NavList:

Personally, I think navigators where aware of negative numbers and used them, if necessary. Usually they did calculations by use of logarithms. I think, they might have tried to avoid negative numbers, because for using logarithms with negative numbers is kind of "tricky" (logarithms are not defined for negative real numbers). I've read (German) textbooks for navigators from around 1850 up to present. As long as they taught using logarithms, the "trick" calculating with nagative numbers was to find the logarithm of the positive number and note a little "n" (for "negative") after this logarithm. (I never saw in navigational textbooks the opposite: adding a "p" for "positive".) Then one can calculate as follows: adding two logarithms of numbers with an added "n" (i.e. multiplying the two negative numbers) gives an "positive" logarithm; adding a "positive" logarithm and a logarithm with an added "n" (i.e. multipyling a positive and a negative number) gives a logarithm with an added "n" again (which translates to be a negative number). In this system they could do calculations for positive and negative numbers and angels as well. Using this added "n" was done by other people too at this time, not only navigators.

Best regards,

Uwe