Nicholas Mercator

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A separate article is about the cartographer Gerardus Mercator, eponym of the Mercator projection.

Nicholas (Nikolaus) Mercator (c.1620 Eutin-1687 Versailles), also known by his Germanic name Kauffmann, was a 17th-century mathematician.

Lived in the Netherlands (1642-1648); lectured at the University of Copenhagen (1648-1654); lived in Paris (1655-1657); Mathematics tutor to Joscelyne Percy, son of the 10th Earl of Northumberland, at Petworth, Sussex (1657); taught mathematics in London (1658-1682); became member of the Royal Society in 1666; designed a marine chronometer for Charles II; designed and constructed the fountains at the Palace of Versailles (1682-1687).

Mathematically, he is most well-known for his treatise Logarithmo-technica on logarithms, published in 1668. In this treatise he described the Mercator series, also independently discovered by Gregory Saint-Vincent:

$\ln(1 + x) = x - \frac{1}{2}x^2 + \frac{1}{3}x^3 - \frac{1}{4}x^4 + \cdots$

It was also in this treatise that the first known use of the term natural log for the natural log appears, in the Latin form log naturalis; his use of this term is somewhat surprising, since it predates the development of calculus, in which the most natural properties of this logarithm appear.

To the field of music he contributed the first precise account of 53 equal temperament, which was of theoretical importance, but not widely practiced.