Spherical Trigonometry, for the Use of Colleges and Schools: With Numerous Examples |
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Page 11
... supplements of the angles and sides of the primitive triangle . For let the arc B'C ' , produced if necessary , meet the arcs AB , AC , produced if necessary , at ... supplement of the angle A. This we may express for SPHERICAL GEOMETRY . 11.
... supplements of the angles and sides of the primitive triangle . For let the arc B'C ' , produced if necessary , meet the arcs AB , AC , produced if necessary , at ... supplement of the angle A. This we may express for SPHERICAL GEOMETRY . 11.
Page 12
... supplement of B , and A'B ' the supplement of C. And since ABC is the polar triangle of A'B'C ' , it follows that BC , CA , AB are respectively the supplements of A ' , B ' , C ' ; that is , A ' , B ' , C ' are respectively the ...
... supplement of B , and A'B ' the supplement of C. And since ABC is the polar triangle of A'B'C ' , it follows that BC , CA , AB are respectively the supplements of A ' , B ' , C ' ; that is , A ' , B ' , C ' are respectively the ...
Page 20
... supplement of B , and thus sin PED is still equal to sin B. 43. To shew that cot a sin b cot A sin C + cos b cos C .. We have cos a = cos b cos c + sin b sin c cos A , cos c = cos a cos b + sin a sin b cos C ' , == sin C sin c sin a ...
... supplement of B , and thus sin PED is still equal to sin B. 43. To shew that cot a sin b cot A sin C + cos b cos C .. We have cos a = cos b cos c + sin b sin c cos A , cos c = cos a cos b + sin a sin b cos C ' , == sin C sin c sin a ...
Page 23
... supplements of the corresponding angles and the angle into the supplement of the corresponding side ; thus cos ( π — A ) = cos ( π — В ) cos ( π — С ' ) + sin ( π – В ) sin ( π-— C ' ) cos ( π −α ) , that is , cos A Similarly cos B and ...
... supplements of the corresponding angles and the angle into the supplement of the corresponding side ; thus cos ( π — A ) = cos ( π — В ) cos ( π — С ' ) + sin ( π – В ) sin ( π-— C ' ) cos ( π −α ) , that is , cos A Similarly cos B and ...
Page 27
... supplemental triangles were proved geometrically in Art . 27 , and by means of these properties the formulæ in Art ... supplements of the corresponding angles and sides , the fundamental formula of Art . 39 hold good , and therefore also ...
... supplemental triangles were proved geometrically in Art . 27 , and by means of these properties the formulæ in Art ... supplements of the corresponding angles and sides , the fundamental formula of Art . 39 hold good , and therefore also ...
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Common terms and phrases
ambiguity angular points approximately arcs drawn arcs which join bisecting centre circular measure cos a cos cos² cos³ cosb cosines Crown 8vo deduce denote equation equilateral escribed circles example expression faces fixed points formulæ formulæ of Art greater Hence inscribed Legendre's Theorem less Let ABC lune meet middle point Napier's analogies Napier's Rules obtain octahedron opposite angle 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 sin² sin³ sine small circle described solid angles solution sphere spherical excess spherical triangle Spherical Trigonometry ß³ straight lines subtended suppose surface tangent tetrahedron Trigono
Popular passages
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.