### Contents

 INTRODUCTION PAGE 1 CHAPTER I 9 CHAPTER II 59 CHAPTER III 100 CHAPTER IV 125
 CHAPTER V 171 APPENDIX 185 INDEX 207 Copyright

### Popular passages

Page 144 - If two spherical triangles on the same sphere, or equal spheres, have two sides and the -included angle of one equal respectively to two sides and the included angle of the other, I. They are equal if the equal parts occur in the same order. II. They are symmetrical if the equal parts occur in the reverse order. D
Page 177 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 118 - The lateral area of a frustum of a cone of revolution is equal to one half the sum of the circumferences of its bases multiplied by its slant height. Given L the lateral area, C and C...
Page 93 - Assuming that 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...
Page 155 - The shortest line that can be drawn on the surface of a sphere between two points is the arc of a great circle, not greater than a semicircumference, joining the two points.
Page 43 - 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 161 - The surface of a sphere is equal to four times the area of a circle...
Page 166 - The volume of a spherical sector is equal to the product of the zone which forms its base into one-third the radius of the sphere.
Page 153 - The area of a lune is to the surface of the sphere as the angle of the lune is to four right angles, or as the arc which measures that angle is to the circumference.
Page 174 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.