# Elements of Plane Geometry

American book Company, 1901 - Geometry, Modern - 247 pages

### Contents

 PLANE GEOMETRY 9 BOOK I 15 Commensurable quantities 342 22 Problem 23 Converse 72 28 Corresponding angles 113 38 Harmonical division 509 43 ADDITIONAL EXERCISES 71
 Quadrant 346 163 Ratio 340 169 ADDITIONAL EXERCISES 173 Parallel lines 107 176 BOOK IV 181 Pentagon 152 184 Rays of pencil 512 194 Perpendicular lines 16 196

 opposite 75 BOOK II 79 ADDITIONAL EXERCISES 122 BOOK III 129 Median of a triangle 173 140 Straight line 6 148 Oblique angle 17 152
 ADDITIONAL EXERCISES 213 Interior angles 113 216 BOOK V 220 Axioms list of 27 228 Sector 343 238 ADDITIONAL EXERCISES 243 Copyright

### Popular passages

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 any 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 that are equally distant from the center are equal.
Page 53 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...
Page 195 - Similar triangles are to each other as the squares of their homologous sides.
Page 30 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 120 - If a quadrilateral is circumscribed about a circle, the sum of one pair of opposite sides is equal to the sum of the other pair.
Page 203 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.
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 72 - The lines joining the middle points of the opposite sides of a quadrilateral bisect each other.