# Plane and Solid Geometry

Macmillan, 1913 - Geometry, Plane - 321 pages

### Contents

 Introduction 1 Rectilinear Figures 35 The Circle 89 Proportion Similarity 126 Part IV 148 Miscellaneous Exercises 157 Areas of Polygons Pythagorean Theorem 162 Regular Polygons and Circles 186
 Dihedral Angles 228 Miscellaneous Exercises on Chapter VI 235 Part II 253 Part III 263 Part IV 274 The Sphere 284 Tables 322 Index xxix

### Popular passages

Page 168 - 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 140 - 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 154 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
Page 53 - If two parallel lines are cut by a transversal, the alternate interior angles are equal.
Page 133 - 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 66 - If two triangles have two sides of the one equal to two sides of the...
Page 309 - 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 294 - 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 134 - 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.
Page 67 - The perpendicular is the shortest line that can be drawn from a point to a straight line.