# Elements of Plane and Solid Geometry

American Book Company, 1903 - Geometry - 384 pages

### Contents

 PLANE GEOMETRY 9 RECTILINEAR FIGURES 15 Incommensurable quantities 342 18 Center of circle 19 Problem 23 Angles adjacent 15 38 ADDITIONAL EXERCISES 71 CIRCLES 79
 Pentagon 152 198 ADDITIONAL EXERCISES 213 Pentedecagon 152 215 MEASUREMENT OF THE CIRCLE 220 Axioms list of 27 228 Sector 343 238 ADDITIONAL EXERCISES 243 POINTS AND LINES IN SPACE 251

 ADDITIONAL EXERCISES 122 PROPORTIONS SIMILAR POLYGONS 129 Median of a triangle 173 137 Oblique angle 17 152 Quantities commensurable 342 163 Converse 72 164 ADDITIONAL EXERCISES 173 Parallel lines 107 176 AREAS OF POLYGONS 181 Radius 20 190 Ratio 340 196
 ADDITIONAL EXERCISES 283 Tangent circles and lines 306 ADDITIONAL EXERCISES 317 Theorem 22 337 ADDITIONAL EXERCISES 340 Polar 521 345 Interior angles 113 351 Variable 340 375 ADDITIONAL EXERCISES 382 Copyright

### Popular passages

Page 167 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 139 - A line parallel to one side of a triangle divides the other two sides proportionally.
Page 187 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 202 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Page 180 - In an inscribed quadrilateral, the product of the diagonals is equal to the sum of the products of the opposite sides.
Page 90 - In the same circle, or in equal circles, equal chords are equally distant from the center; and, conversely, chords equally distant from the center are equal.
Page 195 - Since similar triangles are to each other as the squares of their homologous sides, ABC : DBE : : AB' : BD3 ; whence BD = AB J ^5| ~ AB A/— ^ — . j A150 f in -f- n The construction of Fig.
Page 129 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D ; and read, A is to B as C to D.
Page 15 - 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.
Page 17 - If two triangles have two angles and the included side of one equal respectively to two angles and the included side of the other, the triangles are congruent.