# An Elementary Treatise on Plane and 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. Monroe, 1852 - Trigonometry - 359 pages

### Contents

 Sines Tangents and Secants 6 Right Triangles 17 General Formulas 22 Values of the Sines Cosines Tangents Cotangents Secants and Cosecants of certain Angles 30 Oblique Triangles 38 Logarithmic and Trigonometrical Series 52 NAVIGATION AND SURVEYING 63 Plane Sailing 65
 38 144 52 145 65 151 72 155 75 156 78 157 84 160 СНАР PAGE 167

 Traverse Sailing 72 Parallel Sailing 75 Middle Latitude Sailing 78 Mercators Sailing 84 Surveying 96 Heights and Distances 106 SPHERICAL TRIGONOMETRY 115 Definitions 117 Right Triangles 120 Oblique Triangles 138
 96 245 Longitude 255 8 271 72 278 Aberration 279 106 280 117 286 121 292 138 304 Copyright

### Popular passages

Page 105 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 31 - 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 28 - To find a side, work the following proportion: — 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 156 - Secondaries to the celestial equator are called circles of declination; of these 24, which divide the equator into equal parts of 15° each, are called hour circles.
Page 231 - Solar Day is the interval of time between two successive transits of the sun over the same meridian ; and the hour angle of the sun is called Solar Time. This is the most natural and direct measure of time. But the intervals between the successive returns of the sun to the meridian are not exactly equal, but depend upon the variable> motion of the sun in right ascension. - The want of uniformity in the sun's motion in right ascension arises from two different causes ; one, that the sun does not move...
Page 150 - The cosine of half the sum of two sides of a spherical triangle is to the cosine of half their difference as the cotangent of half the included angle is to the tangent of half the sum of the other two angles. The sine of half the sum of two sides of a spherical...
Page 67 - This method of calculating the difference of longitude may be rendered perfectly accurate by applying to the middle latitude a correction," which is given in the Navigator, and the method of computing which will be explained in the succeeding chapter.
Page 113 - II. The sine of the middle part is equal to the product of the cosines of the opposite parts.
Page 156 - ... equator and the ecliptic, and hence, also, the position of the equinoxes. In expressing the positions of stars, referred to the vernal equinox, at any given instant, the actual position of the equinox at the instant is understood, unless otherwise stated. The right ascension of a point of the sphere is the arc of the equator intercepted between its circle of declination and the vernal equinox, and is reckoned from the vernal equinox eastward from 0° to 360°, or, in time, from 0* to 24*.
Page 130 - XXIII, the following rule is obtained for finding the third side, when two sides and the included angle are given.