Spherical Trigonometry ... |
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Page 4
... figure of the preceding Article , the angle between the great circles CD and CE is the angle MON . In the figure to Art . 6 , since PO is perpen- dicular to the plane ACB , every plane which contains PO is at right angles to the plane ...
... figure of the preceding Article , the angle between the great circles CD and CE is the angle MON . In the figure to Art . 6 , since PO is perpen- dicular to the plane ACB , every plane which contains PO is at right angles to the plane ...
Page 5
... figure of preceding Article . ) For suppose PA and PC to be quadrants and O the centre of the sphere ; then since PA and PC are quadrants , the angles POC and POA are right angles . Hence PO is at right angles to the plane AOC , and P ...
... figure of preceding Article . ) For suppose PA and PC to be quadrants and O the centre of the sphere ; then since PA and PC are quadrants , the angles POC and POA are right angles . Hence PO is at right angles to the plane AOC , and P ...
Page 7
... figure on the surface of the sphere is bounded by more than three arcs of great circles , and is called a spherical polygon . 17. The three arcs of great circles which form a spherical triangle are called the sides of the spherical ...
... figure on the surface of the sphere is bounded by more than three arcs of great circles , and is called a spherical polygon . 17. The three arcs of great circles which form a spherical triangle are called the sides of the spherical ...
Page 8
... figure of the preceding Article , the arc AB forms one side of the spherical 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 ...
... figure of the preceding Article , the arc AB forms one side of the spherical 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 ...
Page 9
... figure , the arc ADEB is greater than a semicircle , and we might , if we pleased , consider ADEB , AC and BC as forming a triangle , having its angular points at A , B , and C. But we agree to exclude such triangles from our ...
... figure , the arc ADEB is greater than a semicircle , and we might , if we pleased , consider ADEB , AC and BC as forming a triangle , having its angular points at A , B , and C. But we agree to exclude such triangles from our ...
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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
Popular passages
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