"Napier worked at least twenty years upon the theory. His idea was to simplify multiplications involving sines, and it was a later thought that included other operations, applying logarithms to numbers in general. He may have been led to his discovery by the relationsin A\;sin B = \frac{1}{2}(cos\overline{A - B} - cos\overline{A + B})for, as Lord Moulton says, in no other way can we "conceive that the man to whom so bold an idea occurred should we have so needlessly and so aimlessly restricted himself to sines in his work, instead of regarding it as applicable to numbers in general.""
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History of logarithms
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