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Spherical Trigonometry: For Colleges and Secondary Schools - Primary Source ...
Daniel Alexander Murray
No preview available - 2014
altitude ambiguous astronomy axis celestial sphere centre circle passing compute cosē deduced Delambre's Analogies denote derived described in Art diedral earth earth's surface ecliptic equal equator EXAMPLES face angles Find the area formulas frustum geometry Hence horizon hour angle included angle intersection latitude law of cosines law of sines logarithms longitude lune of angle means of right meridian miles Napier's Analogies NOTE number of degrees original triangle perpendicular plane angle plane triangle Plane Trigonometry polar triangle polyedron radians radii relations right angles right ascension right spherical triangle right triangles right-angled triangles semicircle Show sides and angles sin b sin sinē solid angle solution Solve ABC Solve the polar Solve the triangle sphere of radius spherical degree measure spherical excess spherical measure spherical polygon spherical sector spherical triangle ABC spherical trigonometry star subtended sun's declination three angles triedral angle vernal equinox 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...