Nicole Oresme

Philosopher, economist, mathematician, and physicist, one of the principal founders of modern science; b. in Normandy, in the Diocese of Bayeux; d. at Lisieux, 11 July, 1382. In 1348 he was a student of theology in Paris; in 1356 grand master of the Collège de Navarre; in 1362, already master of theology, canon of Rouen; dean of the chapter, 28 March, 1364. On 3 August, 1377, he became Bishop of Lisieux. There is a tradition that he was tutor to the dauphin, afterwards Charles V, but this is irreconcilable with the dates of Oresme's life. Charles seems to have had the highest esteem for his character and talents, often followed his counsel, and made him write many works in French for the purpose of developing a taste for learning in the kingdom. At Charles's instance, too, Oresme pronounced a discourse before the papal court at Avignon, denouncing the ecclesiastical disorders of the time. Several of the French and Latin works attributed to him are apocryphal or doubtful. Of his authentic writings, a Christological treatise, "De communicatione idiomatum in Christo", was commonly used as early as the fifteenth century by the theological Faculty of Paris.

But Oresme is best known as an economist, mathematician, and a physicist. His economic views are contained in a Commentary on the Ethics of Aristotle, of which the French version is dated 1370; a commentary on the Politics and the Economics of Aristotle, French edition, 1371; and a "Treatise on Coins". These three works were written in both Latin and French; all three, especially the last, stamp their author as the precursor of the science of political economy, and reveal his mastery of the French language. The French Commentary on the Ethics of Aristotle was printed in Paris in 1488; that on the Politics and the Economics, in 1489. The treatise on coins, "De origine, natura, jure et mutationibus monetarum", was printed in Paris early in the sixteenth century, also at Lyons in 1675, as an appendix to the "De re monetaria" of Marquardus Freherus, and is included in the "Sacra bibliotheca sanctorum Patrum" of Margaronus de la Bigne IX, (Paris, 1859), p. 159, and in the "Acta publica monetaria" of David Thomas de Hagelstein (Augsburg, 1642). The "Traictié de la première invention des monnoies" in French, was printed at Bruges in 1477.

His most important contributions to mathematics are contained in "Tractatus de figuratione potentiarum et mensurarum difformitatum", still in manuscript. An abridgment of this work printed as "Tractatus de latitudinibus formarum" (1482, 1486, 1505, 1515), has heretofore been the only source for the study of his mathematical ideas. In a quality, or accidental form, such as heat, the Scholastics distinguished the intensio (the degree of heat at each point) and the extensio (e.g., the length of the heated rod): these two terms were often replaced by latitudo and longitudo, and from the time of St. Thomas until far on in the fourteenth century, there was lively debate on the latitudo formæ. For the sake of lucidity, Oresme conceived the idea of employing what we should now call rectangular co-ordinates: in modern terminology, a length proportionate to the longitudo was the abscissa at a given point, and a perpendicular at that point, proportional to the latitudo, was the ordinate. He shows that a geometrical property of such a figure could be regarded as corresponding to a property of the form itself only when this property remains constant while the units measuring the longitudo and latitudo vary. Hence he defines latitudo uniformis as that which is represented by a line parallel to the longitude, and any other latitudo is difformis; the latitudo uniformiter difformis is represented by a right line inclined to the axis of the longitude. He proves that this definition is equivalent to an algebraical relation in which the longitudes and latitudes of any three points would figure: i. e., he gives the equation of the right line, and thus forestalls Descartes in the invention of analytical geometry. This doctrine he extends to figures of three dimensions.

