# A Treatise on Special Or Elementary Geometry

Sheldon & Company, 1879
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### Contents

 INTRODUCTION 1 EXERCISES IN GEOMETRICAL INVENTION 5 PART I 12 THEOREMS IN SPECIAL OR ELEMENTARY GEOMETRY 243267 19 PROBLEMS IN SPECIAL OR ELEMENTARY GEOMETRY 267276 25 CHAPTER I 60 SECTION III 70 SECTION IV 78
 Of Quadrilaterals 129130 129 SECTION IX 138 OF SIMILARITY 144152 144 SECTION XI 153 CHAPTER II 164 SECTION II 175 Of Polyedrals 185186 185 SECTION IV 199

 SECTION V 86 SECTION VI 94 SECTION VII 104 SECTION VIII 121
 SECTION V 209 Spherical Angles 215218 215 Polar or Supplemental Triangles 226228 226 Volume of Sphere 235239 235

### Popular passages

Page 219 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 222 - 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.
Page 141 - The area of a trapezoid is equal to the product of its altitude...
Page 233 - If two semicircumferences of great circles intersect on the surface of a hemisphere, the sum of the two opposite triangles thus formed is equivalent to a lune whose angle is that included by the semicircumferences. DEM. — Let the semicircumferences CEB and DEA intersect at E on the surface of the...
Page 209 - A sphere is a solid, bounded by one continued convex surface, every point of which is equally distant from a point within, called the centre.
Page 106 - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
Page 138 - Theorem — Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other.
Page 127 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.
Page 53 - Similar triangles are to each other as the squares of their homologous sides.
Page 2 - LEMMA 4. — A common divisor of two numbers is a divisor of their sum and also of their difference.