Spherical Trigonometry ...Macmillian and Company, limited, 1859 - 275 páginas |
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Página 7
... on spherical trigonometry consists of theorems relating to spherical triangles ; it is therefore necessary to obtain an accurate conception of a spherical triangle SPHERICAL TRIANGLES . 7 18. Thus, let O be the centre of a ...
... on spherical trigonometry consists of theorems relating to spherical triangles ; it is therefore necessary to obtain an accurate conception of a spherical triangle SPHERICAL TRIANGLES . 7 18. Thus, let O be the centre of a ...
Página 10
... theorems which involve the sides and angles themselves , and not their trigo- nometrical ratios . 25. Polar Triangle . Let ABC be any spherical triangle , and let the points A ' , B ' , C ' be those poles of the arcs BC , CA , AB # B ...
... theorems which involve the sides and angles themselves , and not their trigo- nometrical ratios . 25. Polar Triangle . Let ABC be any spherical triangle , and let the points A ' , B ' , C ' be those poles of the arcs BC , CA , AB # B ...
Página 12
... theorem be demonstrated with respect to the sides and angles of any spherical triangle it holds of course for the polar triangle also . Thus any such theorem will remain true when the angles are changed into the supplements of the ...
... theorem be demonstrated with respect to the sides and angles of any spherical triangle it holds of course for the polar triangle also . Thus any such theorem will remain true when the angles are changed into the supplements of the ...
Página 25
... theorem of Algebra , and also sin A + sin B m = sin a + sin b sin Asin B m - sin a sin b ( 1 ) , ( 2 ) . Now cos A + cos B cos C = sin B sin C cos a = m sin C sin b cos a , and cos B + cos A cos C = sin A sin C cos b = m sin C sin a cos ...
... theorem of Algebra , and also sin A + sin B m = sin a + sin b sin Asin B m - sin a sin b ( 1 ) , ( 2 ) . Now cos A + cos B cos C = sin B sin C cos a = m sin C sin b cos a , and cos B + cos A cos C = sin A sin C cos b = m sin C sin a cos ...
Página 26
... Theorems . We have cos c = cos a cos b + sin a sin b cos C ' ; therefore , 1 + cos a cos b + sin a sin b ( cos3 C— sin2 4C ) 1 + cos c = = = { 1 + cos ( a − b ) } cos3 C + { 1 + cos ( a + b ) } sin3 § C ′ ; therefore cos2 c = cos2 1 ...
... Theorems . We have cos c = cos a cos b + sin a sin b cos C ' ; therefore , 1 + cos a cos b + sin a sin b ( cos3 C— sin2 4C ) 1 + cos c = = = { 1 + cos ( a − b ) } cos3 C + { 1 + cos ( a + b ) } sin3 § C ′ ; therefore cos2 c = cos2 1 ...
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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