# The Elements of Plane and Solid Geometry ...

D. Van Nostrand Company, 1890 - Geometry - 393 pages
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### Contents

 INTRODUCTION 1 Angular Measure 8 PLANE GEOMETRY 14 Parallel Lines 23 Triangles 33 Quadrilaterals 46 Polygons 52 Symmetry 64
 The Measure of the Circle 215 Problems of Construction 224 Value of π Method of Perimeters 231 Exercises Theorems 243 PLANE AND SOLID ANGLES 250 Parallel Planes 258 Diedral Angles Definitions 264 Polyedral Angl�s Definitions 276

 BOOK II 74 Relative Position of Two Circles 88 Quadrilaterals 102 Exercises Theorems 123 Proportional Lines 143 Similar Figures 149 Similar Polygons 156 Problems of Construction 168 Exercises Theorems 175 Comparison of Areas 187 Applications 200 BOOK V 207
 Exercises Theorems 282 Pyramids 302 Similar Polyedrons 316 General Properties of Polyedrons 325 BOOK VIII 334 Spherical Triangles and Polygons 342 Polar Triangles 349 Exercises Theorems 360 BOOK IX 366 The Sphere 378 Exercises Theorems 386 Copyright

### Popular passages

Page 74 - A circle is a plane figure bounded by a curved line, called the circumference, every point of which is equally distant from a point within called the center.
Page 188 - 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 45 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Hyp. In A ABC and A'B'C' AB = A'B'; AC = A'C'; ZA>ZA'.
Page 137 - Terms of the proportion. The first and fourth terms are called the Extremes, and the second and third the Means.
Page 12 - AXIOMS. 1. Things which are equal to the same thing are equal to each other. 2. If equals be added to equals, the sums will be equal.
Page 57 - 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 334 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 253 - Equal oblique lines from a point to a plane meet the plane at equal distances from the foot of the perpendicular ; and of two unequal oblique lines the greater meets the plane at the greater distance from the foot of the perpendicular.
Page 378 - The circumferences of the sections made by the planes are called the bases of the zone, and the distance between the planes is the altitude of the zone.