## Spherical Trigonometry: For Colleges and Secondary Schools (Google eBook) |

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accordingly altitude angular astronomy axis celestial sphere centre circle passing construct cos2 deduced denote derived described in Art diedral angle draw drawn earth earth's surface ecliptic equator EXAMPLES face angles Find the distance formulas frustum geometry given point greater than 90 Hence hour angle included angle intersection law of cosines law of sines logarithms longitude meridian miles Napier's Analogies Napier's rules Note number of degrees parallel perpendicular plane angle plane triangle Plane Trigonometry polar triangle Proposition radians radii relations respectively equal right angles right ascension right spherical triangle right triangles right-angled triangles satisfies the given semicircle Show sides and angles sin a sin sin2 solid angle solution Solve ABC Solve the triangle sphere of radius spherical angle spherical degree measure spherical excess spherical measure spherical polygon spherical pyramid spherical sector spherical triangle ABC spherical trigonometry star subtended sun's declination three angles triedral

### Popular passages

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 36 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.

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...

Page 15 - ADC ; the last two are therefore right angles ; hence the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is perpendicular to the base, and bisects the vertical angle. PROPOSITION XVI.