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> In 1614, John Napier introduced logarithms. > Napier’s main motivation was to find an easier way to do multiplication and division. > Next, mathematicians d
by mci 6y ago
> In 1614, John Napier introduced logarithms.
> Napier’s main motivation was to find an easier way to do multiplication and division.
> Next, mathematicians decided to combine these tables. If you wanted to multiply trigonometric functions, you could find the values in a trigonometric table and then convert them to logarithms.
Actually, Napier's 1614 Mirifici Logarithmorum Canonis Descriptio contains tables of −10⁷ ln(sin x/10⁷) [0]. Non-trigonometric log tables appeared later.
[0] https://jscholarship.library.jhu.edu/bitstream/handle/1774.2/34187/31151005337641.pdf#page=25 https://jscholarship.library.jhu.edu/bitstream/handle/1774.2...
- the_origami_fox 6y agoYes you're right. It has to do with how he derived the approximation formula for the natural logarithm. He needed a function y=sin(x) for his log(y) calculations. But I am not sure when the log(f(x))) tables for the other trigonometric functions came about. As far I understood, initially a single log(y) table sufficed.
- mci 6y agoWell, I suppose Napier presaged the concept of a single source of truth. Aren't other log-trig tables a waste of paper if you can look up log(cos x) under log(sin(90°−x)) and quickly calculate log(tan x) as log(sin x)−log(cos x)?