### Contents

 PART I 9 CHAPTER III 22 CHAPTER IV 31 CHAPTER V 43 CHAPTER VI 51 CHAPTER VII 57 MISCELLANEOUS PROBLEMS RELATING TO PLANE TRIANGLES 75 CHAPTER X 85
 CHAPTER XIV 127 CHAPTER XV 135 Development of any power of the Cosine of the Simple Angle in a Series 141 GENERAL FORMULE 149 CHAPTER II 167 CHAPTER III 178 144 191 CHAPTER IV 214

 CHAPTER XII 105 TRIGONOMETRIC SERIES 115
 CHAPTER V 229 CHAPTER VII 241

### Popular passages

Page 151 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides, plus the product of the sines of those sides into the cosine of their included angle ; that is, (1) cos a = cos b...
Page 169 - The sine of any middle part is equal to the product of the tangents of the Adjacent parts. RULE II. The sine of any middle part is equal to the product of the cosines of the opposite parts.
Page 2 - Union, in the Clerk's Office of the District Court of the Eastern District of Pennsylvania. PREFACE.
Page 58 - 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 229 - THEOREM. The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle.
Page 64 - As the sine of the angle opposite the given side, is to the sine of the angle opposite the required side ; so is the given side to the required side.
Page 15 - The sum of the two acute angles of a right triangle is equal to one right angle, or 90�.
Page 65 - The side opposite the given angle is to the side opposite the required angle as the sine of the given angle is to the Bine of the required angle.
Page 181 - ... cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos b + sin a sin b cos C.
Page 150 - The law of sines states that in any spherical triangle the sines of the sides are proportional to the sines of their opposite angles: sin a _ sin b __ sin c _ sin A sin B sin C...