## 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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A₁ ABC fig aberration adjacent angles angle given April 25 ascension and declination Calculate celestial celestial equator centre circle column Corollary corr cosec cotan course D₁ departure diff difference of latitude difference of longitude dist earth eclipse of April equator equinox find the sine formula gives Greenwich Greenwich mean Hence horizon horizontal parallax hour angle hypothenuse included angle interval latitude and longitude logarithm mean meridian altitude method middle latitude miles moon moon's motion Nautical Almanac Navigator obliquity obtuse parallax parallel sailing perpendicular plane pole prime vertical Problem proportional R₁ radius reduced right ascension Scholium secant second member semidiameter sideral Solar eclipse Solution solve the triangle spherical right triangle spherical triangle star star's sun's Table tang tangent Theorem transit triangle ABC Trig true latitude vernal equinox 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...