# Elements of Geometry

Harper & brothers, 1897 - Geometry - 354 pages
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### Contents

 FUNDAMENTAL CONCEPTIONS 3 PARALLEL LINES AND SYMMETRICAL FIGURES 15 TRIANGLES 30 PARALLELOGRAMS 53 THE CIRCLE 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

 BOOK IV 135 PROBLEMS OF DEMONSTRATION 154 PROBLEMS OF CONSTRUCTION 155 PROBLEMS OF DEMONSTRATION 182 PERPENDICULAR AND OBLIQUE LINES AND PLANES 189 PARALLEL LINES AND PLANES 196 DIEDRAL ANGLES 207
 MEASUREMENT OF SPHERICAL FIGURES 293 PROBLEMS OF DEMONSTRATION 300 PROBLEMS OF DEMONSTRATION 330 58 336 135 342 TABLE OF WEIGHTS AND MEASURES 345 CONSTRUCTIONS 353

### Popular passages

Page 170 - 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 204 - If a line is perpendicular to one of two parallel lines, it is perpendicular to the other also.
Page 106 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.
Page 5 - If the first of three quantities is greater than the second, and the second is greater than the third, then the first is greater than the third.
Page 82 - An angle formed by a tangent and a chord is measured by one-half its intercepted arc.
Page 73 - A line perpendicular to a radius at its extremity is tangent to the circle.
Page 177 - C and area S. To PROVE S — ^RxC. Circumscribe a regular polygon and call its perimeter C' and area S'. Then S
Page 285 - 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 45 - If, from a point within a triangle, two straight lines are drawn to the extremities of either side, their sum will be less than the sum of the other two sides of the triangle.
Page 83 - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.