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Spherical Trigonometry: For Colleges and Secondary Schools - Primary Source ...
Daniel Alexander Murray
No preview available - 2014
Spherical Trigonometry, for Colleges and Secondary Schools
Daniel A. Murray
No preview available - 2018
accordingly altitude Analogies astronomy axis base called centre CHAPTER circle compute construction corresponding cosines declination denote derived described determined difference direction distance draw drawn earth earth's surface ecliptic equal equator EXAMPLES faces feet figure Find formulas geometry given greater Hence horizon hour inches intersection known latitude length less longitude lune means measure meridian method miles Napier's NOTE observer obtained opposite parallel passing perpendicular plane Plane Trigonometry polar triangle pole polygon positive problems proposition Prove quadrant radius reference relations respectively right angles right triangles rules sector segment Show shown sides Similarly sin b sin sinē sines solid angle solution Solve sphere spherical degree spherical excess spherical triangle spherical triangle ABC star sun's surface triedral angle volume Write zenith
Page 46 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 102 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Page 46 - A sin B sin C Cosine Law: cos a = cos b cos c + sin b sin c cos A cos b = cos c cos a + sin c sin a cos B cos c = cos a cos b...
Page 69 - The area of a lune is to the surface of the sphere as the angle of the lune is to four right angles, or as the arc which measures that angle is to the circumference.
Page 66 - The lateral area of a frustum of a cone of revolution is equal to one-half the sum of the circumferences of its bases multiplied by its slant height. Hyp. S is the lateral area, C and C...
Page 4 - A diameter of a sphere is a straight line passing through the centre and terminated at both ends by the surface.
Page 89 - ... since the altitude of the pole is equal to the latitude of the place (art.
Page 10 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The...