## 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 |

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### Common terms and phrases

acute adjacent altitude apparent azimuth bearing becomes beginning Calculate called centre circle column computed Corollary correction corresponding cosec cosine cotan course declination departure determined diff difference difference of latitude distance earth equal equator equinox error EXAMPLES formula given gives greater greatest Greenwich Hence horizon hour angle hypothenuse increase interval known latitude less logarithm longitude mean meridian method middle miles minutes moon moon's motion Navigator nearly object obliquity observed obtained obtuse opposite parallax perpendicular plane pole position preceding Problem proportional radius reduced right ascension Rules sailing sideral sides sine Solar eclipse Solution solve the triangle spherical right triangle spherical triangle star substituted sun's Table tang tangent transit true whence zenith

### Popular passages

Page 156 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.

Page 145 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.

Page 48 - 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.

Page 50 - 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.

Page 41 - 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.

Page 53 - 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.

Page 182 - 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...