Spherical Trigonometry ... |
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Page 4
... quadrant , and is at right angles to the circumference . C A B Let P be a pole of the great circle ABC ; the arc PA is a quad- rant and at right angles to ABC . For let O be the centre of the sphere , and draw PO . Then PO is at right ...
... quadrant , and is at right angles to the circumference . C A B Let P be a pole of the great circle ABC ; the arc PA is a quad- rant and at right angles to ABC . For let O be the centre of the sphere , and draw PO . Then PO is at right ...
Page 5
... quadrant , P is a pole of the great circle through A and C. ( See 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 ...
... quadrant , P is a pole of the great circle through A and C. ( See 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 ...
Page 11
... quadrant ( Art . 10 ) ; and since C ' is a pole of BA , the arc AC " is a quadrant ; there- fore A is a pole of B'C ' ( Art . 11 ) . Also A and A ' are on the same side of B'C ' ; for A and A ' are by hypothesis on the same side of BC ...
... quadrant ( Art . 10 ) ; and since C ' is a pole of BA , the arc AC " is a quadrant ; there- fore A is a pole of B'C ' ( Art . 11 ) . Also A and A ' are on the same side of B'C ' ; for A and A ' are by hypothesis on the same side of BC ...
Page 14
... 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 the base ...
... 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 the base ...
Page 17
... quadrant or equal to a quadrant . ( 1 ) Suppose only one of the sides greater than a quadrant , for example , AB . Produce BA and BC to meet in B ; and put AB'c ' , CB'a ' . B B Then we have from the triangle ABC , by what has been ...
... quadrant or equal to a quadrant . ( 1 ) Suppose only one of the sides greater than a quadrant , for example , AB . Produce BA and BC to meet in B ; and put AB'c ' , CB'a ' . B B Then we have from the triangle ABC , by what has been ...
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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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