### Contents

 Preliminary Definitions 1 Parallel Lines 17 Quadrilaterals 33 Polygons 40 Definitions 46 On Measurement 56 Problems in Construction 65 RATIO AND PROPORTION SIMILAR FIGURES 78
 REGULAR POLYGONS AND CIRCLES 124 Maxima and Minima 139 SOLID GEOMETRY 145 Diedral Angles 155 POLYEDRONS CYLINDERS AND Cones 164 Pyramids 178 THE SPHERE 192 The Sphere 204

### Popular passages

Page 46 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Page 105 - ... any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 403. The area of a triangle is equal to half the product of its base by its altitude.
Page 190 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Page 173 - The volume of a triangular prism is equal to the product of its base by its altitude. A~ Let V denote the volume, B the base, and H the altitude of the triangular prism CEA-E'.
Page 108 - Two triangles having 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.
Page 80 - In any proportion the terms are in proportion by Composition; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
Page 81 - If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Page 146 - A STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.
Page 30 - In an isosceles triangle, the angles opposite the equal sides are equal.
Page 79 - If the product of two quantities is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Let ad = ос.