Spherical Trigonometry: For the Use of Colleges and SchoolsMacmillan and Company, 1863 - 132 páginas |
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Página 75
... c + cos b cosc cos A. If the sides of the triangle are small compared with the radius of the sphere , EF will not differ much from A ; suppose EF - A - 0 , then approximately cos EF = cos A + 0 sin A ; and sin b sin c = sin3 1 ( b ( 75 )
... c + cos b cosc cos A. If the sides of the triangle are small compared with the radius of the sphere , EF will not differ much from A ; suppose EF - A - 0 , then approximately cos EF = cos A + 0 sin A ; and sin b sin c = sin3 1 ( b ( 75 )
Página 76
... approximately by the sine of one second ( Plane Trigonometry , Art . 123 ) . If the lengths of the arcs corre- sponding to a and b respectively be a and ẞ , and r the radius of the α β sphere , we have and as the circular measures of a ...
... approximately by the sine of one second ( Plane Trigonometry , Art . 123 ) . If the lengths of the arcs corre- sponding to a and b respectively be a and ẞ , and r the radius of the α β sphere , we have and as the circular measures of a ...
Página 77
... cos A = cos A ' . By sin ' A ' 622 Suppose A A ' + 0 ; then therefore - cos Acos A ' - sin A ' approximately ; 0 --- By sin A ' 67.2 = S 372 1 where S denotes the area of the plane triangle whose ON CERTAIN APPROXIMATE FORMULE . 77.
... cos A = cos A ' . By sin ' A ' 622 Suppose A A ' + 0 ; then therefore - cos Acos A ' - sin A ' approximately ; 0 --- By sin A ' 67.2 = S 372 1 where S denotes the area of the plane triangle whose ON CERTAIN APPROXIMATE FORMULE . 77.
Página 78
... approximately S A + B + C = A ' + B ' + C ' + S S therefore is approximately equal to the spherical excess of the 2.2 spherical triangle , and thus the theorem is established . It will be seen that in the above approximation the area of ...
... approximately S A + B + C = A ' + B ' + C ' + S S therefore is approximately equal to the spherical excess of the 2.2 spherical triangle , and thus the theorem is established . It will be seen that in the above approximation the area of ...
Página 79
... approximately ; a and С ' = π- A ' - B'π - A - B ' approximately ; then Saß sin C. Hence A ' is known and the plane triangle can be solved , since two sides and the angle opposite to one of them are known . ( 4 ) Suppose two angles and ...
... approximately ; a and С ' = π- A ' - B'π - A - B ' approximately ; then Saß sin C. Hence A ' is known and the plane triangle can be solved , since two sides and the angle opposite to one of them are known . ( 4 ) Suppose two angles and ...
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Términos y frases comunes
a+b+c angular points approximately bisecting calculated centre circle described circular measure cos b cos cos² cos³ cosb cosines Crown 8vo deduce denote equal equation Fcap Fellow of St formed formulæ given greater Hence inscribed John's College late Fellow less Let ABC limp cloth lune M.A. Fellow middle point Napier's analogies Napier's Rules obtain perpendicular plane triangle Plane Trigonometry polar triangle pole polygon preceding article primitive triangle quadrant radius regular polyhedron respectively right angles right-angled triangles School Second Edition Sermons preached shew shewn Similarly sin b sin sin² sin³ sine small circle solid angle solution sphere spherical excess spherical triangle Spherical Trigonometry St John's College suppose surface tangent tetrahedron Third Edition Treatise triangle ABC Trinity College University of Cambridge values vols
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