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    Re: Spherical Law of Cosines
    From: Herbert Prinz
    Date: 2002 Oct 28, 10:46 +0000

    Hello Trevor,
    You wrote:
    > Just for the record, I meant nothing of the kind and did mean exactly
    > what I wrote.
    I apologize for second guessing you. I honestly thought it was a mechanical
    error, when in fact it seems to have been a logical one. Your statement
    "And so we would have to suppose that sin(a)=cos(a)" is simply wrong.
    However, Dan's equations do imply cos(a+b) = 0, if angle(ab) > 0, from
    which a + b = 90deg, which can be translated to sin(a) = cos(b); So, it was
    natural for me to assume that this was what you had in mind. Once again, my
    You wrote further:
    > Herbert has, however, pointed out that the two equations for cos(c)
    > could be simultaneously true if sin(a) was equal to cos(b), as well as
    > if sin(a) was equal to cos(a). I had missed the one while noting the
    > other.
    This is missing the point. You had tried to give a reductio ad absurdum of
    Dan's equations, but you failed, because the inference that you tried to
    make (namely sin(a) = cos(a)) cannot be made. ONLY the one I have given can
    be made.
    It goes without saying that I fully agree with the final result of your
    analysis that we have to reject one of Dan's equations. I only had a small
    problem with the way how you got there.
    Best regards

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