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The Story of Mercator’s Map

Published online by Cambridge University Press:  03 November 2016

H. S. Carslaw
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In 1569 Gerhardt Mercator (1512-1594) constructed the chart now called Mercator’s Map. On it the meridians and parallels are sets of parallel straight lines at right angles, a course on the Earth’s surface always cutting the meridians at the same angle is a straight line cutting the meridians on the map at the same angle, and the shape of any very small area on the map is the same as the shape of the corresponding small area upon the Earth. This chart can be made by gradually increasing the distances between the degrees of latitude in advancing from the equator towards the poles. But though Mercator did, in fact, construct such a map, it is not known on what principle he proceeded, and it is conjectured that he obtained his division of the meridians by observing on a globe on which rhumb-lines had been drawn the intersection of these lines with the different meridians.

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Type
Research Article
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The Mathematical Gazette , Volume 12 , Issue 168 , January 1924, pp. 1 - 7
Copyright
Copyright © Mathematical Association 1924

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References

Page 1 of note * Rhumb is an old word for a compass point, and a rhumb-line is a course always directed to the same point of the compass.

Page 1 of note † Cf. Maseres, Scriptores Logarithmici, vol. 4, p. 314 (1791-1807) (from Wilson’s Dissertation on the Rise and Progress of Navigation).

Page 1 of note ‡ Cf. Certaine Errors in Navigation, p. 9.

Page 2 of note * Cf. Cajori, “On an integration antedating the Integral Calculus,” Bibliotheca Mathematica (3 F.), Bd. 14, p. 312, 1914. And a paper by the same author in the Napier Tercentenary Memorial Volume, p. 95, 1915.

Page 2 of note † In those days the sine, cosine, etc., were lines in a circle of given radius. Sometimes this radius was taken to be 10,000,000, as in Wright’s work. If greater accuracy was needed, this was replaced by 10,000,000,000. The sine of 90° is equal to the radius, and is called the whole sine or sinus totus.

Page 2 of note ‡ In the first edition of Wright’s work (1599) the meridian was divided only to every ten minutes. In the later editions the division was to every minute.

Page 3 of note * No. 13, Phil. Trans. 1666. The quotations are taken from the version in the Abridged Transactions issued in 1722 by Lowther.

Page 3 of note † Napier in the Constructio (1616) used the term artificial number instead of logarithm. And this practice was followed by some writers. In the Descriptio, written later than the Constructio but published in 1614, he used the term logarithm throughout.

Page 3 of note ‡ For Gregory St. Vincent’s work on the Conic Sections, see Abh. zur Geschichte der math. Wiss. Heft xx. 2 Stück, 1907. This property of the hyperbola is given in Prop. CIX. See also CXXV.-CXXX.

Page 4 of note * Cf. Child’s translation of the Lectiones Geometricae, Chicago, 1916.

Page 4 of note † Collins, Commercium Epistolicum, 1712.

Page 4 of note ‡ Brouncker was one of the founders and the first President of the Royal Society.

Page 5 of note * In those days “analogy” meant “proportion,” as for instance in Napier’s Analogies.

Page 5 of note † No. 38, Phil. Trans. 1668. In the Abridged Transactions only the title of this paper appears. The paper itself will be found in Maseres, loc. cit. vol. i.

Page 6 of note * No. 176, Phil. Trans. 1685. Cf. Abridged Transactions, vol. i. p. 572.

Page 6 of note † No. 219, Phil. Trans. 1.696. Cf. Abridged Transactions, vol. i. p. 577