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 258
... correct altitude of Alde- baran was found by observation , in the year 1839 , to be 60 ° 40 ′ 20 ′′ , when its hour ... central altitudes of the sun , when its declination was 20 ° S. were 300 ° 6 ′ 40 ′′ . The hour angles of these ...
... correct altitude of Alde- baran was found by observation , in the year 1839 , to be 60 ° 40 ′ 20 ′′ , when its hour ... central altitudes of the sun , when its declination was 20 ° S. were 300 ° 6 ′ 40 ′′ . The hour angles of these ...
Page 262
... correct central altitude was found , by ob- servation , to be 53 ° 43 ' , when her declination was 14 ° 16 ' N. After an interval , in which the hour angle was 1 ' 44 TM 15o , her correct central altitude was 42 ° 29 ′ , and her ...
... correct central altitude was found , by ob- servation , to be 53 ° 43 ' , when her declination was 14 ° 16 ' N. After an interval , in which the hour angle was 1 ' 44 TM 15o , her correct central altitude was 42 ° 29 ′ , and her ...
Page 268
... altitude of the pole star [ B. p . 206 ] , when the right ascension of the zenith is 9h 7m Ans . 48 ' . 36. The altitude of the pole star was 25 ° 9 ′ , when the right ascension of ... correct central 268 [ CH . IV . SPHERICAL ASTRONOMY .
... altitude of the pole star [ B. p . 206 ] , when the right ascension of the zenith is 9h 7m Ans . 48 ' . 36. The altitude of the pole star was 25 ° 9 ′ , when the right ascension of ... correct central 268 [ CH . IV . SPHERICAL ASTRONOMY .
Page 269
... central altitudes were found by ob- servation to be 30 ° 13 ′ and 50 ° 4 ′ ; his declination was 20 ° 7 ' N. , and ... correct central altitude was 41 ° 33 ′ 12 ′′ , his declination 14 ° N .; after an interval of 1h 30m , his cor- rect ...
... central altitudes were found by ob- servation to be 30 ° 13 ′ and 50 ° 4 ′ ; his declination was 20 ° 7 ' N. , and ... correct central altitude was 41 ° 33 ′ 12 ′′ , his declination 14 ° N .; after an interval of 1h 30m , his cor- rect ...
Page 270
... altitude of Capella was 60 ° 45 ′ 36 ′′ , and her declination 45 ° 48 ′ 21 ′′ N .; at the same instant , the ... central altitude was 37 ° 40 ′ ; the moon's central altitude was 55 ° 20 ′ ; the sun's declination was 0 ° 17 ′ S .; the ...
... altitude of Capella was 60 ° 45 ′ 36 ′′ , and her declination 45 ° 48 ′ 21 ′′ N .; at the same instant , the ... central altitude was 37 ° 40 ′ ; the moon's central altitude was 55 ° 20 ′ ; the sun's declination was 0 ° 17 ′ S .; the ...
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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...