# Mercator, Nicholas

, an eminent mathematician
and astronomer, whose name in High-Dutch was Kauffman,
was born about 1640, at Holstein in Denmark. From his
works we learn, that he had an early and liberal education,
suitable to his distinguished genius, by which he was enabled to extend his researches into the mathematical sciences,
and to make very considerable improvements: for it appears from his writings, as well as from the character given
of him by other mathematicians, that his talent rather lay
in improving, and adapting any discoveries and improvements to use, than invention. However, his genius for
the mathematical sciences was very conspicuous, and introduced him to public regard and esteem in his own
country, and facilitated a correspondence with such as
were eminent in those sciences, in Denmark, Italy, and
| England, In consequence, some of his correspondents
gave him an invitation to this country, which he accepted; and he afterwards continued in England till hi
death. In 1666 he was admitted F. R. S. and gave frequent proofs of his close application to study, as well as
of his eminent abilities in improving some branch or other
of the sciences. But he is charged sometimes with borrowing the inventions of others, and adopting them as his
own, and it appeared upon some occasions that he was not
of an over-liberal mind in scientific communications. Thus,
it had some time before him been observed, that there was
an analogy between a scale of logarithmic tangents and
Wright’s protraction of the nautical meridian line, which
consisted of the sums of the secants; though it does not
appear by whom this analogy was first discovered. It appears, however, to have been first published, and introduced into the practice of navigation, by Henry Bond, who
mentions this property in an edition of Norwood’s Epitome
of Navigation, printed about 1645; and he again treats of
it more fully in an edition of Gunter’s works, printed in
1653, where he teaches, from this property, to resolve all
the cases of Mercator’s sailing by the logarithmic tangents,
independent of the table of meridional parts. This analogy
had only been found to be nearly true by trials, but not
demonstrated to be a mathematical property. Such demonstration seems to have been first discovered by Mercator, who, desirous of making the most advantage of this and
another concealed invention of his in navigation, by a paper
in the Philosophical Transactions for June 4, 1666, invites
the public to enter into a wager with him on his ability to
prove the truth or falsehood of the supposed analogy. This
mercenary proposal it seems was not taken up by any one;
and Mercator reserved his demonstration. Our author,
however, distinguished himself by many valuable pieces on
philosophical and mathematical subjects. His first attempt
was, to reduce astrology to rational principles, which
proved a vain attempt. But his writings of more particular
note, are as follow: 1. “Cosmographia, sive Descriptio
Cceli & Terrse in Circulos, qua fundamentum sterniter sequentibus ordine Trigonometric Sphericorum Logarithmicse, &c. a” Nicolao Hauffman Holsato,“Dantzic, 1651,
12mo. 2.” Rationes Mathematics subductse anno 1653,“Copenhagen, 4to. 3.” De Emendatione annua Diatribae
duae, quibus exponuntur & demonstrantur Cycli Soiis &
| Lunce,“&c. 4to. 4.” Hypothesis Astronomica nova, et
Consensus ejus cum Observationibus,“Lond. 1664, folio.
5.” Logarithmotechnia, sive Method us construendi Logarithmos nova, accurata, et facilis; scripto antehac communicata anno sc. 1667 nonis Augusti; cui nunc accedit,
Vera Quadratura Hyperbolae, & inventio summae Logaritbmorum. Auctore Nicolao Mercatore Holsato e Societate
Regia. Huic etiam jungitur Michaelis Angeli Riccii Exercitatio Geometrica de Maximis et Minimis, hie ob argument! praestantiam & exemplarium raritatem recusa,“Lond. 1668, 4to. 6.” Institutionum Astronomicarum libri duo, de Motu Astrorum communi & proprio, secundum
hypotheses veterum & recentiorum praecipuas deque Hypotheseon ex observatis constructione, cum tabulis Tychonianis, Solaribus, Lunaribus, Lunae-solaribus, & Rudolphinis Solis, Fixarum &*quinque Errantium, earumque usu
prajceptis et exemplis commonstrato. Quibus accedit Appendix de iis, quae uovissimis temporibus coelitus innotuerunt,“Lond. 1676, 8vo. 7.” Euclidis Elementa Geometrica, novo ordine ac methodo fere, demonstrata. Una
cum Nic. Mercatoris in Geometriam Introductione brevi,
qua Magnitudinum Ortus ex genuinis Principiis, & Ortarum Affectiones ex ipsa Genesi derivantur," Lond. 1678,
12mo. His papers in the Philosophical Transactions are,
1. A Problem on some Points of Navigation vol. I. p. 215.
2. Illustrations of the Logarithmo-technia vol. Hi. p. 759.
3. Considerations concerning his Geometrical and Direct
Method for finding the Apogees, Excentricities, and Anomalies of the Planets; vol. V. p. 1168. Mercator died in
1594, about fifty-four years of age. ^{1}

^{1}

Hutton’s Dict. Martin’s Biog. Phil. Usher’s Life and Letters, pp. 607, 6^2. Letters of Eminent Persons, 1813, 3 vols. 8vo, where are some anecdotes of him by Aubrey.