Spherical Trigonometry ... |
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Page 13
... - - · B + π- C is less than 2π ; A + B + C is greater than π . And since each of the angles A , B , C is less than π , A + B + C is less than 3π . the sum 33 . equal . The angles at the base of SPHERICAL GEOMETRY . 13.
... - - · B + π- C is less than 2π ; A + B + C is greater than π . And since each of the angles A , B , C is less than π , A + B + C is less than 3π . the sum 33 . equal . The angles at the base of SPHERICAL GEOMETRY . 13.
Page 14
... base of the spherical triangle . The figure supposes AC and BC to be less than quadrants ; if they are greater than quadrants the tangents to AC and BC will meet on CO produced through O instead of through C , and the demonstration may ...
... base of the spherical triangle . The figure supposes AC and BC to be less than quadrants ; if they are greater than quadrants the tangents to AC and BC will meet on CO produced through O instead of through C , and the demonstration may ...
Page 28
... bases will be equal . We may shew that the bases are equal by applying the first formula in Art . 39 to each triangle ... base of that which has the greater angle will be greater than the 28 RELATIONS BETWEEN THE TRIGONOMETRICAL FUNCTIONS.
... bases will be equal . We may shew that the bases are equal by applying the first formula in Art . 39 to each triangle ... base of that which has the greater angle will be greater than the 28 RELATIONS BETWEEN THE TRIGONOMETRICAL FUNCTIONS.
Page 29
Isaac Todhunter. which has the greater angle will be greater than the base of the other ; and conversely . Let b and c denote the sides which are equal in the two tri- angles ; let a be the base and A the opposite angle of one triangle ...
Isaac Todhunter. which has the greater angle will be greater than the base of the other ; and conversely . Let b and c denote the sides which are equal in the two tri- angles ; let a be the base and A the opposite angle of one triangle ...
Page 46
... base , the triangle is divided into two equal right - angled triangles ; by the solution of one of these right - angled triangles the required elements can be found . ( 3 ) Suppose among the given elements of a triangle there are two ...
... base , the triangle is divided into two equal right - angled triangles ; by the solution of one of these right - angled triangles the required elements can be found . ( 3 ) Suppose among the given elements of a triangle there are two ...
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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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