Nicole Oresme , born in the village of Germany (current the Fleury-on-Flowering ash) in 1325 and died in Lisieux the July 11th 1382, was a economist, Mathématicien, Physicien, Astronome, Philosophe, Psychologue, Musicologue, Théologien and translator French.
Biography
“ I thus do not know that I do not know anything. ”Called the “Einstein of”, this scientist in advance over his time, whose ideas were a prelude to with those of the Renaissance, was one of the principal founders and popularizers of the modern sciences, and probably the most original thinker of his century. One knows practically nothing about his family. The fact that it made its studies with the Collège of Navarre, establishment active and subsidized by the king for the too poor students to pay their school fees with the Université of Paris constitutes a probable indication of its country origins. All its life proceeded during the Guerre One hundred Year old, the Normandy often being then occupied by the England.
He studies the “artes” with Paris (before 1348), with Jean Buridan (recognized like the founder of the French school of natural philosophy), Albert of Saxony and perhaps Marsile d' Inghen and receives his Magister Artium . In 1348, it studies the Théologie in Paris. It obtains its Doctorat in 1356 and becomes, the same year, large-Master of the Collège of Navarre.
The majority of its Latin treaties most interesting go back to before 1360 and prove that it was already an academic established with the most raised reputation, which drew the attention of the royal family and in intimate contact with the future Charles V in 1356 put it. Starting from 1356, during the captivity of his/her father Jean II in England, Charles was regent then king de France of 1364 with 1380. The November 2nd 1359, he becomes secretary of the king before becoming thereafter, chaplain and advising of the king.
A not proven long tradition but also makes him to it tutor of the Dauphin, future Charles V which seems to have held the character and the talents of Nicole Oresme in very high regard, often took its advice and many works in French made it write in order to popularize sciences and to develop the taste of the scholarship in its kingdom. It is with its insistence that he made a speech denouncing the disorders of the Église before the papal court of Avignon. The force of the probable influence of the political, economic, moral thought and philosophical progressist of Nicole Oresme on king Charles “the Wise one” of which he was the friend and the intimate adviser, until the death of this last, still remains to be been studied. It was, at the court of Charles V who often used his great diplomatic matter competences, the most important person of a selected circle of intellectuals including/understanding, inter alia, Raoul de Presles, Philippe de Mézières.
Its sending on mission by the dolphin in 1356, then in 1360 to request a loan near the municipal authorities rouennaises proves royal confidence in its capacities. In 1361, whereas he was still large-Master of the College of Navarre, he is named, with the support of Charles, archdeacon of Bayeux. It is known that this impassioned academic unwillingly returned his station coveted of large-Master. The November 23rd 1362, the year when he becomes Master in theology, he is named Chanoine Cathédrale of Rouen. At the time of its nomination at this station, he teaches always regularly at the university of Paris. The February 10th 1363, it is named canon with the Holy Vault, receives a half-benefit and is high the March 18th 1364 at the station of Doyen of the cathedral of Rouen. It is probable that the Charles dolphin influenced by his suggestions the decisions of his/her father Jean II concerning with the frequent changes of stations of Oresme.
These consecutive stations with the cathedral of Rouen (1364 - 77) do not prevent it from spending much time, particularly for the university businesses, in Paris, without the many documents attesting of its presence in the capital proving that it also taught there. Letters sent by Charles V to Rouen of the August 28th to the November 11th 1372 establish a coincidence between the beginning of its uninterrupted stay with Paris and the beginning of its prolonged activities of translation at the request of the king. Its residence in Paris seems to be prolonged by Charles V until 1380, when it started to work in 1369 with his translation of the Éthique of Aristote, which seems to be completed in 1370. Those of the Political and the Économiques of the same philosopher could be accomplished between the years 1372 and 1374, and the Of caelo and mundo in 1377. Its great work was worth to him, as of 1371, a pension of the royal treasure. Its untiring work for Charles V and the royal family also was worth to him, with the support of the king, the station of bishop of Lisieux, the August 3rd 1377. It took residence with Lisieux only in September 1380 and one does not know large thing over the five last years of his life. It was, with its death which has occurred two years after that of Charles V, buried in the cathedral of Lisieux.
Scientific work
According to the work of Taschow ( Nicole Oresme und der Modern Frühling DER , 2003) Nicole Oresme is especially known as economist, mathematician, and physicist, but also as musicologist, psychologist and philosopher. Its economic sights are contained in the Commentaire on ethics of Aristote , (1370), the Commentaire on the policy and the economic ones of Aristote , (1371) and the Traité currencies ( Of origin, will natura, swears and mutationibus monetarum ). All three written in Latin and French, these works devote, especially the third, their author like the precursor of the science of the political economy while revealing its control of the French language. This made of him the pioneer of the terminology and the language French scientists. He created a great number of French scientific terms and preceded the use of the Latin words in the scientific language of. A short overflight of the universality of the work of Nicole Oresme passes by fields such as mathematics, musicology, psychology, natural philosophy and physics:
Mathematics
Its most important contributions to mathematics are contained in the Tractatus of configuratione qualitatum and motuum , never printed. A compendium of this work printed under the title of Tractatus of latitudinibus formarum of Johannes de Sancto Martino (1482, 1486, 1505 and 1515) was for a long time the only source of study of its mathematical ideas. The Scolastique S distinguished, in a quality or an accidental form such as heat, between the intensio (the degree of heat at each point) and the extensio (the length of the heated stem). These two terms were often replaced by those of latitudo and of longitudo and, as of Thomas d' Aquin up to one advanced period of, the question of the latitudo formae was the subject of animated debates until Nicole Oresme clarifies the question by using what one would call, in modern terms, of the Cartesian coordinates: a length proportioned with the longitudo constituted the X-coordinate at a given point and a perpendicular at this point, proportional to the latitudo constituted the ordinate. Oresme proved that one could consider the geometrical property of such a figure as correspondent with the property of the form itself, the parameters of latitudo and longitudo being able to change or remain constant. Oresme defines the latitudo uniformis as what is represented by a line parallel with longitude and very other latitudo is difformis ; the latitudo uniformiter difformis is represented by a straight line inclined towards the axis of longitude. Nicole Oresme showed that this definition is equivalent to an algebraic relation in which longitudes and the latitudes of three unspecified points would appear: in other words, it gives the equation of the straight line and thus precedes Descartes three centuries in the invention of the analytical Geometry. Oresme extended these doctrines to the figures with three dimensions.Beside longitude and latitude of a form, it considered the will mensura or quantitas of a form proportional to the surface of the figure which represents it. It proved this theorem: a form uniformiter difformis with the same quantity as a form uniformis of the same longitude and whose latitude is the average between the two extreme limits of the first. It then proved that its method to appear the latitude of the forms can apply to the movement of a point, provided that time is taken as longitude and speed like latitude; the space covered in a given time constitutes the quantity then.
The theorem of the latitude uniformiter difformis became, under the terms of this transposition, the law of the space crossed in the event of uniformly varied movement. The demonstration is identical to that to which Galileo will proceed to. This law was never forgotten besides during the interval separating Oresme from Galileo because she was taught with Oxford by William Heytesbury and her disciples, then in Paris and in Italy, by all the following disciples of this school. In the middle of, a long time before Galileo, Dominican the Domingo de Soto applied this law to the uniformly accelerated fall of the heavy bodies and to the rise uniformly decreasing of the projectiles.
In the Algorismus proportionum and the Of proportionibus proportionum , Oresme developed the first method of calculating of the powers with exposing irrational fractional, i.e. calculation with irrational proportions ( proportio proportionum ). The base of this method was the equalization of the continuous sizes and the discrete numbers, idea drawn by Oresme from the theory from the music monocorde ( sectio canonis ). This enabled him to overcome prohibition pythagorician of the regular division of the intervals pythagoricians like 8/9, 1/2, 3/4, 2/3 and enabled him to produce the moderate Gamme two centuries and half before Simon Stevin. Example of division equalizes octave in 12 parts:
Oresme used, for example, this method in its musical section of the Tractatus of configurationibus qualitatum and motuum in the context of its “theory of the partial tonality or Harmonique (see below) to produce proportions of its irrational (ugly stamp or color of tonality) in the direction of the “continuum of partial tonality” (“white vibration”).
Oresme was interested much in the limits, the values threshold and the series by means of vector additions ( Tractatus of configurationibus qualitatum and motuum , Questiones super geometriam Euclidis ) which prepared the way with the infinitesimal calculus of Descartes and of Galileo. It proved the divergence of the series harmonics by means of the standard method always taught in the courses of analyzes mathematical current.
For the prefiguration of Oresme of the Stochastic modern, cf will infra the heading “Philosophy natural”. Taschow indeed showed how Nicole Oresme transformed the graphic method, evoked above, of sound Tractatus of configurationibus qualitatum and motuum of the musical theory of her time. From there one comes to the important contributions from Oresme in the field from musicology.
Musicology
One can see in the “ configuratio qualitatum and the functional pluridimensionality” which is associated there, that they are closely related on the current diagrams musicologic and, which is paramount, to the musical notation, which also measures and visually represents the variations of a sonus granting measurements given of extensio (time intervals) and of intensio (your). The complex representations of musical writing became, in the work of Oresme, configurationes qualitatum or difformitates compositae , the music functioning once more like the paradigm legitimator. Nevertheless, the musical sphere provided not only to the theory of Oresme an empirical legitimation, it also helped it with exemplifier the various types of uniform and deformed configurations which he had developed, in particular the idea that the configurationes were equipped with qualities with specific effects, esthetic or different, of which the geometrical representation would allow the analytical apprehension. This last point helps to explain the understanding esthetic approach of Oresme of the normal phenomena, founded on the conviction that the esthetic evaluation of the significant experiment (graphically representable) provided an adequate principle of analysis. In this context, the music played, once more, a big role as a model with the “esthetics of the complexity and infinite” preferred by the mentality of.Oresme sought the parameters of the sonus by the experimentation on the level microstructurel and acoustics of the simple tonality and on the level macrostructurel of unison or the polyphonic music. While trying analytically to capture the various physical parameters, psychological and esthetics of the sonus according to the extensio and the intensio , Oresme wished to represent them like conditions with the infinitely variable categories of pulchritudo and turpitudo . It pushed this method on a level which, representing the mathematical description most complete of the musical phenomena before the Discorsi of Galileo, does not know any equivalent with the Moyen-âge. It is to note that this research led it to discover not only the your partial or harmonic sounds three centuries before Marin Mersenne, but also to identify the relation between the harmonics and the color of the tonality, which it explained in a detailed physicomathematical theory, whose level of complexity was not to be reached again before with Hermann von Helmholtz.
It is also necessary to mention interpretation mechanist of Oresme in his Tractatus of configuratione and qualitatum motuum of the sonus like a discontinuous specific type of movement (vibration), of resonance like phenomenon of harmonic and the relation of Consonance and Dissonance, which exceeded even the successful but false theory of the coincidence of the consonance formulated with.
The demonstration of Oresme of a correspondence between a mathematical method ( configuratio qualitatum and motuum ) and a physical phenomenon (its) constitutes a particularly rare case, at the same time for, in general, and for the work of Oresme, in particular. The sections of the Tractatus of configurationibus treating music constitute big steps in the development of the spirit of quantification which characterizes the modern time.
Oresme, the youngest friend of Philippe of Vitry, the theorist of the music, type-setter and bishop of Meaux, is the founder of modern musicology. Oresme dealt with almost each category of musicology (see Taschow, COp cit.) with the modern direction like:
- acoustics (in the super Expositio of animated , Quaestiones of animated , causis mirabilium , Of configurationibus , Of commensurabilitate vel incommensurabilitate ),
- musical esthetics (in Of configurationibus , Of commensurabilitate vel incommensurabilitate ),
- vocal and auditive physiology (in the Quaestiones of sensu , super Expositio of animated ),
- auditive psychology (in the Quaestiones of animated , causis mirabilium , Quaestiones of sensu ),
- the musical theory of measurement (in Tractatus specialis of monocordi , Of configurationibus , Algorismus proportionum ),
- the theory of the music (in Of configurationibus ),
- musical execution (in Of configurationibus ),
- the philosophy of music (in Of commensurabilitate vel incommensurabilitate ).
With its very special theory of the species ( multiplicatio specierum ), Oresme correctly formulated the first theory of the wave mechanics of the sound and the light, three centuries before Huygens with its description of a pure transport of energy without material propagation. The final species with the direction where hears Oresme means the same ones as the modern term of “form of wave”.
Oresme also discovered, three centuries years before Mersenne, the phenomenon of the partial or “harmonic” tonalities and, four centuries and half before Joseph Sauveur, the relation between the features and the tonality of color. In its “very detailed physicomathematical theory of the tonalities and partial tonalities of color”, Oresme preceded the theory of Hermann von Helmholtz.
