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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Results 1-5 of 21
Page 100
... tude , and difference of longitude , when one latitude , the distance , and departure are given . [ B. p . 75. ] Solution . The course is found by the formula dep . sin . course = ; dist . the difference of latitude by the formula ( 237 ) ...
... tude , and difference of longitude , when one latitude , the distance , and departure are given . [ B. p . 75. ] Solution . The course is found by the formula dep . sin . course = ; dist . the difference of latitude by the formula ( 237 ) ...
Page 102
... tude , and its distance and bearing from Liverpool . Ans . Distance sailed Longitude 922 miles . = 50 ° 10 ′ W. 1905 miles . Distance from Liverpool Bearing from Liverpool = S. 75 ° 22 ′ W. 7. A ship sails southwesterly from Gibraltar a ...
... tude , and its distance and bearing from Liverpool . Ans . Distance sailed Longitude 922 miles . = 50 ° 10 ′ W. 1905 miles . Distance from Liverpool Bearing from Liverpool = S. 75 ° 22 ′ W. 7. A ship sails southwesterly from Gibraltar a ...
Page 104
... tude . [ B. p . 78. ] 42. Problem . To find the difference of longitude , when the distance , the course , and one latitude are known . Solution . Let AB ( fig . 16 ) be the ship's track . Divide it into the small portions A a , a b ...
... tude . [ B. p . 78. ] 42. Problem . To find the difference of longitude , when the distance , the course , and one latitude are known . Solution . Let AB ( fig . 16 ) be the ship's track . Divide it into the small portions A a , a b ...
Page 115
... tude , the course , and departure are given . [ B. p . 84. ] Solution . The distance is found by ( 236 ) , the difference of latitude by ( 235 ) , and the difference of longitude by ( 258 ) . 54. Problem . To find the course , the ...
... tude , the course , and departure are given . [ B. p . 84. ] Solution . The distance is found by ( 236 ) , the difference of latitude by ( 235 ) , and the difference of longitude by ( 258 ) . 54. Problem . To find the course , the ...
Page 224
... tude of a star , when it is in the horizon . Solution . In this case the side ZB ( fig . 35 ) of the triangle ZPB is 90 ° . The corresponding angle of the polar triangle is , therefore , a right angle , and the polar triangle is a right ...
... tude of a star , when it is in the horizon . Solution . In this case the side ZB ( fig . 35 ) of the triangle ZPB is 90 ° . The corresponding angle of the polar triangle is , therefore , a right angle , and the polar triangle is a right ...
Contents
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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...