# Elements of Plane Geometry

E.H. Butler & Company, 1882 - Geometry - 196 pages

### Contents

 INTRODUCTION 7 DEFINITIONS 9 MATHEMATICAL TERMS 14 PARALLEL LINES 27 TRIANGLES 34 EQUALITY OF TRIANGLES 41 RELATION BETWEEN THE PARTS OF A TRIANGLE 48 POLYGONS 54
 EXERCISES IN INVENTION 71 BOOK III 85 RELATIVE POSITION OF CIRCLES 97 PROBLEMS IN CONSTRUCTION 107 EXERCISES IN INVENTION 124 REGULAR POLYGONS AND THE CIRCLE 179 PROBLEMS IN CONSTRUCTION 188 EXERCISES IN INVENTION 195

### Popular passages

Page 14 - Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.
Page 83 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 85 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 44 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.
Page 14 - 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 136 - 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, minus twice the product of one of these sides and the projection of the other side upon it.
Page 123 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Page 55 - A polygon of three sides is a triangle ; of four, a quadrilateral; of five, a pentagon ; of six, a hexagon ; of seven, a heptagon; of eight, an octagon; of nine, a nonagon; of ten, a decagon; of twelve, a dodecagon.
Page 137 - 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 177 - From this proposition it is evident, that the square described on the difference of two lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines.