Spherical Trigonometry ...Macmillian and Company, limited, 1859 - 275 páginas |
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Página 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 , in ... 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 , in ... supplement of the angle A. This we may express for SPHERICAL GEOMETRY . 11.
Página 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 ...
Página 20
... supplement of B , and thus sin PED is still equal to sin B. 43. To prove 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 sin A ...
... supplement of B , and thus sin PED is still equal to sin B. 43. To prove 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 sin A ...
Página 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 — C ) + sin ( π −В ) sin ( π – С ' ) cos ( π — α ) , COS A -- - cos B cos C + sin B sin ...
... supplements of the corresponding angles and the angle into the supplement of the corresponding side ; thus - COS ( π - A ) = COS ( π – В ) cos ( π — C ) + sin ( π −В ) sin ( π – С ' ) cos ( π — α ) , COS A -- - cos B cos C + sin B sin ...
Página 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 ...
Otras ediciones - Ver todas
Spherical Trigonometry: For the Use of Colleges and Schools Isaac Todhunter Vista de fragmentos - 1949 |
Spherical Trigonometry: For the Use of Colleges and Schools Isaac Todhunter Vista de fragmentos - 1929 |
Términos y frases comunes
A+B+C ambiguity angular points approximately bisecting Cambridge centre circular measure cloth cos b cos cos² cos³ cosine Crown 8vo deduce denote drawn equal angles equilateral example expressed Fcap formulæ formulæ of Art greater Hence hypothenuse inscribed Legendre's Theorem less Let ABC lune meet middle point Napier's analogies Napier's Rules obtained octahedron opposite angle opposite sides parallelopiped perpendicular plane angles plane triangle Plane Trigonometry polar triangle pole polygon preceding article primitive triangle prove quadrant R₁ r₂ radius regular polyhedron respectively right angle right-angled triangles Second Edition shew shewn sides and angles Similarly sin b cos sin b sin sin² sin³ sine solid angle sphere spherical excess spherical triangle Spherical Trigonometry subtended Suppose surface tangent tetrahedron Treatise triangle ABC Trigono Trinity College values π π
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