# Elements of Plane Geometry

Southern Publishing Company, 1910 - Geometry, Modern - 263 pages

### Contents

 INTRODUCTION 1 BOOK I 8 Triangles 15 Parallel Lines 45 Quadrilaterals 57 Polygons 66 BOOK II 79 Measurement 99
 RATIO AND PROPORTION SIMILAR FIGURES 133 Harmonic Division 145 Similar Figures 151 Intersecting Chords Tangents Secants 168 BOOK IV 193 Principle of Homology 208 BOOK V 223 Ratio of Diameter to Circumference 247

### Popular passages

Page 41 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Page 42 - ... if two triangles have two sides of one equal, respectively, to two sides of the other...
Page 179 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
Page 5 - Axioms. 1. Things which are equal to the same thing are equal to each other. 2. If equals are added to equals, the wholes are equal. 3. If equals are taken from equals, the remainders are equal.
Page 135 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.
Page 67 - A Polygon of three sides is called a triangle ; one of four sides, a quadrilateral; one of five sides, a pentagon; one of six sides, a hexagon; one of seven sides, a heptagon; one of eight sides, an octagon ; one of ten sides, a decagon ; one of twelve sides, a dodecagon, &c.
Page 176 - The sum of the squares of two sides of a triangle is equal to twice the square of half the third side increased by twice the square of the median upon that side.
Page 173 - 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 by the projection of the other upon that side.
Page 17 - In a right triangle, the side opposite the right angle is called the hypotenuse, and the other two sides the legs.
Page 202 - Assuming that 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...