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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
apologies.

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

Herbert

   

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