Spherical Trigonometry ... |
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Page 17
... shew that the formula obtained is true when these sides are not less than quad- rants . This we shall do by special examination of the cases in which one side or each side is greater than a quadrant or equal to a quadrant . ( 1 ) ...
... shew that the formula obtained is true when these sides are not less than quad- rants . This we shall do by special examination of the cases in which one side or each side is greater than a quadrant or equal to a quadrant . ( 1 ) ...
Page 26
... shews that tan ( A + B ) and cos ( a + b ) are of the same sign ; thus & ( A + B ) and ( a + b ) are either both less than a right angle or both greater than a right angle . This is expressed by saying that ( A + B ) and ( a + b ) are ...
... shews that tan ( A + B ) and cos ( a + b ) are of the same sign ; thus & ( A + B ) and ( a + b ) are either both less than a right angle or both greater than a right angle . This is expressed by saying that ( A + B ) and ( a + b ) are ...
Page 27
... may be so proved . Thus , for example , the second of Napier's analogies is tan ( 4 - B ) = sin ( a + b ) sin ( a - b ) cot C 2 this shews that ( A - B ) is positive OF THE SIDES AND ANGLES OF A SPHERICAL TRIANGLE . 27.
... may be so proved . Thus , for example , the second of Napier's analogies is tan ( 4 - B ) = sin ( a + b ) sin ( a - b ) cot C 2 this shews that ( A - B ) is positive OF THE SIDES AND ANGLES OF A SPHERICAL TRIANGLE . 27.
Page 28
Isaac Todhunter. this shews that ( A - B ) is positive , negative , or zero , according as ( ab ) is positive ... shew that B and C are the same in the two triangles . It should be observed that the two triangles in this case are ...
Isaac Todhunter. this shews that ( A - B ) is positive , negative , or zero , according as ( ab ) is positive ... shew that B and C are the same in the two triangles . It should be observed that the two triangles in this case are ...
Page 29
... shews that 59 . ( 4 – 4 ' ) ; - ( a − a ) and 4 ( 4 – A ' ) are of the same sign . - If on a sphere any point be taken within a circle which is not its pole , of all the arcs which can be drawn from that point to the circumference ...
... shews that 59 . ( 4 – 4 ' ) ; - ( a − a ) and 4 ( 4 – A ' ) are of the same sign . - If on a sphere any point be taken within a circle which is not its pole , of all the arcs which can be drawn from that point to the circumference ...
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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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