Mercator, Nicolaus [formerly Niklaus Kauffman]

(1620?-1687), mathematician and astronomer

by Christoph J. Scriba

© Oxford University Press 2004 All rights reserved

Mercator, Nicolaus [formerly Niklaus Kauffman] (1620?-1687), mathematician and astronomer, was born near Cismar or in Eutin (both in Holstein, Germany, then united with Denmark), the son of Martin Kauffman (c.1587-1637/8), who had been a Lutheran preacher (diakon) from 1619 in Eutin, and from 1623 in Oldenburg (Holstein), and his wife, Heilwig (d. 1677).

Mercator matriculated in 1632 at the University of Rostock and graduated magister philosophiae on 15 May 1641, with Jacob Fabricius (1576?-1652), a former student of Tycho Brahe, presiding. In 1642 he registered at the University of Leiden in the Netherlands, where he became acquainted with the English mathematician John Pell. Towards the end of the Thirty Years' War he took up a post at the University of Copenhagen. There he was in contact with the professor of mathematics Georg Fromme (1605-1651), another student of Brahe, and his circle.

When Copenhagen University was closed late in 1654 on account of an outbreak of the plague, Mercator travelled to London for a brief stay, and then moved to Paris. Regular correspondence with Samuel Hartlib testifies to their close relations. He returned to England in June 1657 and for about a year acted as tutor at Petworth House to Joceline Percy, son of the tenth earl of Northumberland; then until 1682 he lived in London, teaching mathematics.

In 1666 Mercator made and presented to Charles II a special marine timekeeper. Shortly afterwards he was elected fellow of the Royal Society. In the spring of 1669 he seems to have proposed to the French statesman J. B. Colbert not only his method of sailing into the wind, but also of improving the pendulum clock for use at sea. Years later Colbert commissioned him to construct the fountains at Versailles; in December 1682 he set out for France, but he did not receive the payment that had been agreed upon.

Mercator was married; nothing seems to be known of his wife, but they had a son David. Aubrey described Mercator as:

of little stature, perfect black haire, of a delicate moyst curle; darke grey eie, but of great vivacity of spirit. He is of a soft temper, of great temperance, and of a prodigious invention. He will be acquainted (familialy) with nobody. (Brief Lives, 58)
His frequent moves may have been caused by his constant preoccupation with earning a livelihood.While in Copenhagen, Mercator published a series of elementary university textbooks. In his Cosmographia (1651) he described the physical geography of the earth, while his Astronomia (1651) presented the elements of spherical astronomy. Also issued in 1651 was Trigonometria sphaericorum logarithmica. In Rationes mathematicae (1653) Mercator made a principal distinction between rational and irrational numbers and discussed the consequences for science. For music, Mercator maintained, this implied the distinction between harmony and dissonance, for astronomy that between a Keplerian world harmonics and the observable celestial motions. He also proposed a calendrical reform in De emendatione annua (1653?). His first book printed in England was a small study on the motion of planets, Hypothesis astronomica nova (1664). In it Mercator accepted Kepler's first law describing orbits as ellipses but rejected Kepler's second law, the area law, which determines the speed of the planets, in favour of his own hypothesis. In 1669 Mercator demolished Jean-Dominique (Giandomenico) Cassini's method of determining the line of apsides of a planetary orbit from three solar sightings.

Mercator's Institutiones astronomicae (in two books, 1676), intended for use at the University of Cambridge, emphasized the role of observation and presented an excellent summary of contemporary theory, including that Kepler's third law substantiated the Copernican instead of Brahe's intermediate planetary system. Among others, Newton (with whom Mercator exchanged letters on lunar theory) studied the work carefully, and it was used as a textbook at other universities. Noteworthy in Mercator's Institutio brevis in geometriam (1678) are original definitions of geometrical objects based on his concept of motion or inspired by physical phenomena.

Mercator was also a practical scientist: the 1666 gift to Charles II, of a marine watch from which the equation of time could be obtained, was his own invention; his proposal to Colbert of a pendulum clock for use at sea provoked criticism from Christiaan Huygens who had his own vested interest. Mercator also sought to clarify the theory of map projection of Gerardus Mercator, to whom he was not related, by an article in the Philosophical Transactions (13, 4 June 1666, 215-18).

Among all Mercator's achievements, the publication of his small book Logarithmotechnia (1667; enlarged edn, 1668) is the most outstanding. In it he constructed logarithms from first principles based on rational operations only, and expressed the area under the segment of a hyperbola by a logarithm. Most important, this book was the first to publish a function in the form of an infinite series--obviously independent of similar revolutionary results obtained by Jan Hudde and Newton. Mercator accepted such series as a new type of function in mathematical analysis. His complementary but unpublished Cyclomathia series contained expansions of circle integrals. Also of historical relevance is his Latin translation of the Dutch Algebra ofte Stel-Konst by Gerard Kinckhuysen. It was sent by John Collins to Newton who, from 1673 onwards, introduced revised versions of substantial passages from Mercator into his Lucasian lectures on arithmetic and algebra. Mercator died in Paris in January or February 1687 (according to J. Moller, writing in 1744, from grief at not receiving payment for his Versailles work); he left unpublished works including Latin translations of an astrological text by Benjamin Worsley (c.1657), his own 'Astrologia rationalis', versions of a treatise on music theory which applied logarithms to the division of the musical scale (c.1672), and theorems on the solution of equations, the method of differences, and the construction of tables.


J. E. Hofmann, Nicolaus Mercator (Kauffman): sein Leben und Wirken, vorzugsweise als Mathematiker (Wiesbaden, 1950), 43-103
M. Folkerts, 'Mercator, Nicolaus', Neue deutsche Biographie, ed. Otto, Graf zu Stolberg-Wernigerode, 17 (Berlin, 1994)
D. T. Whiteside, 'Mercator, Nicolaus', DSB
W. Applebaum, 'A descriptive catalogue of the manuscripts of Nicolaus Mercator, FRS, 1620-1687, in Sheffield University Library', Notes and Records of the Royal Society, 41 (1986-7), 21-37
Brief lives, chiefly of contemporaries, set down by John Aubrey, between the years 1669 and 1696, ed. A. Clark, 2 (1898), 58-9, 109, 263

BL, copy of Logarithmotechnia, with MS notes by Pell, MS 4403, no. 1
University of Sheffield, Hartlib collection

Wealth at death  
in debt: Hofmann, Nicolaus Mercator; H. W. Turnbull, ed., James Gregory tercentenary memorial volume (1939), 153

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