Spherical Trigonometry ... |
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Page 7
... triangle if it is bounded by three arcs of great circles ; this will be the case when the solid angle is formed by ... ABC is a spherical triangle , and the arcs AB , BC , CA are its sides . Suppose Ab the tangent at A to the arc AB ...
... triangle if it is bounded by three arcs of great circles ; this will be the case when the solid angle is formed by ... ABC is a spherical triangle , and the arcs AB , BC , CA are its sides . Suppose Ab the tangent at A to the arc AB ...
Page 8
... triangle ABC , and the plane angle AOB is measured by the frac- arc AB tion radius OA and thus the arc AB is proportional to the angle AOB so long as we keep to the same sphere . The angles of a spherical triangle are the inclinations ...
... triangle ABC , and the plane angle AOB is measured by the frac- arc AB tion radius OA and thus the arc AB is proportional to the angle AOB so long as we keep to the same sphere . The angles of a spherical triangle are the inclinations ...
Page 10
... ABC be any spherical triangle , and let the points A ' , B ' , C ' be those poles of the arcs BC , CA , AB # B ' B C C " respectively which lie upon the same sides of them as the opposite ... triangle be the polar triangle of another ( 10 )
... ABC be any spherical triangle , and let the points A ' , B ' , C ' be those poles of the arcs BC , CA , AB # B ' B C C " respectively which lie upon the same sides of them as the opposite ... triangle be the polar triangle of another ( 10 )
Page 11
Isaac Todhunter. 26. If one triangle be the polar triangle of another , the latter will be the polar triangle of the former . Let ABC be any triangle , A'B'C ' the polar triangle ; then ABC will be the polar triangle of A'B'C ' . C ' E B ...
Isaac Todhunter. 26. If one triangle be the polar triangle of another , the latter will be the polar triangle of the former . Let ABC be any triangle , A'B'C ' the polar triangle ; then ABC will be the polar triangle of A'B'C ' . C ' E B ...
Page 12
... 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 supplements of BC , CA , AB . From these properties a primitive ...
... 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 supplements of BC , CA , AB . From these properties a primitive ...
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Common terms and phrases
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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