Background

Nikolaus Mercator was born Niklaus Kauffman in 1620 in Eutin, Duchy of Holstein, Holy Roman Empire (now Schleswig-Holstein, Germany). He later changed his family name, which was a common thing to do at this time, to Mercator which was the Latin form of 'merchant'. Nicolaus's father was Martin Kauffman who was a schoolmaster at Oldenburg in Holstein from 1623 until his death in 1638.

Education

Although there is no evidence to prove that Nicholas Mercator attended his father's school, it is impossible to believe that he would attend any other than the one in Oldenburg where his father taught.

Mercator entered the University of Rostock in 1632, received a degree in 1641, then went to Leiden for a short period.

Career

After his return to Rostock in 1642 he was appointed to a post in the Faculty of Philosophy at the University. In 1648 Mercator moved to the University of Copenhagen. While he was working there, he published a number of textbooks on spherical trigonometry, geography, and astronomy. In 1648 he superintended a “Disputatio physica de spiritibus et innato calido” and over the next five years produced several short textbooks on elementary astronomy and spherical trigonometry; one of his title-pages at this time describes him as “mathematician and writer on travels to the Indies.”

Mercator's tract on calendar improvement (1653) caught Cromwell’s eye in England and, whether invited or not, he subsequently left Denmark for London. There he resided for almost thirty years and came universally to be known by his Latinized name, an “anglization” which he himself soon adopted. Unable to find a position in a university, Mercator earned a living as a mathematical tutor, but soon he made the acquaintance of Oughtred, Pell, Collins, and other practitioners. In November 1666, on the strength of his newly invented marine chronometer, he was elected a fellow of the Royal Society; earlier, in Oldenburg’s Philosophical Transactions of the Royal Society, he had wagered the profits (seemingly nonexistent) from his invention against anyone who could match his expertise in the theory of Gerard Mercator’s map. Through his Latin version (1669) of Kinckhuysen’s Dutch Algebra, commissioned by Collins at Seth Ward’s suggestion, he came into contact with Newton, and the two men later exchanged letters on lunar theory. In September 1676 Hooke unsuccessfully proposed Mercator as Mathematical Master at Christ’s Hospital. In 1683 he accepted Colbert’s commission to plan the waterworks at Versailles, but died soon afterward, having fallen out with his patron.

Mercator’s early scientific work is known only through the university textbooks which he wrote in the early 1650s; if not markedly original, they show his firm grasp of essentials. His Trigonometria sphaericoram logarithmica (1651) gives neat logarithmic solutions of the standard cases of right and oblique triangles and tabulates the logarithms of sine, cosine, tangent, and cotangent functions (his “Logarithmus,” “Antilogarithmus,” “Hapsologarithmus,” and “Anthapsologarithmus”) at l’ intervals. His Cosmographia (1651) and Astronomia (1651) deal respectively with the physical geography of the earth and the elements of spherical astronomy.

Mercator’s first published book in England, Hypothesis astronomica nova (1664), in effect combines Kepler’s hypothesis (that planets travel in elliptical orbits round the sun, with the sun at one focus) with his vicarious hypothesis (in which the equant circle is centered in the line of apsides at a distance from the sun roughly 5/8 times the doubled eccentricity): Mercator sets this ratio exactly equal to the “divine section,” with an error even in the case of Mars of less than 2’.

Subsequently, in 1670, he showed his skill in theoretical astronomy by demolishing G. D. Cassini’s 1669 method for determining the lines of apsides of a planetary orbit, given three solar sightings. He showed that it reduced to the Boulliau-Ward hypothesis of mean motion round an upper-focus equant and pointed out its observational inaccuracy. (His enunciation of the “true” Keplerian hypothesis, that time in orbit is proportional to the focal sector swept out by the planet’s radius vector, may well have been the source of Newton’s knowledge of this basic law.) The two books of his Institutiones astronomicae (1676) offered the student an excellent grounding in contemporary theory, and Newton used them to fill gaps in his rather shaky knowledge of planetary and lunar theory. Some slight hint of the practical scientist is afforded by the barometric measurements made during the previous half-year, which Mercator registered at the Royal Society in July 1667. No working drawings are extant of the Huygenian pendulum watch - which he designed in 1666 - or of its marine mounting (by gimbal suspension), but an example “of a foote diameter” was made.

