# An Elementary Treatise on Plane & Spherical Trigonometry: With Their Applications to Navigation, Surveying, Heights, and Distances, and Spherical Astronomy, and Particularly Adapted to Explaining the Construction of Bowditch's Navigator, and the Nautical Almanac

J. Munroe, 1845 - 449 y[W

r[܂łB

### ڎ

 PLANE TRIGONOMETRY 3 General Formulas 27 Values of the Sines Cosines Tangents Cotangents 37 Oblique Triangles 47 Logarithmic and Trigonometrical Series 65 Plane Sailing 83 Traverse Sailing 90 Middle Latitude Sailing 97
 The Diurnal Motion 212 The Meridian 226 Latitude 239 The Ecliptic 274 Precession and Nutation 288 Time 306 Longitude 322 Aberration 353

 Surveying 119 Heights and Distances 131 CHAP PAGE I The Celestial Sphere and its Circles 207
 Refraction 369 Parallax 380 Eclipses 400

### lĈp

156 y[W - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
145 y[W - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
48 y[W - 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. Thus, if a (fig.
50 y[W - The third side is found by the proportion. As the sine of the given angle is to the sine of the angle opposite the required side, so is the side opposite the given angle to the required side.
41 y[W - Since, when an angle is acute its supplement is obtuse, it follows from the preceding proposition, that the sine and cosecant of an obtuse angle are positive, while its cosine, tangent, cotangent, and secant, are negative.
53 y[W - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.
182 y[W - But a' = 180 - A, b' = 180 - ß, c' = 180 - C. and A' = 180 - a. Therefore, — cos A = (— cos B)(— cos C) + sin B sin C(— cos a...