The musical esthetics of Oresme formulated a “modern subjective theory of the perception”, which was not the perception of the objective beauty of divine creation, but the constructive process of the perception, which causes the significant perception of the beauty or the ugliness. Consequently, one can see that each individual perceives another “world”.
Several of the intuitions of Oresme in other disciplines like mathematics, physics, philosophy, psychology, which announces the image of oneself modern times, are closely related to the musical model, which is unusual in the current thought. The Musica functioned like a kind of “medieval computer” and in this direction, an extensive anthem with the new analytico-quantitative conscience represented of.
Psychology
The work of Taschow also made it possible to show that Oresme was a exceptional Psychologue. He studied, thanks to the use of a strongly empirical method, the complexity of the totality of the phenomena of psyché human. Oresme relied in the activity of the “interior directions” ( sensus interior ) and on the constructibility, the complexity and the subjectivity of the apprehension of the world. The use of these completely progressive devices made of Oresme a typical partisan of the Parisian psychological School of Buridan, Barthélemy of Bruges, Jean de Jandun, Henri de Hesse (Heinrich von Langenstein) etc) and its work was closely related to the scientists of the optical system (Alhazen, Roger Bacon, Vitellion, John Peckham etc), but moreover, the innovating and bold spirit of Oresme preceded very important facts of the psychology of, particularly, in the fields of the cognitive Psychologie, of the psychology of perception, of psychology of the conscience and the Psychophysical . He discovered the “psychological Inconscient” and his great importance for perception and the behavior. On this basis, he formulated, five centuries before Hermann von Helmholtz, his own theory inspired of the “unconscious conclusions of perception” and, as in the theories of, his “assumption of the two attentions” on the conscious and unconscious attention.In its “theory of modern knowledge”, Oresme proved that no thought, category, limiting, quality or quantity exist out of the conscience. He uncovered, for example, alleged “primary qualities” as the size, the position, the shape, the movement or the rest, etc of the scientists of such as Galileo, Locke etc, who had been regarded as objective in external nature, but which was to be seen like very complex cognitive constructions of psyché under the various individual conditions of the bodies and the heart human. Since reality exists only at the time “without expansion” ( instantia ), Oresme in deduced that no movement, except in the conscience, could exist. This means that the movement results from human perception and of the memory within the meaning of the composition the “front one activates” and “afterwards”. This sagacious theory becomes plausible, for example, in the field of the sound. Oresme wrote: “if there was a creature without memory, this one could never hear any sound… The sound is thus nothing more than one human construction.
In its “psycho-cybernetics” and its “information theory” modern, Oresme solved the problem of the dualism of the physical and psychic world by employing the diagram of the species in three parts “species” “matter” “quality significant” of its brilliant “theory of the species” (in modern terms: information - medium - significance). The transportable species (information), like a “form of wave” of sound, changes medium (wood, air, water, nervous system, etc) and the interior direction ( sensus interior ) built, from it, a subjective significance by means of “unconscious conclusions”.
Oresme had already developed a psychophysical first which shows many similarities with the approach of Gustav Theodor Fechner, the founder of psychophysical modern. The designs of psyché of Oresme are strongly mechanists. The physical and psychic processes are equivalent in their structure of movement ( configuratio qualitatum and motuum ). Each structure being equipped one qualitative moment (physical) and quantitative (psychic), the psychological processes (intensities) can consequently be measured like the physical processes. Oresme thus ensured the first scientific legitimation of the measurement of psyché and even, against Aristote and the scholastics, of the “immaterial heart”.
Oresme nevertheless primarily concentrated on the psychology of perception. the weather composed, was single with the Middle Ages, a special treaty on perception and its disturbance and mislaying ( Of causis mirabilium ) in many parts of its writings, where it examined each direction (seen, hearing, touch, sense of smell, taste) and the cognitive functions. With the same method as that used by the psychologists of, namely by the analysis of mislayings and the disturbances, Oresme had already identified many essential laws of perception, for example the figurative laws five centuries before Christian von Ehrenfels, the limits (maximum and minimum) of perception, etc (see Taschow, COp cit.)
