A new Method of computing Logarithms. This method is founded upon... 1. That the sums of any two Numbers is the Logarithm of the Product of those two… - Brook Taylor

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A new Method of computing Logarithms.
This method is founded upon...
1. That the sums of any two Numbers is the Logarithm of the Product of those two Numbers Multiplied together.
2. That the Logarithm of Unite is nothing; and consequently that the nearer any Number is to Unite, the nearer will its Logarithm be to 0.
3rdly. That the Product by Multiplication of two Numbers, whereof one is bigger, and the other less than Unite, is nearer to Unite than that of the two Numbers which is on the same side of Unite with its self; for Example the two Numbers being <math>\frac{2}{3}</math> and <math>\frac{4}{3}</math>, the Product <math>\frac{8}{9}</math> is less than Unite, but nearer to it than <math>\frac{2}{3}</math>, which is also less than Unite. Upon these Considerations, I found the present Approximation... best explain'd by an Example. ...[T]o find the Relation of the Logarithms of 2 and of 10... take two Fractions <math>\frac{128}{100}</math> and <math>\frac{8}{10}</math>, viz. <math>\frac{2^7}{10^2}</math> and <math>\frac{2^3}{10^1}</math>... one... bigger, and the other less than 1.