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 130
... ; also a a ' cc2.5 ch . , d d'1 ch .; to find the Ans . Required area 3 ch . , b b'— 2 ch . , area of ABC . 2 A. 3 R. 36 r . Horizon . CHAPTER VII . HEIGHTS AND DISTANCES . Bearing 130 [ CH . VI NAVIGATION AND SURVEYING .
... ; also a a ' cc2.5 ch . , d d'1 ch .; to find the Ans . Required area 3 ch . , b b'— 2 ch . , area of ABC . 2 A. 3 R. 36 r . Horizon . CHAPTER VII . HEIGHTS AND DISTANCES . Bearing 130 [ CH . VI NAVIGATION AND SURVEYING .
Page 131
... Horizon . CHAPTER VII . HEIGHTS AND DISTANCES . Bearing . 65. The plane of the sensible horizon at any place , is the tangent plane to the earth's surface at that place . [ B. p . 48. ] The horizontal plane coincides with that of the ...
... Horizon . CHAPTER VII . HEIGHTS AND DISTANCES . Bearing . 65. The plane of the sensible horizon at any place , is the tangent plane to the earth's surface at that place . [ B. p . 48. ] The horizontal plane coincides with that of the ...
Page 137
... horizon . Solution . I. If light moved in a straight line , and if A ( fig . 27 ) were the eye of the observer , and B the object , the straight line APB would be that of the visual ray . The point P , at which the ray touches the ...
... horizon . Solution . I. If light moved in a straight line , and if A ( fig . 27 ) were the eye of the observer , and B the object , the straight line APB would be that of the visual ray . The point P , at which the ray touches the ...
Page 138
... horizon . h = AC , H = BD , 1 = PA , L = PB , R- the earth's radius . = Since BP is a tangent , and BOE a secant to the earth , we have BE : BP BP : BD ; and BD is so small in comparison with the radius , that we may take and the above ...
... horizon . h = AC , H = BD , 1 = PA , L = PB , R- the earth's radius . = Since BP is a tangent , and BOE a secant to the earth , we have BE : BP BP : BD ; and BD is so small in comparison with the radius , that we may take and the above ...
Page 139
... horizon . L2 H = = H 14 R 3 L2 1 H1 = H — H = & H = 7R ( 284 ) whence ( 285 ) L = √ ( 3 RH1 ) . III . In calculating the value of L by ( 285 ) , it is usually desired in statute miles , while the height H , is given in feet . Now we ...
... horizon . L2 H = = H 14 R 3 L2 1 H1 = H — H = & H = 7R ( 284 ) whence ( 285 ) L = √ ( 3 RH1 ) . III . In calculating the value of L by ( 285 ) , it is usually desired in statute miles , while the height H , is given in feet . Now we ...
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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...