"In Napier's time sin φ was a line, not a ratio. The radius was called the sinus totus, and when this was equal to unity the length of the sine was simply stated as sinφ. If r was not unity, the length was r sinφ. With this statement we may consider Napier's definition of a logarithm:The logarithme therefore of any sine is a number very neerely expressing the line, which increased equally in the meane time, whiles the line of the whole sine decreased proportionally into that sine, both motions being equal-timed, and the beginning equally swift.From this it follows that the logarithm of the sinus totus is zero. Napier saw later that it was better to take log 1 = 0."
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History of logarithms
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