Spherical Trigonometry ... |
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Page 13
... four right angles ( Euclid , XI . 21 ) ; therefore therefore , AB BC CA + + ΟΑ OA ΟΑ is less than 2π , AB + BC + CA is less than 2π × ОA ; that is , the sum of the arcs is less than the circumference of a great circle . 31. The ...
... four right angles ( Euclid , XI . 21 ) ; therefore therefore , AB BC CA + + ΟΑ OA ΟΑ is less than 2π , AB + BC + CA is less than 2π × ОA ; that is , the sum of the arcs is less than the circumference of a great circle . 31. The ...
Page 26
... thus sin ( A + B ) cos c = cos ( a - b ) cos C ... ( 3 ) , sin ( AB ) sin c = sin ( a - b ) cos & C . 1 ( 4 ) . The last four formulæ are called Gauss's Theorems , although 26 RELATIONS BETWEEN THE TRIGONOMETRICAL FUNCTIONS.
... thus sin ( A + B ) cos c = cos ( a - b ) cos C ... ( 3 ) , sin ( AB ) sin c = sin ( a - b ) cos & C . 1 ( 4 ) . The last four formulæ are called Gauss's Theorems , although 26 RELATIONS BETWEEN THE TRIGONOMETRICAL FUNCTIONS.
Page 27
Isaac Todhunter. The last four formulæ are called Gauss's Theorems , although they are really due to Delambre . 55. The properties of supplemental triangles were proved geometrically in Art . 27 , and by means of these properties the ...
Isaac Todhunter. The last four formulæ are called Gauss's Theorems , although they are really due to Delambre . 55. The properties of supplemental triangles were proved geometrically in Art . 27 , and by means of these properties the ...
Page 37
... four cases need not have been given , since it is obvious that they are only repetitions of what had previously been given ; the seventh and eighth are repetitions of the fifth and sixth , and the ninth and tenth of the third and fourth ...
... four cases need not have been given , since it is obvious that they are only repetitions of what had previously been given ; the seventh and eighth are repetitions of the fifth and sixth , and the ninth and tenth of the third and fourth ...
Page 47
... - Bain Then may is four fou this case sw - found in : of tws waive 로스 sended in observa tu : to the greater age . Ora Art . 54 , with a free f Sven 4.- assume tan 0 = tan b cos C ; then. SOLUTION OF OBLIQUE - ANGLED TRIANGLES . 47.
... - Bain Then may is four fou this case sw - found in : of tws waive 로스 sended in observa tu : to the greater age . Ora Art . 54 , with a free f Sven 4.- assume tan 0 = tan b cos C ; then. SOLUTION OF OBLIQUE - ANGLED TRIANGLES . 47.
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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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