# The Elements of Plane and Solid Geometry: With Numerous Exercises

D.C. Heath & 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 nl Method of Perimeters 231 Exercises Theorems 243 Definitions 250 Parallel Planes 258 Diedral Angles Definitions 264 Polyedral Angles Definitions 276

 BOOK II 74 Relative Position of Two Circles 88 Quadrilaterals 102 Exercises Theorems 123 SIMILAR FIGURES 134 Proportional Lines 143 Similar Figures 149 Similar Polygons 155 Problems of Construction 168 Exercises Theorems 175 Comparison of Areas 187 Applications 200 BOOK V 208
 Exercises Theorems 283 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 206 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.
Page 97 - BAC, inscribed in a segment greater than a semicircle, is an acute angle ; for it is measured by half of the arc BOC, less than a semicircumference.
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 12 - LET it be granted that a straight line may be drawn from any one point to any other point.
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.