Nicole Oresme

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Allemagne (west of Riez), France
11 July 1382
Lisieux, France

Nicole Oresme was a French mathematician who invented coordinate geometry long before Descartes. He was the first to use a fractional exponent and also worked on infinite series.


Nicholas Oresme, whose name is given in French as Nicole Oresme, was of Norman origin. Nothing is known of his early life, and the first that is known is that he studied for an Arts Degree in Paris in the early 1340s where he was taught by Jean Buridan at the University of Paris.

Buridan was a philosopher and logician who made contributions to probability, optics and mechanics. He added to Aristotle's theory of motion by understanding that motion was retarded by resistance from the air. Although his views were in many respects close to those of Ockham, he disagreed with some of Ockham's views and attacked them in 1340. About 35 years later the followers of Ockham would retaliate by placing Buridan's works on the Index of Forbidden Books. Buridan had a major influence in interesting Oresme in natural philosophy and in encouraging him to question the ideas of Aristotle.

Oresme's name appears on the list of scholarship holders in theology at the College of Navarre at the University of Paris in the year 1348. He was awarded the degree of Master of Theology in 1355 and, in the following year, he was appointed as Grand Master of the College of Navarre. Not long after this Oresme became friendly with the dauphin Charles who went on to become Charles V of France in 1362. The friendship between Charles and Oresme was one which continued throughout their lives. Charles was in intellectual and religious man who enjoyed the company of scholars such as Oresme.

After six years as the Grand Master of the College of Navarre, Oresme left in 1362 to become canon of the Cathedral of Rouen. The following year he took on the additional duties of canon at the Sainte-Chapelle in Paris. In 1364 he became dean of the Cathedral of Rouen and, his friend Charles becoming King of France on 8 April of that year, Oresme was appointed as Charles' chaplain and councillor. From 1370 he lived mainly in Paris, advising Charles on financial matters as well as translating from Latin into French Aristotle's Ethics, Politics and On the Heavens and the Aristotle style work Economics. These translations were very important, introducing many new technical terms into the French language. As a reward for this work Charles appointed Oresme bishop of Lisieux in 1377 and he was consecrated in the following year.

At a time when Aristotle's ideas were accepted almost without question, Oresme did indeed question them. For example he rejected Aristotle's definition of time, which was based on uniform motion, and proposed a definition independent of motion. Similarly he rejected Aristotle's definition of the position of a body, which was the boundary of the surrounding space, and replaced it with a definition in terms of the space which the body occupies.

Oresme invented a type of coordinate geometry before Descartes, finding the logical equivalence between tabulating values and graphing them in De configurationibus qualitatum et motuum. He proposed the use of a graph for plotting a variable magnitude whose value depends on another variable. It is possible that Descartes was influenced by Oresme's work since it was reprinted several times over the 100 years following its first publication. Oresme was the first to prove Merton's theorem, namely that the distance travelled in a fixed time by a body moving under uniform acceleration is the same as if the body moved at a uniform speed equal to its speed at the midpoint of the time period.

Another work by Oresme De proportionibus proportionum contains the first use of a fractional exponent, although, of course, not in modern notation. He examined the question as to whether the ratio of the periods of two heavenly bodies was a rational number asking:-
... if anyone should make a mechanical clock, would he not make all the wheels move as harmoniously as possible?
He then answered his own question, arguing that the irrationality of ratios will not rob the heavens of their beauty and will also not be inconsistent with regular movement. Oresme also worked on infinite series and argued for an infinite void beyond the Earth.

