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    Re: Azimuth and Declination formulae
    From: Herbert Prinz
    Date: 2005 Jul 20, 12:56 -0400

    Lu Abel wrote:
    > The whole reason for versines and haversines was to allow sight
    > reductions to be done using logarithms (and therefore the requisite
    > multiplications become additions); but logs are not defined for negative
    > numbers, hence the need to shift everything to have a positive value.
    The fact that the trigonometric functions are much older than negative
    numbers and basically all spherical trig problems could be solved before
    the introduction of negative numbers shows that something is not right
    with this historical theory.
    > Therefore all
    > GPS's actually use the haversine formula for calculating the distance
    > between two points.
    Since all GPS receivers currently on the market display distance along
    the geodesic, I would be surprised if _any_ of them used the haversine
    formula. But how would you know? Did you look inside?
    Herbert Prinz

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