Spherical Trigonometry ... |
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Page 3
... Suppose a great circle to pass through the points P and D ; then the chord PD is constant , and therefore the arc of a great circle intercepted between P and D is constant for all positions of D on the circle AB , Thus the distance of a ...
... Suppose a great circle to pass through the points P and D ; then the chord PD is constant , and therefore the arc of a great circle intercepted between P and D is constant for all positions of D on the circle AB , Thus the distance of a ...
Page 5
... 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 is a pole of the great circle AC . 12 ...
... 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 is a pole of the great circle AC . 12 ...
Page 6
... plane faces are inclined to each other . 16. Suppose that the angular point of a solid angle is made the centre of a sphere ; then the planes which form the solid angle will cut the sphere in arcs of great circles . 6 SPHERICAL TRIANGLES .
... plane faces are inclined to each other . 16. Suppose that the angular point of a solid angle is made the centre of a sphere ; then the planes which form the solid angle will cut the sphere in arcs of great circles . 6 SPHERICAL TRIANGLES .
Page 7
... suppose a solid angle formed at O by the meeting of three plane angles . Let B AB , BC , CA be the arcs of great circles in which the planes cut the sphere ; then ABC is a spherical triangle , and the arcs AB , BC , CA are its sides .
... suppose a solid angle formed at O by the meeting of three plane angles . Let B AB , BC , CA be the arcs of great circles in which the planes cut the sphere ; then ABC is a spherical triangle , and the arcs AB , BC , CA are its sides .
Page 8
... suppose both the angles and sides of a spherical triangle expressed in circular measure . ( Plane Trigonometry , Art . 20. ) 21. In future , unless the contrary be distinctly stated , any arc drawn on the surface of a sphere will be ...
... suppose both the angles and sides of a spherical triangle expressed in circular measure . ( Plane Trigonometry , Art . 20. ) 21. In future , unless the contrary be distinctly stated , any arc drawn on the surface of a sphere will be ...
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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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