Mercator is remembered above all as a mathematician. In 1666 he claimed to be able to prove the identity of “the logarithmical Tangent-line beginning at 45 deg.” with the “true Meridian-line of the Sea-Charte” (Mercator map). This declaration is not authenticated but not necessarily empty. It is difficult to determine how far his researches into finite differences - which were restricted to the advancing-differences formula - were independent of Harriot’s unpublished manuscripts on the topic, to which Mercator perhaps had access.

The circulation by Collins of the “De analysi,” composed hurriedly by Newton as a riposte, seems to have effectively blocked Mercator’s plans to publish a complementary Cyclomathia with allied expansions (on Newtonian lines) of circle integrals. The “Introductio brevis” which he added in 1678 to Martyn’s second edition of the anonymous Euclidis elementa geometrica commendably sought to simplify the Euclidean definitions for the beginner by introducing motion proofs: a circle is generated as the ripple on the surface of a stagnant pool when a stone is dropped at its center, a line as the instantaneous meet of two such congruent wave fronts. His Hypothesis astronomica nova contains the first publication of the polar equation of an ellipse referred to a focus.

Achievements

• Among all Mercator's achievements, the publication of his small book Logarithmotechnia 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 importantly, 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.

Works

More photos

• book

  • Institutionum Astronomicarum Libri Duo, De Motu Astrorum Communi Et Proprio 1676
  • Philosophical Transactions of the Royal Society: Volume 1 1666
  • Logarithmo-Technia 1668
  • Philosophical Transactions of the Royal Society: Volume 3 1668
  • Philosophical Transactions of the Royal Society: Volume 5 1670

Religion

In Mercator's Hypothesis astronomica nova a mystical streak in his personality gleams through, for he compares his hypothesis to a knock-kneed man standing with arms outstretched, a “living image of Eternity and the Trinity.” He later expounded similar insights in an unpublished manuscript on Astrologia rationalis. Even though his exact denomination is unclear his belief in the concept of the Holy Trinity seems to show that he was Christian. Some sources suppose him to be Lutheran.

Views

Mercator’s early scientific work is known only through the university textbooks which he wrote in the early 1650s; if not markedly original, they show his firm grasp of essentials. His Trigonometria sphaericoram logarithmica (1651) gives neat logarithmic solutions of the standard cases of right and oblique triangles and tabulates the logarithms of sine, cosine, tangent, and cotangent functions (his “Logarithmus,” “Antilogarithmus,” “Hapsologarithmus,” and “Anthapsologarithmus”) at l’ intervals. His Cosmographia (1651) and Astronomia (1651) deal respectively with the physical geography of the earth and the elements of spherical astronomy.

In his Rationes mathematicae (1653) Mercator insists on drawing a basic distinction between rational and irrational numbers: the difference in music is that between harmony and dissonance; in astronomy that between a Keplerian “harmonice mundi” and the observable solar, lunar, and planetary motions. In the tract De emendatione annua (1653) he urges the reform of the 365–day year into months of (in sequence) 29, 29, 30, 30, 31, 31, 32, 31, 31, 31, 30, and 30 days.

Mercator’s first published book in England, Hypothesis astronomica nova (1664), in effect combines Kepler’s hypothesis (that planets travel in elliptical orbits round the sun, with the sun at one focus) with his vicarious hypothesis (in which the equant circle is centered in the line of apsides at a distance from the sun roughly 5/8 times the doubled eccentricity): Mercator sets this ratio exactly equal to the “divine section”, with an error even in the case of Mars of less than 2’.

Membership

• 

  Royal Society , United Kingdom

  1666 - 1687

Personality

Quotes from others about the person

• "[Mercator is ] of little stature, perfect; black haire, … darke eie, but of great vivacity of spirit … of a soft temper (amat Venerem aliquantum): of a prodigious invention, and will be acquainted (familiarly) with nobody." - John Aubrey's portrayal of Mercator in his London times

Connections

There is no information on whether Nikolaus Mercator was ever married or had any children.

Father:

Martin Kauffman

pupil:

Josceline Percy

Mercator was a mathematics tutor to Joscelyne Percy, future 11th Earl of Northumberland, at Petworth, Sussex in 1657.

Acquaintance:

Isaac Newton

References

• Dictionary of Scientific Biography: Volumes 9 & 10
  1981