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 81
... latitude are the circumferences of small circles , the planes of which are parallel to the equator . 3. Meridians are the semicircumferences of great circles , which pass from one pole to the other . The first meridian is one ...
... latitude are the circumferences of small circles , the planes of which are parallel to the equator . 3. Meridians are the semicircumferences of great circles , which pass from one pole to the other . The first meridian is one ...
Page 82
... Latitude . Longitude . has been taken as the first meridian which passes through the capital of the country . But , in the United States , we have usually adhered to the English custom , and we consider the meridian , which passes ...
... Latitude . Longitude . has been taken as the first meridian which passes through the capital of the country . But , in the United States , we have usually adhered to the English custom , and we consider the meridian , which passes ...
Page 84
... Latitude and Departure , when either two of them are known . [ B. p . 52. ] 13. Problem . To find the difference of latitude and departure , when the distance and course are known . [ B. p . 54. ] Solution . First . When the distance is ...
... Latitude and Departure , when either two of them are known . [ B. p . 52. ] 13. Problem . To find the difference of latitude and departure , when the distance and course are known . [ B. p . 54. ] Solution . First . When the distance is ...
Page 85
... latitude , and BC is the depart- ure . Then , by ( 21 and 22 ) , Diff . of lat . dist . X cos . course . Departure ... latitude respectively of A and a , a and b , b and c , & c . Also a m , bn , c p , & c . are the departures of the ...
... latitude , and BC is the depart- ure . Then , by ( 21 and 22 ) , Diff . of lat . dist . X cos . course . Departure ... latitude respectively of A and a , a and b , b and c , & c . Also a m , bn , c p , & c . are the departures of the ...
Page 86
... latitude and departure are given in pages 1-6 , Tables I. and II . of the Navigator , which might be calculated by ( 211 and 212 ) . 14. Problem . To find the distance and difference of latitude , when the course and departure are known ...
... latitude and departure are given in pages 1-6 , Tables I. and II . of the Navigator , which might be calculated by ( 211 and 212 ) . 14. Problem . To find the distance and difference of latitude , when the course and departure are known ...
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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...