# Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with Practical Exercises

Sheldon, 1883 - Geometry - 333 pages

### Contents

 AXIOMS AND POSTULATES 30 CHAPTER I 39 SECTION II 48 PARALLELS 55 RELATIVE POSITIONS OF STRAIGHT LINES AND CIRCUMFERENCES 6879 68 RELATIVE POSITIONS OF CIRCUMFERENCES 80 8086 87 MEASUREMENT OF ANGLES 88102 88
 SECTION XI 184 PERIMETERS AND THE RECTIFICATION OF THE CIRCUMFER 191 AREA OF THE CIRCLE 197199 197 SOLID GEOMETRY 205 OF SOLID ANGLES 225 OF TRIEDRALS 231244 231 OF POLYEDRALS 244 SECTION IV 265

 EXERCISES 103104 103 SECTION VIII 130 DETERMINATION OF TRIANGLES 139143 139 DETERMINATION OF POLYGONS 147149 147 AREA 155163 155 EXERCISES 163164 163
 SECTION V 284 SPHERICAL ANGLES 293296 293 POLAR OR SUPPLEMENTAL TRIANGLES 309312 309 LUNES 317323 317 VOLUME OF SPHERE 324327 324 APPENDIX 331333 331

### Popular passages

Page 286 - A Sphere is a solid bounded by a surface every point in which is equally distant from a point within called the Centre.
Page 134 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the third sides are unequal, and the greater third side belongs to the triangle having the greater included angle.
Page 14 - LEMMA 4. — A common divisor of two numbers is a divisor of their sum and also of their difference.
Page 303 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.
Page 298 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 169 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Page 323 - A spherical sector is the portion of a sphere generated by the revolution of a circular sector about any diameter of the circle of which the sector is a part.
Page 106 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 158 - Theorem. — The area of a trapezoid is equal to the product of its altitude...