# Elements of Geometry

Harper & brothers, 1897 - Geometry - 354 pages

### Contents

 INTRODUCTION 3 PARALLEL LINES AND SYMMETRICAL FIGURES 15 TRIANGLES 30 PARALLELOGRAMS 53 BOOK II 62 MEASUREMENT 75 PROBLEMS OF DEMONSTRATION 87 PROBLEMS OF DEMONSTRATION 129
 POLYEDRAL ANGLES 215 PROBLEMS OF DEMONSTRATION 221 PYRAMIDS 243 SIMILAR POLYEDRONS 257 PROBLEMS OF CONSTRUCTION 264 THE SPHERE 272 SPHERICAL ANGLES 278 POLAR TRIANGLES 287

### Popular passages

Page 242 - The volume of any prism is equal to the product of its base by its altitude. Let V denote the volume, B the base, and H the altitude of the prism DA'.
Page 12 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles.
Page 73 - A line perpendicular to a radius at its extremity is tangent to the circle.
Page 253 - The volume of a triangular pyramid is equal to one-third the product of its base and altitude.
Page 238 - COR. 2. The volume of a rectangular parallelopiped is equal to the product of its base by its altitude.
Page 177 - The area of a regular polygon is equal to onehalf the product of its apothem and perimeter.
Page 287 - 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 126 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Page 61 - The perpendiculars from the vertices of a triangle to the opposite sides meet in a point.
Page 256 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.