# Elements of Geometry: Plane geometry

Harper & Brothers, 1896 - Geometry, Plane
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### Contents

 INTRODUCTION 3 PARALLEL LINES AND SYMMETRICAL FIGURES 15 TRIANGLES 32 PARALLELOGRAMS 60 PROBLEMS 66 BOOK II 73 MEASUREMENT 87 PROBLEMS OF DEMONSTRATION 106
 PROBLEMS OF DEMONSTRATION 154 PROBLEMS FOR COMPUTATION 160 BOOK IV 170 PROBLEMS OF DEMONSTRATION 193 BOOK V 202 PROBLEMS OF CONSTRUCTION 230 BOOK II 237 BOOK IV 244

### Popular passages

Page 10 - 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 46 - ... 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 248 - The area of a regular hexagon inscribed in a circle is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Page 5 - If the first of three quantities is greater than the second, and the second is greater than the third, then the first is greater than the third.
Page 215 - The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or as the squares of their apothems.
Page 67 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Page 145 - If from a point without a circle a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and its external segment.
Page 71 - The perpendiculars from the vertices of a triangle to the opposite sides meet in a point.
Page 180 - Two triangles which have an angle of one equal to the supplement of an angle of the other are to each other as the products of the sides including the supplementary angles.
Page 149 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.