Spherical Trigonometry ... |
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Page 8
... denote the angles of a spherical triangle , and the letters a , b , c are used to denote the sides . As in the case of plane triangles , A , B , and C may be used to denote the numerical values of the angles expressed in terms of any ...
... denote the angles of a spherical triangle , and the letters a , b , c are used to denote the sides . As in the case of plane triangles , A , B , and C may be used to denote the numerical values of the angles expressed in terms of any ...
Page 9
... denote the point in which the arc BC , if produced , will meet AE ; then BED is a semicircle by Art . 9 , and therefore BEA is greater than a semicircle ; thus the proposed triangle is not one of those which we consider . III ...
... denote the point in which the arc BC , if produced , will meet AE ; then BED is a semicircle by Art . 9 , and therefore BEA is greater than a semicircle ; thus the proposed triangle is not one of those which we consider . III ...
Page 12
... denote respectively the angles and sides of a spherical triangle all expressed in circular measure , and A ' , B ' , C ' , a ' , b ' , c ′ those of the polar triangle , we have A ' = π — α , Ᏼ = π - b , С = π — C , a = - A , b = π - В ...
... denote respectively the angles and sides of a spherical triangle all expressed in circular measure , and A ' , B ' , C ' , a ' , b ' , c ′ those of the polar triangle , we have A ' = π — α , Ᏼ = π - b , С = π — C , a = - A , b = π - В ...
Page 13
... denoted by A , B , C , D. Then therefore , ABBC is greater than AC ; AB + BC + CD is greater than AC + CD , and à fortiori greater than AD . Again , if there be any polygon which has each of its angles less than two right angles , the ...
... denoted by A , B , C , D. Then therefore , ABBC is greater than AC ; AB + BC + CD is greater than AC + CD , and à fortiori greater than AD . Again , if there be any polygon which has each of its angles less than two right angles , the ...
Page 22
... denote it by n , so that and n2 = sin s sin ( s− a ) sin ( s — b ) sin ( s — c ) , 4 n2 = 1 - cos3 a cos2 b - cos c + 2 cos a cos b cos c . -- 4 47. To express the cosine of a side of 22 RELATIONS BETWEEN THE TRIGONOMETRICAL FUNCTIONS.
... denote it by n , so that and n2 = sin s sin ( s− a ) sin ( s — b ) sin ( s — c ) , 4 n2 = 1 - cos3 a cos2 b - cos c + 2 cos a cos b cos c . -- 4 47. To express the cosine of a side of 22 RELATIONS BETWEEN THE TRIGONOMETRICAL FUNCTIONS.
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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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