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    Re: Azimuth and Declination formulae
    From: Herbert Prinz
    Date: 2005 Jul 20, 12:39 -0400

    Lu Abel wrote:
    
    > In order to use logs (optional, but it makes multiplying
    > 4 or 5 digit numbers a hell of a lot easier!), you need to use
    > haversines.
    
    Using the transformation (-a)*b = -(a*b), you can use whatever trig
    formula you want. Besides, the trig functions are normally tabulated in
    the first quadrant only, leading to the distinction of "cases" rather
    than negative numbers.
    
    > 1.  Sight reduction formulae (actually, spherical triangle formulae) --
    > developed by Euclid and pals 2500 years ago.
    
    The first spherical triangle formula in Greek mathematics appears around
    100AD (Theorem of Menelaos.) The formulae for the right spherical
    triangle we owe to the Arabs. We know the first explicit statement of
    the cosine theorem (the basis for the GCD formula) from Regiomontanus.
    It might surprise you to learn that he used only sines and versines in
    the formulation. At that time the cosine was rarely used and its name
    not yet standardized. The versine, on the other hand, is as old as Hindu
    trigonometry. See also the archives for a message that I posted on this
    subject on Oct 6, 2004.
    
    Herbert Prinz
    
    
    

       
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