Nicholas (Nikolaus) Mercator (c. 1620,

Holstein Holstein (; nds, label=Northern Low Saxon, Holsteen; da, Holsten; Latin and historical en, Holsatia, italic=yes) is the region between the rivers Elbe and Eider. It is the southern half of Schleswig-Holstein, the northernmost state of German ...

– 1687,

Versailles The Palace of Versailles ( ; french: Château de Versailles ) is a former royal residence built by King Louis XIV located in Versailles, about west of Paris, France. The palace is owned by the French Republic and since 1995 has been managed, ...

), also known by his

German German(s) may refer to: * Germany (of or related to) ** Germania (historical use) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizens of Germany, see also German nationality law **Ge ...

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, structure, space, models, and change. History On ...

. He was born in

Eutin Eutin () is the district capital of Eastern Holstein county located in the northern German state of Schleswig-Holstein. As of 2020, the town had some 17,000 inhabitants. History The name Eutin (originally Utin) is of Slavic origin. Its meaning i ...

Schleswig-Holstein Schleswig-Holstein (; da, Slesvig-Holsten; nds, Sleswig-Holsteen; frr, Slaswik-Holstiinj) is the northernmost of the 16 states of Germany, comprising most of the historical duchy of Holstein and the southern part of the former Duchy of Sc ...

Germany Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwe ...

and educated at

Rostock Rostock (), officially the Hanseatic and University City of Rostock (german: link=no, Hanse- und Universitätsstadt Rostock), is the largest city in the German state of Mecklenburg-Vorpommern and lies in the Mecklenburgian part of the state, ...

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 119,713, but the city forms one densely connected agglomeration wit ...

after which he lived from 1642 to 1648 in the

Netherlands ) , anthem = ( en, "William of Nassau") , image_map = , map_caption = , subdivision_type = Sovereign state , subdivision_name = Kingdom of the Netherlands , established_title = Before independence , established_date = Spanish Netherl ...

. He lectured at the

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

during 1648–1654 and lived in

Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), ma ...

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

Earl of Northumberland The title of Earl of Northumberland has been created several times in the Peerage of England and of Great Britain, succeeding the title Earl of Northumbria. Its most famous holders are the House of Percy (''alias'' Perci), who were the most po ...

, at Petworth, Sussex (1657). He taught mathematics in London (1658–1682). On 3 May 1661 he observed a

transit of Mercury frameless, upright=0.5 A transit of Mercury across the Sun takes place when the planet Mercury passes directly between the Sun and a superior planet. During a transit, Mercury appears as a tiny black dot moving across the Sun as the planet obs ...

with Christiaan Huygens and

Thomas Streete Thomas Street (also spelled Streete) (1621–1689) was an English astronomer, known for his writings on celestial motions. He has sometimes been confused with Thomas Street the judge, who lived from 1626 to 1696. The crater Street on the Moon is ...

from

Long Acre Long Acre is a street in the City of Westminster in central London. It runs from St Martin's Lane, at its western end, to Drury Lane in the east. The street was completed in the early 17th century and was once known for its coach-makers, and la ...

, 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 judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural knowledge, including mathemat ...

. 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, 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 is the inverse function to exponentiation. That means the logarithm of a number to the base is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 of ...

, published in 1668. In this treatise he described the

Mercator series In mathematics, the Mercator series or Newton–Mercator series is the Taylor series for the natural logarithm: :\ln(1+x)=x-\frac+\frac-\frac+\cdots In summation notation, :\ln(1+x)=\sum_^\infty \frac x^n. The series converges to the natural ...

: :

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

To the field of music, Mercator contributed the first precise account of

53 equal temperament In music, 53 equal temperament, called 53 TET, 53 EDO, or 53 ET, is the tempered scale derived by dividing the octave into 53 equal steps (equal frequency ratios). Each step represents a frequency ratio of 2, or 22.6415& ...

, which was of theoretical importance, but not widely practised.Benjamin Wardhaugh (July 2010
A Plague of Ratios
from

Mathematics Association of America The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure a ...

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 first journa ...

1: 215–18 * 1668
Logarithmo-technia
from HathiTrust o
Logarithmtechnia
from

Internet Archive The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, ...

* 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 Euclid Speidell (died 1702) was an English customs official and mathematics teacher known for his writing on logarithms. Speidell published revised and expanded versions of texts by his father, John Speidell. He also published a book called ''Logar ...

(1688) * Francis Maseres &

Charles Hutton Charles Hutton FRS FRSE LLD (14 August 1737 – 27 January 1823) was a British mathematician and surveyor. He was professor of mathematics at the Royal Military Academy, Woolwich from 1773 to 1807. He is remembered for his calculation of the ...

(1791
Scriptores Logarithmici
link from

Google Books Google Books (previously known as Google Book Search, Google Print, and by its code-name Project Ocean) is a service from Google Inc. that searches the full text of books and magazines that Google has scanned, converted to text using optical ...

. *

John Aubrey John Aubrey (12 March 1626 – 7 June 1697) was an English antiquary, natural philosopher and writer. He is perhaps best known as the author of the '' Brief Lives'', his collection of short biographical pieces. He was a pioneer archaeologist ...

(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