## Spherical Trigonometry: For Colleges and Secondary Schools |

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Spherical Trigonometry: For Colleges and Secondary Schools - Primary Source ... Daniel Alexander Murray No preview available - 2014 |

### Common terms and phrases

ABC Fig accordingly altitude ambiguous angular celestial sphere centre circle passing compute construct cosē deduced Delambre's Analogies denote derived described in Art diedral angle draw drawn earth ecliptic equator EXAMPLES face angles formulas frustum geometry given point greater than 90 Hence hour angle included angle intersection latitude law of cosines Law of Sines logarithms longitude meridian Napier's Analogies NOTE number of degrees original triangle perpendicular plane angle plane triangles Plane Trigonometry polar triangle polyedron Proposition radians radii relations respectively equal right angles right ascension right spherical triangle right triangles right-angled triangle satisfies the given semicircle Show sides and angles sin b sin sinē solid angle solution Solve ABC Solve the triangle sphere of radius spherical angle spherical degree measure spherical excess spherical measure spherical polygon 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.