# Elements of Plane Geometry

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

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### Contents

 INTRODUCTION 1 BOOK I 8 Axiom 12 Triangles 15 Base angles of triangle 27 Parallel Lines 45 Quadrilaterals 57 Polygons 66
 Correlativity and continuity 112 Bisector of triangle 131 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 II 79 Base of parallelogram 85 Bisected angle 93 Measurement 99 Angles formed by Chords Tangents Secants 106
 BOOK V 223 Ratio of Diameter to Circle 247 Centersect of circles 259 Copyright

### 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 243 - The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R
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 62 - Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle 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 21 - Two triangles are congruent if two angles and the included side of one are equal respectively to two angles and the included side of the other.