Nicole Oresme (pronounced [nikɔl ɔʁɛm],[1] c. 1320–5 – July 11, 1382), also known as Nicolas Oresme, Nicholas Oresme, or Nicolas d'Oresme, was a significant philosopher of the later Middle Ages. He wrote influential works on economics, mathematics, physics, astronomy, philosophy, and theology; was Bishop of Lisieux, a translator, a counselor of King Charles V of France, and probably one of the most original thinkers of the 14th century.[2]
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Nicole Oresme was born c. 1320–1325 in the village of Allemagne (today's Fleury-sur-Orne) in the vicinity of Caen, Normandy, in the diocese of Bayeux. Practically nothing is known concerning his family. The fact that Oresme attended the royally sponsored and subsidized College of Navarre, an institution for students too poor to pay their expenses while studying at the University of Paris, makes it probable that he came from a peasant family.[3]
Oresme studied the “artes” in Paris, together with Jean Buridan (the so-called founder of the French school of natural philosophy), Albert of Saxony and perhaps Marsilius of Inghen, and there received the Magister Artium. He was already a regent master in arts by 1342, during the crisis over William of Ockham's natural philosophy.[4]
In 1348, he was a student of theology in Paris, in 1356, he received his doctorate and in the same year he became grand master (grand-maître) of the College of Navarre. In 1364 he was appointed dean of the Cathedral of Rouen. Around 1369 he began a series of translations of Aristotelian works at the request of Charles V, who granted him a pension in 1371 and, with royal support, was appointed bishop of Lisieux in 1377. It was in this city that he died in 1382.[5]
In his Livre du ciel et du monde Oresme discussed a range of evidence for and against the daily rotation of the Earth on its axis.[6] From astronomical considerations, he maintained that if the Earth were moving and not the celestial spheres, all the movements that we see in the heavens that are computed by the astronomers would appear exactly the same as if the spheres were rotating around the Earth. He rejected the physical argument that if the Earth were moving the air would be left behind causing a great wind from east to west. In his view the Earth, Water, and Air would all share the same motion.[7] As to the scriptural passage that speaks of the motion of the sun, he concludes that "this passage conforms to the customary usage of popular speech" and is not to be taken literally.[8] He also noted that it would be more economical for the small Earth to rotate on its axis than the immense sphere of the stars.[9] Nonetheless, he concluded that none of these arguments were conclusive and "everyone maintains, and I think myself, that the heavens do move and not the Earth."[10]
In discussing the propagation of light and sound, Oresme adopted the common medieval doctrine of the multiplication of species,[11] as it had been developed by optical writers such as Alhacen, Robert Grosseteste, Roger Bacon, John Pecham, and Witelo.[12] Oresme maintained that these species were immaterial, but corporeal (i.e., three-dimensional), entities.[13]
Like most of his scholarly contemporaries, Oresme wrote primarily in Latin, but at the urging of King Charles V, he also wrote in French, providing French versions of his own works and of selected works by Aristotle.
His most important contributions to mathematics are contained in Tractatus de configurationibus qualitatum et motuum. In a quality, or accidental form, such as heat, he distinguished the intensio (the degree of heat at each point) and the extensio (as the length of the heated rod). These two terms were often replaced by latitudo and longitudo. For the sake of clarity, Oresme conceived the idea of visualizing these concepts by plane figures, approaching what we would now call rectangular co-ordinates. The intensity of the quality was represented by a length or latitudo proportional to the intensity erected perpendicular to the base at a given point on the base line, which represents the longitudo. Oresme proposed that the geometrical form of such a figure could be regarded as corresponding to a characteristics of the quality itself. Oresme defined a uniform quality as that which is represented by a line parallel to the longitude, and any other quality is difform. Uniformly difform qualities are represented by a straight line inclined to the axis of the longitude, while he described many different cases of difformly difform qualities. Oresme extended this doctrine to figures of three dimensions. He considered this analysis applicable to many different qualities such as hotness, whiteness, and sweetness. Significantly for later developments, Oresme applied this concept to the analysis of local motion where the latitudo or intensity represented the speed, the longitudo represented the time, and the area of the figure represented the distance travelled.[14]
He 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 latitudo uniformiter difformis became the law of the space traversed in case of uniformly varied motion; thus Oresme manages to anticipate Galileo´s discovery.[15][16]
Significantly, Oresme developed the first (if somewhat obscure) proof of the divergence of the harmonic series, something that was only replicated in the later centuries by the likes of the Bernoulli brothers. His proof, an alternative to other "standard" tests for divergence (the ratio test, etc.), elegantly stated that for any value of 1/n, the closest n that is a member of the sequence 2n, the preceding n/2 terms must be greater than 1/2. Thus, using the comparison test and the squeeze theorem, the series must be greater than the series 1 + 1/2 + 1/2 + 1/2 + ... + 1/2 (which is obviously divergent), which means the harmonic series whose terms are 1/n must be divergent. Oresme was the only mathematician to prove this fact, and held that honor for the next few centuries.
With his Treatise on the origin, nature, law, and alterations of money, one of the earliest manuscripts devoted to an economic matter, Oresme brings an interesting insight on the medieval conception of money.