# The Elements of Geometry

Leach, Shewell & Sanborn, 1886 - Geometry - 371 pages

### Contents

 PRELIMINARY DEFINITIONS 1 PERPENDICULARS AND OBLIQUE LINES 8 PARALLEL LINES 16 TRIANGLES 24 QUADRILATERALS 39 MISCELLANEOUS THEOREMS 47 POLYGONS 53 THE CIRCLE 60
 SYMMETRICAL FIGURES 207 ADDITIONAL EXERCISES 217 39 220 92 226 SOLID GEOMETRY 227 DIEDRAL ANGLES 242 POLYEDRAL ANGLES 253 PAGE 260

 ON MEASUREMENT 76 EXERCISES 87 PROBLEMS IN CONSTRUCTION 94 POLYGONS 111 PROPORTIONAL LINES 118 5 141 AREAS OF POLYGONS 150 24 171 REGULAR POLYGONS MEASUREMENT 182 MEASUREMENT OF THE CIRCLE 197
 PYRAMIDS 279 SIMILAR POLYEDRONS 295 MISCELLANEOUS THEOREMS 306 THE CONE 312 SPHERICAL ANGLES 323 MEASUREMENT OF SPHERICAL POLYGONS 338 MEASUREMENT OF THE CYLINDER CONE 346 THE SPHERE 361 ANSWERS TO THE NUMERICAL EXAMPLES 369

### Popular passages

Page 60 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Page 277 - The volume of a triangular prism is equal to the product of its base and altitude. Let AE be the altitude of the triangular prism ABC-C'. To prove that volume ABC-C' = ABC x AE. Construct the parallelopiped ABCD-D' having its edges equal and parallel to AB, BC, and BB'.
Page 112 - If the product of two quantities is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Let ad = ос.
Page 31 - If two triangles have two sides of 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.
Page 313 - A Sphere is a solid bounded by a curved surface all points of which are equally distant from a point within called the centre.
Page 50 - 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 44 - If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram.
Page 161 - The areas of two triangles which have 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. To prove that Proof. A Let the triangles ABC and ADE have the common angle A. A ABC -AB X AC Now and A ADE AD X AE Draw BE.
Page 46 - Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other.
Page 167 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.