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
... right ascension of a star is the arc of the equator intercepted between its circle of declination and the vernal equinox . [ B. p . 49. ] Right ascension is either estimated in degrees , minutes , & c . from 0 ° to 360 ° ; or in hours ...
... right ascension of a star is the arc of the equator intercepted between its circle of declination and the vernal equinox . [ B. p . 49. ] Right ascension is either estimated in degrees , minutes , & c . from 0 ° to 360 ° ; or in hours ...
Page 214
... right ascension of the meridian expressed in time . [ B. p . 208. ] The meridian changes its right ascension at each instant , precisely as if the celestial sphere were stationary , while the observer , with his meridian and zenith , is ...
... right ascension of the meridian expressed in time . [ B. p . 208. ] The meridian changes its right ascension at each instant , precisely as if the celestial sphere were stationary , while the observer , with his meridian and zenith , is ...
Page 230
... right ascension . The upper passage of one of these stars is to be observed , and the lower passage of the other . Then any deviation in the plane of the instrument from the meridian , will evidently produce contrary effects upon the ...
... right ascension . The upper passage of one of these stars is to be observed , and the lower passage of the other . Then any deviation in the plane of the instrument from the meridian , will evidently produce contrary effects upon the ...
Page 231
... right ascension . The error in the position of the telescope is , in this case , equal to the difference in the errors of the observed transits , instead of the sum , as in the preceding method . 44. In making calculations where angles ...
... right ascension . The error in the position of the telescope is , in this case , equal to the difference in the errors of the observed transits , instead of the sum , as in the preceding method . 44. In making calculations where angles ...
Page 244
... right ascension and declination of the star . Of these corrections the first is the same as that of the Navigator , and is computed from ( 421 ) by using the pole star's mean right ascension and declination for the year ; and the third ...
... right ascension and declination of the star . Of these corrections the first is the same as that of the Navigator , and is computed from ( 421 ) by using the pole star's mean right ascension and declination for the year ; and the third ...
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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...