equal to the product of the diameter of the circumscribed circle and the altitude upon the third side.