### Contents

 INTRODUCTION 1 STRAIGHT LINES AND ANGLES 7 SUPERPOSITION ΙΟ 15 PERPENDICULAR LINES 23 PARALLEL LINES 31 OBLIQUE LINES 40 GENERAL SCHOLIATHEORY OF LOCI SCIENCE OF GEOMETRY 49 EQUAL TRIANGLES 56
 EQUAL PRODUCTS 206 PLANE FIGURES 214 TRIANGLES 223 QUADRILATERALS 230 REGULAR POLYGONS 237 Circles 246 SYNOPSIS 255 PARTS OF TRIANGLES 266

 EQUAL PARTS 66 UNEQUAL PARTS 75 referred to in the Table of Contents at the end of the respective sections 77 ANGLES 82 CONCURRENT LINES 90 QUADRILATERALS 102 ANGLES 112 EQUAL AREAS 124 COMPARISON OF AREAS 130 GENERAL SCHOLIAMAXIMA AND MINIMA THEORY OF LIMITS 148 EQUAL CHORDS AND ARCS 154 UNEQUAL CHORDS AND ARCS 161 CHORDS and PerpenDICULARS 167 ANGLES AND ARCS 175 Two CIRCLES 184 GENERAL SCHOLIACONCYCLIC POINTS INSCRIBED AND ESCRIBED 198 PAGE 199
 POLYGONS 274 CIRCLES 280 PROPORTIONAL AREAS 290 290 SYNOPSIS 301 Two PLANES 311 SEVERAL PLANES 318 SOLIDS WITH PLANE SURFACES 325 SURFACES 335 EQUIVALENT SOLIDS 342 PROPORTIONAL SOLIDS 348 SOLIDS WITH CURVED SURFACES 360 SECTION IISURFACES 371 VOLUMES 379 POLARITY AND SYMMETRY 387 SPHERICAL TRIANGLES 397 Copyright

### Popular passages

Page 166 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.
Page 275 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Page 93 - 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 127 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Page 146 - A CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the center; as the figure ADB E.
Page 78 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Page 61 - If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal.
Page 62 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 131 - 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 107 - The line which joins the mid-points of two sides of a triangle is parallel to the third side and equal to one half of it.