Further to my comment of 13 August 2016, the formula I mention of (1-0.9999999) to the power of 10 million, shows how logarithms can be calculated more accurately. There are the same number of 9s in 0.9999999 as there are 0s in 10 million. For even greater accuracy you add on the same number of 9s to 0.9999999 as 0s to 10,000000. This I think probably explains how Henry Briggs and others soon after 1614 were able to calculate logarithms to a much higher accuracy than Napier was able to achieve.

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