Natural philosophy
The work of Taschow also reveals the very complex universe of the philosophical thought of Oresme which preceded many sights essential of the image of oneself at modern times, such as its intuition of the incommensurability of the normal proportions, of the Complexité, of the indetermination and of the infinite variability of the world, etc In the linearly progressive world of Oresme, all is single each time and, thus, it also goes from there in the same way for human knowledge.The excellent model of this new infinite world of (contrary to the repetitions without end of the ancient musica mundana ) lay in the machina musica of Oresme for which the music proved in a similar way infinitely that with a limited number of proportions and parameters, one could produce very complex structures, changeantes and never repeating itself ( configurationibus qualitatum and motuum , Of commensurabilitate vel incommensurabilitate , Quaestio countered divinatores ). The message is the same one as in the theory of the chaos of where the iteration of the simplest formulas an extremely complex world stripped of any foreseeability of behavior produces.
Oresme ended up creating, starting from the principles musico-mathematics of incommensurability , irrationality and complexity , a dynamic model structural for the constitution of the substantial species and the individuals of nature, the theory known as of perfection of the species (“perfectio specierum”) ( Of configurationibus qualitatum and motuum , super Quaestiones of generatione and corruptione , Tractatus of perfectionibus specierum ) where the individual oresmien changes, thanks to the use of an analogy of musical qualities with “qualities first and seconds” of Empédocle, in car-organized system which takes the trouble to enter its state of optimal system in order to defend against the environmental influences dérangeantes. This “automatic loop of check” influences the substantial form ( formed substantialis ), already presents to the modern direction, in the principles of the biological evolution, the Adaptation and the change of the genetic material.
It is completely obvious that the revolutionary theory of Oresme exceeded the dogma scholastic aristotelician of the invariable substantial species and preceded the principles of the “theory of the system”, of the “car-organization” and the “biological evolution” of Darwin.
Another very progressive approach of Oresme was its extensive research to the approximate values and statistical measures by means of margins of error. He formulated his “theory of probability” in the fields of psychology, physics and mathematics. He, for example, laid down two psychological rules ( Of causis mirabilium ), the first rule saying that the probability of the erroneous judgments increases with the increase in the number of unconscious judgments of perception (depth of the significance) and therefore, the probability of the errors of perception. The second rule says that the more the number of “unconscious judgments” of perception exceeds a diffuse limit and the more improbable one fundamental error of perception is, because it never breaks up the large majority of the unconscious judgments. The consequence for the theoretical knowledge of those according to one or the other of these rules is that perception is nothing more than one value of probability in the fuzzy zone of these two rules. Perception is never an objective “photography” but a complex construction without absolute obviousness.
Oresme provides an example of the mathematical prefiguration by elements of the Stochastique when it states in its proportionibus proportionum : “if we take a finished multitude of positive integers, then it is the number of perfect integers or the number of cubes lower than of other numbers. ” Moreover, more we take numbers and more the relation of not-cubic with the cubes or imperfect integers with the integers is large. Consequently, if we do not know something about a number, it is then probable ( verisimile ) that this number is not a cube. It is as in a play ( sicut is in ludis ) where somebody asks whether a hidden number is a cube. It is surer to answer “Not” because it is what appears most probable ( probabilius and verisimilius ). Oresme considered then a multitude of 100 various mathematical objects which it had made of a certain manner and it determined that from this one, one could form (100 * 99): 2 = 4950 combinations of two elements each one. Those, 4925 show a certain interesting quality E, while the remainders do not have this quality E Finally., Oresme calculated quotient 4925: 25 = 197: 1 to conclude from it that it was probable ( verisimile ) that, if somebody seeks such an unknown combination, this one will have quality E. Oresme thus calculated the number of successful and unfavourable outcomes and their quotients, but it did not have yet the quotient of the number of the number of favorable and the integer of cases of equal possibility. It did not have yet the “measurement of the modern probability”, but it had however developed a brilliance tool to judge “facility” to arrive quantitatively at an event. Oresme had recourse, in its probability calculuses, in the terms like verisimile , probabile / probabilius , improbabile / improbabilius , verisimile / verisimilius / maxim verisimile and possibile equaliter . Nobody before him, and even a long time after him, used of these terms in the context of the plays and the random probabilities. One will find the methods of Oresme later at Galileo and Pascal with.
An example of the use of the theory of probability of Oresme in physics appears in Of commensurabilitate vel incommensurabilitate , Of proportionibus proportionum , AD pauca respicientes etc when Oresme states: “if we take two unknown normal sizes like the movement, time, the distance, etc, it is more probable ( verisimillius and probabilius ) that the relationship between these two is irrational rather than rational. This theorem which, according to Oresme, generally applies to very whole nature, in the terrestrial and celestial world, has a great effect on the sights of Oresme of the Nécessité and the contingency, and therefore, on its sights of the natural law ( light naturae ) and its criticism of the Astrologie.
