Spherical Trigonometry, for the Use of Colleges and Schools: With Numerous Examples
Macmillan, 1879 - Spherical trigonometry - 158 pages
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Common terms and phrases
2pÁv a+b+c ambiguity angular points approximately arcs drawn arcs which join bcos bisecting centre circular measure cos b cos cos TU cos▓ cos│ cosines Crown 8vo deduce denote equation equilateral escribed circles example expression faces fixed points formulŠ formulŠ in Art greater Hence inscribed Legendre's Theorem 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 primitive triangle quadrant r₁ regular polyhedron respectively result right angles right-angled triangles shew shewn Similarly sin b cos sin b sin sin▓ sin│ sine small circle described solid angles solution sphere spherical excess spherical triangle Spherical Trigonometry straight lines subtended suppose surface tangent tetrahedron
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 49 - 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 12 - Any two sides of a spherical triangle are together greater than the third side.
Page 19 - Thus the sines of the angles of a spherical triangle are proportional to the sines of the opposite sides.
Page 30 - From this proposition, it is obvious that if one angle of a triangle be equal to the sum of the other two angles, that angle is a right angle, as is shewn in Euc.
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 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 15 - If one angle of a spherical triangle be greater than another, the side opposite the greater angle is greater than the side opposite the less angle.