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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Alexandre Eremenko
Date: 2024 Mar 7, 09:10 -0800
Thanks to all those who answered this question.
When I asked it, I meant by "arithmetic with negative numbers" mainly their MULTIPLICATION. That is, the rule (negative)×(negative)=positive.
From the answers I infer that this was not stated in most old manuals. Then a question arises, how they handled the trigonometric formula for solution of a spherical triangle.
For example, in the formula
sin(h) = sin(latitude)·sin(declination) + cos(latitude)·cos(declination)·cos(t),
where h is the altitude over the horizon and t is the hour angle, some entries can be negative. My Russian manual (1971) accompanies this formula with a table of all possible sign combinations :-). To be sure, the manual recommends the use of reduction tables associated with this formula, but the author thinks that a user must be familiar with what these tables exactly tabulate.
Alex.
