In the Constructio paragraph 44, Napier rather obscurely states a formula for calculating the logarithms of sine 89 39/40 degrees down to log sine 75 degrees. This is 10^7 X (0.9999999)^5000s equals 10^7 - 5000s + 5/4 s^2. If s is 1, then we have an equality where the shortfall is about 3200. However if s is about 69, we have the log of sine 75 degrees. From log sine 75 degrees to log sine 45 degrees, sine 75 degrees raised to the power of 10 is sine 45 degrees. This power of 10 can be split up to measure the intervening logarithms. It is no use expecting modern mathematicians to know anything about this, submitted by Peter L. Griffiths.

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