Spherical Trigonometry, for the Use of Colleges and Schools: With Numerous Examples |
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Common terms and phrases
A'BC A+B+C ambiguity angular points approximately arcs drawn arcs which join bcos bisecting centre circular measure cos b cos cos TU cos² cos³ cosines cot A cot Crown 8vo deduce denote equation escribed circles example expression faces fixed points formed formulæ formulæ in Art greater Hence inscribed less Let ABC lune meet middle point Napier's analogies Napier's Rules obtain octahedron opposite sides parallelepiped Plane Geometry plane triangle Plane Trigonometry polar triangle pole polygon position preceding Article quadrant R₁ regular polyhedron respectively result right angles right-angled triangles shew shewn Similarly sin b cos sin b sin sin² sin³ sine small circle described solid angles solution sphere spherical excess spherical triangle Spherical Trigonometry straight lines subtended suppose surface tangent tetrahedron
Popular passages
Page 23 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 19 - That is. the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles.
Page 30 - C and c. 2. If one angle of a triangle be equal to the sum of the other two, the greatest side is double of the distance of its middle point from the opposite angle.
Page 62 - A circle which touches one side of a triangle and the other two sides produced, is called an escribed circle of the triangle.
Page 156 - RESEARCHES IN THE CALCULUS OF VARIATIONS, principally on the Theory of Discontinuous Solutions: an Essay to which the Adams' Prize was awarded in the University of Cambridge in 1871.
Page 1 - A sphere is a solid bounded by a surface, every point of which is equally distant from a fixed point called the centre.
Page 12 - Any two sides of a spherical triangle are together greater than the third side.
Page 85 - An Account of the Measurement of two Sections of the Meridional Arc of India, bounded by the Parallels of 18° 3' 15", 24° 7' 11", 29a 30
Page 17 - 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...