Nicholas (Nikolaus) Mercator (c. 1620, Holstein – 1687,

Versailles The Palace of Versailles ( ; ) is a former royal residence commissioned by King Louis XIV located in Versailles, Yvelines, Versailles, about west of Paris, in the Yvelines, Yvelines Department of Île-de-France, Île-de-France region in Franc ...

), also known by his German name Kauffmann, was a 17th-century

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

. He was born in

Eutin Eutin () is the district capital of Ostholstein, Eastern Holstein county located in the northern German state of Schleswig-Holstein. As of December 2022, the town had some 17,000 inhabitants. History The name Eutin (originally Utin) is of Slavic ...

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and educated at

Rostock Rostock (; Polabian language, Polabian: ''Roztoc''), officially the Hanseatic and University City of Rostock (), is the largest city in the German States of Germany, state of Mecklenburg-Vorpommern and lies in the Mecklenburgian part of the sta ...

and

Leyden Leiden ( ; ; in English and archaic Dutch also Leyden) is a city and municipality in the province of South Holland, Netherlands. The municipality of Leiden has a population of 127,046 (31 January 2023), but the city forms one densely connecte ...

after which he lived from 1642 to 1648 in the

Netherlands , Terminology of the Low Countries, informally Holland, is a country in Northwestern Europe, with Caribbean Netherlands, overseas territories in the Caribbean. It is the largest of the four constituent countries of the Kingdom of the Nether ...

. He lectured at the

University of Copenhagen The University of Copenhagen (, KU) is a public university, public research university in Copenhagen, Copenhagen, Denmark. Founded in 1479, the University of Copenhagen is the second-oldest university in Scandinavia, after Uppsala University. ...

during 1648–1654 and lived in

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from 1655 to 1657. He was mathematics tutor to Joscelyne Percy, son of the 10th Earl of Northumberland, at Petworth,

Sussex Sussex (Help:IPA/English, /ˈsʌsɪks/; from the Old English ''Sūþseaxe''; lit. 'South Saxons'; 'Sussex') is an area within South East England that was historically a kingdom of Sussex, kingdom and, later, a Historic counties of England, ...

(1657). He taught mathematics in London (1658–1682). On 3 May 1661 he observed a transit of Mercury with

Christiaan Huygens Christiaan Huygens, Halen, Lord of Zeelhem, ( , ; ; also spelled Huyghens; ; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor who is regarded as a key figure in the Scientific Revolution ...

and Thomas Streete from Long Acre, London. On 14 November 1666 he was elected a

Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the Fellows of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...

. He designed a marine chronometer for Charles II. In 1682 Jean Colbert invited Mercator to assist in the design and construction of the fountains at the

Palace of Versailles The Palace of Versailles ( ; ) is a former royal residence commissioned by King Louis XIV located in Versailles, Yvelines, Versailles, about west of Paris, in the Yvelines, Yvelines Department of Île-de-France, Île-de-France region in Franc ...

, so he relocated there, but a falling-out with Colbert followed. Mathematically, he is most well known for his treatise ''Logarithmo-technia'' on

logarithms In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of to base is , because is to the rd power: . More generally, if , the ...

, published in 1668. In this treatise he described the Mercator series: :

\ln(1 + x) = x - \fracx^2 + \fracx^3 - \fracx^4 + \cdots.

Nicholas Mercator was the first person to use the term

natural logarithm The natural logarithm of a number is its logarithm to the base of a logarithm, base of the e (mathematical constant), mathematical constant , which is an Irrational number, irrational and Transcendental number, transcendental number approxima ...

. To the field of music, Mercator contributed the first precise account of 53 equal temperament, which was of theoretical importance, but not widely practised.Benjamin Wardhaugh (July 2010
A Plague of Ratios
from Mathematics Association of America He died at Versailles in 1687.

Works

* 1676: ''Institutionum astronomicarum'', London (1685, Padua) * * Kinkhuysen (1661) ''Algebra ofte Stelkonst'', translated by N. Mercator, appears 1968 in ''Mathematical Papers of Isaac Newton'' II: 295–364 with Newton commentary 364–446. * 1664: ''Hypothesis astronomica nova'', London * 1666: "Certain problems touching some points of navigation",

Philosophical Transactions of the Royal Society ''Philosophical Transactions of the Royal Society'' is a scientific journal published by the Royal Society. In its earliest days, it was a private venture of the Royal Society's secretary. It was established in 1665, making it the second journ ...

1: 215–18 * 1668
Logarithmo-technia
from

HathiTrust HathiTrust Digital Library is a large-scale collaborative repository of digital content from research libraries. Its holdings include content digitized via Google Books and the Internet Archive digitization initiatives, as well as content digit ...

o
Logarithmtechnia
from

Internet Archive The Internet Archive is an American 501(c)(3) organization, non-profit organization founded in 1996 by Brewster Kahle that runs a digital library website, archive.org. It provides free access to collections of digitized media including web ...

* Wallis (1668) Review of ''Logarithmotechnia'', ''Philosophical Transactions of the Royal Society'' 3: 753–9, followed by "Some further Illustration" by N. Mercator, pp 759–64. * 1670: "Some considerations … method of Cassini", ''Philosophical Transactions of the Royal Society'' 5: 1168–75.

References

* Euclid Speidell (1688) * Francis Maseres & Charles Hutton (1791
Scriptores Logarithmici
link from

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. *

John Aubrey John Aubrey (12 March 1626 – 7 June 1697) was an English antiquary, natural philosopher and writer. He was a pioneer archaeologist, who recorded (often for the first time) numerous megalithic and other field monuments in southern England ...

(1813) ''Letters and Lives of Eminent Men'' II: 450,1, 473

External links

Some Contemporaries of Descartes, Fermat, Pascal, and Huygens: N. Mercator
* {{DEFAULTSORT:Mercator, Nicholas 1620s births 1687 deaths People from Eutin 17th-century German mathematicians Music theorists Fellows of the Royal Society