Spherical Trigonometry: For the Use of Colleges and SchoolsMacmillan and Company, 1863 - 132 σελίδες |
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Σελίδα
... Inscribed Cireles 6 IO 16 32 46 VII . VIII . Area of a Spherical Triangle . Spherical Excess IX . On certain approximate Formulæ X. Geodetical operations · XI . On small variations in the parts of a Spherical Triangle , and on the ...
... Inscribed Cireles 6 IO 16 32 46 VII . VIII . Area of a Spherical Triangle . Spherical Excess IX . On certain approximate Formulæ X. Geodetical operations · XI . On small variations in the parts of a Spherical Triangle , and on the ...
Σελίδα 59
... INSCRIBED CIRCLES . 89. To find the angular radius of the small circle inscribed in a given triangle . F E B C Let ABC be the triangle ; bisect the angles A and B by arcs meeting at P ; from P draw PD , PE , PF perpendicular to the ...
... INSCRIBED CIRCLES . 89. To find the angular radius of the small circle inscribed in a given triangle . F E B C Let ABC be the triangle ; bisect the angles A and B by arcs meeting at P ; from P draw PD , PE , PF perpendicular to the ...
Σελίδα 60
... ( S ′ – B ) + cos ( S – C ) ; hence we have from ( 4 ) cotr = 1 COS 24 { cos 2N S + cos ( S – A ) + cos ( S – B ) + cos ( S - ......... . ( 5 ) . 90. To find the angular radius of the small circle 60 CIRCUMSCRIBED AND INSCRIBED CIRCLES .
... ( S ′ – B ) + cos ( S – C ) ; hence we have from ( 4 ) cotr = 1 COS 24 { cos 2N S + cos ( S – A ) + cos ( S – B ) + cos ( S - ......... . ( 5 ) . 90. To find the angular radius of the small circle 60 CIRCUMSCRIBED AND INSCRIBED CIRCLES .
Σελίδα 61
... inscribed in A'BC , and the sides of A'BC are a , π - b , π - c respectively . Hence if r ̧ be the required radius , and s denote as usual 1⁄2 ( a + b + c ) , we have from Art . 89 , A tan r = tan sin s ... 2 . ( 1 ) . From this result ...
... inscribed in A'BC , and the sides of A'BC are a , π - b , π - c respectively . Hence if r ̧ be the required radius , and s denote as usual 1⁄2 ( a + b + c ) , we have from Art . 89 , A tan r = tan sin s ... 2 . ( 1 ) . From this result ...
Σελίδα 62
... inscribed and escribed circles of a given triangle are the same as the circles inscribed in the system of associated triangles of which the given triangle is the fundamental triangle . 92. To find the angular radius of the small circle ...
... inscribed and escribed circles of a given triangle are the same as the circles inscribed in the system of associated triangles of which the given triangle is the fundamental triangle . 92. To find the angular radius of the small circle ...
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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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