### Contents

 TRIGONOMETRIC FUNCTIONS 1 CHAPTER II 17 ARTICLE PAGE 24 CHAPTER III 35 ARTICLE 52 CHAPTER IV 66 ARTICLE PAGE 77 CHAPTER V 102
 proved geometrically 130 Analytic proof 132 Formulas 162 and 163 175 163 214 229 Construction on a globe 246 Given two sides and the included angle 257258 257 Given the three sides 265 265 B The Mariners Compass 272 272

 CHAPTER VII 126

### Popular passages

Page x - In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 182 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 148 - Two sides of a triangle, and the angle opposite one of them, being given, to describe the triangle. Let A and B be the given sides, and C the given angle.
Page 144 - The area of a triangle is equal to the product of its three sides divided by four times the radius of its circumscribed circle.
Page 166 - That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles.
Page 167 - The extremities of that diameter of a sphere which is perpendicular to the plane of a circle are called the poles of that circle.
Page 23 - If 2 men start from the same place and travel in opposite directions, one at the rate of 4 miles an hour, and the other at the rate of 5 miles an hour, how far apart will they be at the end of 1 hour ? At the end of 2 hours ? 5 hours?
Page 169 - C) + sin B sin C(— cos a). ... cos A = — cos B cos C + sin B sin C cos a. (3) Similarly, cos B = — cos C cos A + sin C sin A cos b, cos C = — cos A cos B + sin A sin B cos c.
Page 128 - CB : CA : : sin A : sin B. For, with A as a centre, and AD equal to the less side...