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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Page 209
... the celes- tial sphere above the observer , is called the zenith ; the opposite point , where this line meets the sphere . below the observer , is called the nadir . Prime vertical . Cardinal points . Hence the vertical line 18 *
... the celes- tial sphere above the observer , is called the zenith ; the opposite point , where this line meets the sphere . below the observer , is called the nadir . Prime vertical . Cardinal points . Hence the vertical line 18 *
Page 210
... Prime vertical . Cardinal points . Hence the vertical line is a radius of the celestial sphere perpendicular to the horizon ; and the zenith and nadir are the poles of the horizon . [ B. p . 48. ] 12. Circles whose planes pass through ...
... Prime vertical . Cardinal points . Hence the vertical line is a radius of the celestial sphere perpendicular to the horizon ; and the zenith and nadir are the poles of the horizon . [ B. p . 48. ] 12. Circles whose planes pass through ...
Page 218
... prime vertical with the elevated pole ; but , in the latter case , it is below the horizon , and on the same side of the prime vertical with the depressed pole . 31. Corollary . If the star is in the celestial equator , as in ( fig . 36 ) ...
... prime vertical with the elevated pole ; but , in the latter case , it is below the horizon , and on the same side of the prime vertical with the depressed pole . 31. Corollary . If the star is in the celestial equator , as in ( fig . 36 ) ...
Page 221
... 3m 20s . Ans . Its altitude = 25 ° 58 ' . Its azimuth from the South = 34 ° 45 ' . 10. Find the altitude and azimuth of a star in the celes- Altitude of a star in the prime vertical . tial 19 * $ 33 . ] 221 DIURNAL MOTION .
... 3m 20s . Ans . Its altitude = 25 ° 58 ' . Its azimuth from the South = 34 ° 45 ' . 10. Find the altitude and azimuth of a star in the celes- Altitude of a star in the prime vertical . tial 19 * $ 33 . ] 221 DIURNAL MOTION .
Page 222
... prime vertical . tial equator , to an observer at Stockholm , when the hour angle is 9 ' 30 " . Ans . Its depression below the horizon = 23 ° 51 ' . Its azimuth from the North = 41 ° 45 ' . 11. Find the altitude and azimuth of Fomalhaut ...
... prime vertical . tial equator , to an observer at Stockholm , when the hour angle is 9 ' 30 " . Ans . Its depression below the horizon = 23 ° 51 ' . Its azimuth from the North = 41 ° 45 ' . 11. Find the altitude and azimuth of Fomalhaut ...
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Common terms and phrases
A₁ aberration altitude and azimuth angle given ascension and declination azimuth celestial equator celestial sphere centre circle computed Corollary corr correct central altitude corresponding cosec cosine cotan diff difference of latitude difference of longitude dist earth eclipse of April equal to 90 formula gives Greenwich Hence horizon horizontal parallax hour angle hypothenuse included angle interval latitude and longitude lunar distance mean meridian altitude method middle latitude moon's motion N₁ Napier's Rules Nautical Almanac Navigator Nutation obliquity obtuse perpendicular plane polar triangle prime vertical Problem R₁ radius reduced right ascension sailing Scholium second member semidiameter sideral sideral day solar eclipse Solution solve the triangle spherical right triangle spherical triangle star's sun's Table XXIII tang tangent Theorem transit triangle ABC Trig true latitude tude vernal equinox whence
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...