Besides the longitude and latitude of a form, he considers the mensura, or quantitas, of the form, proportional to the area of the figure representing it. He proves this theorem: A form uniformiter difformis has the same quantitiy as a form uniformis of the same longitude and having as latitude the mean between the two extreme limits of the first. He then shows that his method of figuring the latitude of forms is applicable to the movement of a point, on condition that the time is taken as longitude and the speed as latitude; quantity is, then, the space covered in a given time. In virtue of this transposition, the theorem of the latitude uniformiter difformis became the law of the space traversed in case of uniformly varied motion: Oresme's demonstration is exactly the same as that which Galileo was to render celebrated in the seventeenth century. Moreover, this law was never forgotten during the interval between Oresme and Galileo: it was taught at Oxford by William Heytesbury and his followers, then, at Paris and in Italy, by all the followers of this school. In the middle of the sixteenth century, long before Galileo, the Dominican Dominic Soto applied the law to the uniformly accelerated falling of heavy bodies and to the uniformly decreasing ascension of projectiles.

Oresme's physical teachings are set forth in two French works, the "Traité de la sphère", twice printed in Paris (first edition without date; second, 1508), and the "Traité du ciel et du monde", written in 1377 at the request of King Charles V, but never printed. In most of the essential problems of statics and dynamics, Oresme follows the opinions advocated in Paris by his predecessor, Jean Buridan de Béthune, and his contemporary, Albert de Saxe (see Saxe, Albert de). In opposition to the Aristotelean theory of weight, according to which the natural location of heavy bodies is the centre of the world, and that of light bodies the concavity of the moon's orb, he proposes the following: The elements tend to dispose themselves in such manner that, from the centre to the periphery their specific weight diminishes by degrees. He thinks that a similar rule may exist in worlds other than this. This is the doctrine later substituted for the Aristotelean by Copernicus and his followers, such as Giordano Bruno. The latter argued in a manner so similar to Oresme's that it would seem he had read the "Traité du ciel et du monde". But Oresme had a much stronger claim to be regarded as the precursor of Copernicus when one considers what he says of the diurnal motion of the earth, to which he devotes the gloss following chapters xxiv and xxv of the "Traité du ciel et du monde". He begins by establishing that no experiment can decide whether the heavens move form east to west or the earth from west to east; for sensible experience can never establish more than one relative motion. He then shows that the reasons proposed by the physics of Aristotle against the movement of the earth are not valid; he points out, in particular, the principle of the solution of the difficulty drawn from the movement of projectiles. Next he solves the objections based on the texts of Holy Scripture; in interpreting these passages he lays down rules universally followed by Catholic exegetists of the present day. Finally, he adduces the argument of simplicity for the theory that the earth moves, and not the heavens, and the whole of his argument in favour of the earth's motion is both more explicit and much clearer than that given by Copernicus.

MEUNIER, Essai sur la vie et les ouvrages de Nicole Oresme (Paris, 1857); WOLOWSKI, ed., Traictié de la première invention des monnoies de Nicole Oresme, textes français et latin d'après les manuscrits de la Bibliothèque Impériale, et Traité de la monnoie de Copernic, texte latin et traduction française (Paris, 1864); JOURDAIN, Mémoire sur les commencements de l'Economie politique dans les écoles du Moyen-Age in Mémoires de l'Académie des Inscriptions et Belles-Lettres, XXVIII, pt. II (1874); CURTZE, Der Algorismus proportionum des Nicolaus Oresme in Zeitschr. für Mathematik und Physik, XIII, Supplementary (Leipzig, 1868), 65-79; IDEM, Der Tractatus de Latitudinibus Formarum des Nicolaus Oresme (Ibid., 1868), 92-97; IDEM, Die mathematischen Schriften des Nicole Oresme (Berlin, 1870); SUTER, Eine bis jetszt unbekannte Schrift des Nic. Oresme in Zeitschr. für Mathematik und Physik, XXVII, Hist.-litter. Abtheilung (Leipzig, 1882), 121-25; CANTOR, Vorlesungen über die Gesch. der Mathematik, II (2nd ed., Leipzig, 1900), 128-36; DUHEM, Un précurseur français de Copernic: Nicole Oresme (1377) in Revue générale des Sciences (Paris, 15 Nov., 1909); IDEM, Dominique Soto et la Scolastique parisienne in Bulletin hispanique (Bourdeaux, 1910-11).

PIERRE DUHEM