In 1873 Charles Hermite proved that the base of the Napierian logarithms cannot be a root of a rational algebraical equation of any degree.3 To prove the same proposition regarding 7r is to prove that a Euclidean construction for circle-quadrature is impossible.

In the same year (1624) Kepler published at Marburg a table of Napierian logarithms of sines with certain additional columns to facilitate special calculations.

The logarithms introduced by Napier in the Descriptio are not the same as those now in common use, nor even the same as those now called Napierian or hyperbolic logarithms. The change from the original logarithms to common or decimal logarithms was made by both Napier and Briggs, and the first tables of decimal logarithms were calculated by Briggs, who published a small table, extending to 1000, in 1617, and a large work, Arithmetica Logarithmica, 1 containing logarithms of numbers to 30,000 and from 90,000 to Ioo,000, in 1624.

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E, Base of Napierian logarithms.

Hyperbolic or Napierian logarithms (i.e.

Similarly the continued fraction given by Euler as equivalent to 1(e - 1) (e being the base of Napierian logarithms), viz.

This is the largest Napierian canon that has ever been published.