Practical Astronomy and Geodesy: Including the Projections of the Sphere and Spherical Trigonometry. For the Use of the Royal Military CollegeLongman, Brown, Green, and Longmans, 1845 - 427 pages |
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Page 46
... substituting COS . AB 1 = - sin . for secant , and for tangent , COS . A C COS . BC whence cos . AC cos . BC COS . sin . AC sin . BC COS . A C COS . BC COS . ACB ; cos . A B sin . AC sin . BC cos . AC B ― and COS . ACB = COS . A B Cos ...
... substituting COS . AB 1 = - sin . for secant , and for tangent , COS . A C COS . BC whence cos . AC cos . BC COS . sin . AC sin . BC COS . A C COS . BC COS . ACB ; cos . A B sin . AC sin . BC cos . AC B ― and COS . ACB = COS . A B Cos ...
Page 47
... substituting for them their equiva- lents in the complemental triangle BFE ( Sph . Geom . , 18. ) , AG , AF , CE , and GE being quadrants and the angles at C , G , and F , right angles ; c also the angles at A and E , being measured by ...
... substituting for them their equiva- lents in the complemental triangle BFE ( Sph . Geom . , 18. ) , AG , AF , CE , and GE being quadrants and the angles at C , G , and F , right angles ; c also the angles at A and E , being measured by ...
Page 48
... substituting in the formulę ( a ) , ( b ) , ( c ) , art . 60. , terms taken from the latter triangle which are the equivalents of the sines and cosines of the sides , and the cosines of the angles belonging to the first triangle ...
... substituting in the formulę ( a ) , ( b ) , ( c ) , art . 60. , terms taken from the latter triangle which are the equivalents of the sines and cosines of the sides , and the cosines of the angles belonging to the first triangle ...
Page 49
... substituting for the terms in this last formula their equivalents in the complemental triangle EN M , we get ... r cos . EMN tan . MN cotan . EM . · · ( ƒ ' ) . COR . 2. The equation preceding ( į ) , omitting the ac- cents , is cos ...
... substituting for the terms in this last formula their equivalents in the complemental triangle EN M , we get ... r cos . EMN tan . MN cotan . EM . · · ( ƒ ' ) . COR . 2. The equation preceding ( į ) , omitting the ac- cents , is cos ...
Page 53
... substituting in the numerator of the second member the equivalent of the difference between the two cosines ( Pl . Trigon . , art . 41. ) , the last equation becomes 2 sin . § ( AC + BC + AB ) sin . † ( AC + BC —AB ) sin . AC sin . BC 2 ...
... substituting in the numerator of the second member the equivalent of the difference between the two cosines ( Pl . Trigon . , art . 41. ) , the last equation becomes 2 sin . § ( AC + BC + AB ) sin . † ( AC + BC —AB ) sin . AC sin . BC 2 ...
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Practical Astronomy and Geodesy: Including the Projections of the ..., Volume 5 John Narrien No preview available - 2016 |
Common terms and phrases
angular distance apparent ascension and declination astronomical azimuth bisected celestial body celestial sphere centre circle passing circumference colatitude computed considered correction corresponding cosine cotan degrees described determined diameter difference earth ecliptic ellipse equal equator equatorial equinoctial point expressed fixed star formula geocentric given graduation Greenwich Greenwich mean horary motions horizontal parallax hour angle index error instant instrument interval latitude latter let fall limb longitude mean noon meridian micrometer moon moon's Nautical Almanac node observed altitude obtained optical axis orbit parallax parallel perihelion perpendicular plane passing polar distance pole position projection radius refraction represented revolution revolve right angles right ascension satellite screw sector semidiameter side sidereal sidereal clock sine sphere spherical triangle star's station subtended subtracted supposed surface tangent transit telescope true variation vertical wire zenith distance zero
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