# Elements of Geometry

Harper & brothers, 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
 SIMILAR POLYEDRONS 326 REGULAR POLYEDRONS 335 PROBLEMS OF DEMONSTRATION 348 SPHERICAL ANGLES 378 POLAR TRIANGLES 390 MEASUREMENT OF SPHERICAL FIGURES 398 LOCI 410 THE CONE 420

 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 PRISMS AND PARALLELOPIPEDS 308
 THE SPHERE 430 PROBLEMS FOR COMPUTATION 445 MAXIMA AND MINIMA OF PLANE FIGURES 456 EXERCISES 465 BOOK V 476 BOOK VIII 485 MODERN GEOMETRY 493 INVERSION 500 THE STEREOGRAPHIC PROJECTION 508 PERSPECTIVE 515 INVOLUTION 523

### Popular passages

Page 180 - Two triangles which have an angle of one equal to the supplement of an angle of the other are to each other as the products of the sides including the supplementary angles.
Page 5 - If of three quantities the first is greater than the second and the second greater than the third, then the first is greater than the third.
Page 432 - The area of a zone is equal to the product of its altitude by the circumference of a great circle.
Page 393 - 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...
Page 185 - To construct a square equivalent to the sum of any number of given squares.
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 67 - 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 70 - The three medians of any triangle intersect in a common point which is two-thirds of the distance from each vertex to the middle of the opposite side.
Page 474 - The area of any regular polygon inscribed in a circle is a mean proportional between the areas of the inscribed and circumscribed polygons of half the number of sides.
Page 71 - The perpendiculars from the vertices of a triangle to the opposite sides meet in a point.