Clagett writes in [3]:-
This brilliant scholar has been credited with ... the invention of analytic geometry before Descartes, with propounding structural theories of compounds before nineteenth century organic chemists, with discovering the law of free fall before Galileo, and with advocating the rotation of the Earth before Copernicus. None of these claims is, in fact, true, although each is based on discussion by Oresme of some penetration and originality ...
In Livre du ciel et du monde (1377) Oresme opposed the theory of a stationary Earth as proposed by Aristotle and in this work he proposed rotation of the Earth some 200 years before Copernicus. However he rather spoilt this fine piece of thinking by rejecting his own ideas at the end of the work and so, as Clagett writes, cannot be regarded as claiming that the Earth rotated before Copernicus. He wrote Questiones Super Libros Aristotelis de Anima dealing with the nature of light, reflection of light, and the speed of light. Oresme's work on light is discussed in detail in [16].

References (show)

  1. M Clagett, Biography in Dictionary of Scientific Biography (New York 1970-1990).
    See THIS LINK.
  2. Biography in Encyclopaedia Britannica.
  3. M Clagett, Nicole Oresme and the Medieval Geometry of Quantities and Motions (Madison, 1968).
  4. M Clagett (ed.), Nicole Oresme and the medieval geometry of qualities and motions. A treatise on the uniformity and difformity of intensities known as 'Tractatus de configurationibus qualitatum et motuum' (Madison, Wis.-London, 1968).
  5. G W Coopland, Nicole Oresme and the Astrologers: A Study of His 'Livre de divinacions' (1952).
  6. E Grant (ed.), Nicole Oresme and the kinematics of circular motion. 'Tractatus de commensurabilitate vel incommensurabilitate motuum celi' (Madison, Wis.-London, 1971).
  7. H-J Ilgauds, Nicole Oresme, in H Wussing and W Arnold, Biographien bedeutender Mathematiker (Berlin, 1983).
  8. O Pederson, Nicole Oresme (Copenhagen, 1956).
  9. G Schuppener, Geschichte der Zeta-Funktion von Oresme bis Poisson, Deutsche Hochschulschriften 533 (Egelsbach, 1994).
  10. H L L Busard, Die Quellen von Nicole Oresme, Janus 58 (1971), 161-193.
  11. E Grant, Nicole Oresme and the Commensurability or Incommensurability of Celestial Motions, Archive for History of Exact Science 1 (1961), 420-.
  12. E Grant, Nicole Oresme and his De proportionibus proportionum, Isis 51 (1960), 293-314.
  13. L Gribaudo, Was Oresme a precursor of Descartes? (Italian), Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 113 (1-2) (1979), 155-164.
  14. L Gribaudo, La serie geometrica nell'opera 'Quaestiones super geometriam Euclidis' di Nicole Oresme, Rend. Sem. Mat. Univ. e Politec. Torino 35 (1976/77), 147-158.
  15. L Maieru, The theory of proportions in the 'Quaestiones super geometriam Euclidis' of Nicole Oresme (Italian), Arch. Internat. Hist. Sci. 40 (125) (1990), 258-277.
  16. P Marshall, Nicole Oresme on the nature, reflection, and the speed of light, Isis 72 (1981), 357-374.
  17. P Rusnock, Oresme on ratios of lesser inequality, Arch. Internat. Hist. Sci. 45 (135) (1995), 263-272.
  18. E G Valabrega, La questione dell'incommensurabilità della diagonale in N Oresme (Italian), Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 105 (1971), 245-250.
  19. J von Plato, Oresme's proof of the density of rotations of a circle through an irrational angle, Historia Math. 20 (4) (1993), 428-433.
  20. J von Plato, Nicole Oresme and the ergodicity of rotations, Acta Philos. Fenn. 32 (1981), 190-197.
  21. V P Zubov, Notes au traité de N Oresme, Istor.-Mat. Issled. 11 (1958), 720-731.
  22. V P Zubov, Le traité 'De confinguratione qualitatum' de Nicole Oresme, Istor.-Mat. Issled. 11 (1958), 601-635.

Additional Resources (show)

Honours (show)

Honours awarded to Nicholas Oresme

  1. Lunar features Crater Oresme

Cross-references (show)

Written by J J O'Connor and E F Robertson
Last Update April 2003