Spherical Trigonometry ...Macmillian and Company, limited, 1859 - 275 páginas |
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Página 7
... Similarly angles formed in like manner at B and C are the other angles of the spherical triangle . 19. The principal part of a treatise on spherical trigonometry consists of theorems relating to spherical triangles ; it is therefore ...
... Similarly angles formed in like manner at B and C are the other angles of the spherical triangle . 19. The principal part of a treatise on spherical trigonometry consists of theorems relating to spherical triangles ; it is therefore ...
Página 11
... Similarly it may be shewn that B is a pole of C'A ' , and that B and B ' are on the same side of C'A ' ; also that C ' is a pole of A'B ' , and that C and C " are on the same side of A'B ' . Thus ABC is the polar triangle of A'B'C ...
... Similarly it may be shewn that B is a pole of C'A ' , and that B and B ' are on the same side of C'A ' ; also that C ' is a pole of A'B ' , and that C and C " are on the same side of A'B ' . Thus ABC is the polar triangle of A'B'C ...
Página 12
... Similarly it may be shewn that C'A ' is 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 ...
... Similarly it may be shewn that C'A ' is 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 ...
Página 20
... Similarly , PD = OP sin b sin C ; therefore OP sin c sin B = OP sin b sin C ; therefore sin B sin b sin C sin c The figure supposes b , c , B , and C all less than a right angle ; it will be found on examination that the proof will hold ...
... Similarly , PD = OP sin b sin C ; therefore OP sin c sin B = OP sin b sin C ; therefore sin B sin b sin C sin c The figure supposes b , c , B , and C all less than a right angle ; it will be found on examination that the proof will hold ...
Página 23
... Similarly and cos B cos C cos A + sin C sin A cos b , cos C - cos A cos B + sin A sin В cos c . 48. The formulæ in Art . 44 will of course remain true when the angles and sides are changed into the supplements of the cor- responding ...
... Similarly and cos B cos C cos A + sin C sin A cos b , cos C - cos A cos B + sin A sin В cos c . 48. The formulæ in Art . 44 will of course remain true when the angles and sides are changed into the supplements of the cor- responding ...
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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