Spherical Trigonometry ... |
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Page 9
... less than two right angles . For suppose a triangle formed by BC , CA and BEDA having the angle BCA greater than two right angles . Then suppose D to denote the point in which the arc BC , if produced , will meet AE ; then BED is a ...
... less than two right angles . For suppose a triangle formed by BC , CA and BEDA having the angle BCA greater than two right angles . Then suppose D to denote the point in which the arc BC , if produced , will meet AE ; then BED is a ...
Page 11
... less than a quadrant ; and since A is a pole of B'C ' and AA ' is less than a quadrant , A and A ′ are on the same side of 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 ...
... less than a quadrant ; and since A is a pole of B'C ' and AA ' is less than a quadrant , A and A ′ are on the same side of 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 ...
Page 12
... the difference of the other two . 30. The sum of the three sides of a spherical triangle is less than the circumference of a great circle . ( See fig . to Art . 18. ) For the sum of the three plane angles which form 12 SPHERICAL GEOMETRY .
... the difference of the other two . 30. The sum of the three sides of a spherical triangle is less than the circumference of a great circle . ( See fig . to Art . 18. ) For the sum of the three plane angles which form 12 SPHERICAL GEOMETRY .
Page 13
... less than 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 ...
... less than 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 ...
Page 14
... 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 be completed as before . If AC and BC are quadrants , the angles at ...
... 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 be completed as before . If AC and BC are quadrants , the angles at ...
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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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