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Fred Hebard wrote:

> I believe the "short" vs "rigorous" solutions to which Jan refers are
> based on whether the relevant equations are solved explicitly rather
> than by some approximation to the solution, such as substitution of the
> first term of a Taylor series for a sine function.  In this sense,
> couldn't St. Hilaire's method be either short or rigorous depending on
> how one determines Hc?

The modern intercept method cannot be classified as a rigorous solution to
the combined altitude problem, because the true position (the intersection
of the two circles of equal altitude) is approximated by the intersection
of two tangents to these circles. The error depends on how close the
assumed position is to the true position.

As for the original Marcq St Hilaire method, the inventor called it
"methode du point rapproche", which says it all.

Best regards

Herbert Prinz

   

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