### Contents

 Introduction 1 The Principal Ideas used in Geometry 10 Statements for Reference 26 Rectilinear Figures 35 The Circle 89 Proportion Similarity 126 Part III 139 Part IV 148
 Areas of Polygons Pythagorean Theorem 162 Regular Polygons and Circles 186 Maxima and Minima 206 Lines and Planes in Space 215 Polyhedrons Cylinders Cones 238 The Sphere 284 Tables 322 Index xxx

### Popular passages

Page 160 - The area of a rectangle is equal to the product of its base and altitude ; that is, A = ab. 443. Corollary 1. The area of a square is equal to the square of its side. 444. Corollary 2. Tiro rectangles are to each other as the products of their bases and altitudes.
Page 132 - 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 132 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Page 125 - If the product of two numbers is equal to the product of two other numbers, either two may be made the means, and the other two the extremes of a proportion.
Page 301 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180� and less than 540�. (gr). If A'B'C' is the polar triangle of ABC...
Page 64 - If two triangles have two sides of the one equal to two sides of the...
Page 286 - The axis of a circle of a sphere is the diameter of the sphere which is perpendicular to the plane of the circle. The ends of the axis are called the poles of the circle.
Page 222 - Theorem. —A line perpendicular to one of two parallel lines is perpendicular to the other.
Page 310 - The area of a lune is to the area of the surface of the sphere as the angle of the lune is to four right angles.
Page 126 - If four quantities are in proportion, they are in proportion by inversion; that is, the second term is to the first as the fourth is to the third.