It is obvious that the searchs for Oresme on the music inspired its theory of probability in physics, mathematics and psychology of perception: division monocorde ( sectio canonis ) proved the direction of hearing, and the mathematical reason proved clearly that the majority of divisions of cord produce irrational intervals, i.e. dissonant.
Physics
The precepts of physics of Oresme are exposed in two French works, the Traité sphere , twice printed with Paris (first edition without date; second, 1508) and the Treated sky and world , written in 1377 at the request of Charles V, but never printed. In the majority of the essential problems of statics and dynamics, Oresme follows the recommended opinions to Paris by its predecessor, Jean Buridan of Béthune and its Albert contemporary of Saxony. Oresme countered the theory aristotelician of the weight which stated that the normal place of the heavy bodies is in the center of the world and that of the light bodies is in the concavity of the round body of the moon, while proposing what follows: “the elements tend to be laid out in such a way that their unit weight decreases per degrees of the center to the periphery. ” Oresme thought that a similar rule could exist in other worlds that ours. It is there the doctrines which were substituted thereafter for that of Aristote by Copernic and its disciples, such as Giordano Bruno whose arguments are besides so similar to those of Oresme that it would seem that he had read the Traité sky and world , but of right of Oresme to be regarded as the precursor of Copernic appears as much more firmly established when one considers what he says of the daily movement of the Earth, on which he glosé in the chapters XXIV and XXV Traité sky and world . It starts by establishing that no experiment can decide if the skies move of is in west or if the ground moves of west in is insofar as the significant experiment can never establish more than one relative movement. It then proved that the reasons suggested by physics aristotelician against the earthmoving were inadmissible. Oresme specified, in particular, the principle of the solution of the difficulty drawn from the movement of the projectiles. It then laid down rules of interpretation to solve the objections based on passages of the biblical text which are still universally followed by the current catholic exégètes. In conclusion, it supports the theory of the sky and earthmoving not thanks to the argument of simplicity, and the totality of its argument in favor of the earthmoving is at the same time more explicit and much more clearly than that which Copernic gave.It is not surprising that, dealing with questions of wave mechanics, the sound and the light, Oresme was the first to be theorized that the nature of the color and the light are identical. It was right completely to suppose that the color is only of the broken and reflected white light, i.e. “the colors belong to the white light”. This brilliant theory moreover was inspired by its musicologic investigations: in its theory of the harmonics and color of tonality, it established an analogy between these musical facts and the phenomenon of the mixture of colors on a lathe.
Lastly, it there with the brilliant discovery of Oresme of the curve of the light by atmospheric refraction: in its treaty Of views stellarum , it asks whether the stars are really where they appear to be. The use of optics enabled him to answer by the negative one. Two centuries before the scientific revolution, Oresme proposed the qualitatively correct solution with the problem of the atmospheric refraction, namely that the light travels along a curve by a medium of density uniformly variable. Oresme arrived at this solution while making use of infinitesimal to throw the doubt about all the visual significant data by concluding that almost nothing in the skies or on ground is really where it is seen. This solution which had escaped with Ptolémée and Alhazen had even escaped with Kepler with and until now, it is Hooke which was credited for its discovery and Newton for its mathematical resolution.
These fragments of the monumental work of Oresme show that it was one of the most innovating scientists at the dawn of the modern age and a pioneer of the modern world.
Works
- Treated currencies and other monetary writings of (Jean Buridan, Bartole de Sassoferrato) the , Claude Dupuy, Frederic Chartres-native, Lyon, Manufacture, 1989
- Expositio and quaestiones in Aristotelis Of animated , ED. Benoit Patar, Leuwen, ED. Peeters, 1995
- the book of policies of Aristote , Albert D. Menut, Philadelphia, American Philosophical Society, 1970
- the book of the sky of the world; text and comment , ED. Albert D. Menut, Alexandre Joseph Denomy, New York, London, 1941-1943
- Quaestiones super geometriam Euclidis , ED. H.L.L. Harrier, Leiden, E.J. Brill, 1961
- Tractatvs of origin and will natura, iure & mutationibus monetarvm , Düsseldorf: Verlag Wirtschaft und Finanzen, 1995,1485
- Traictie of the first invention of the monnoies of Nicole oresme texts French and Latin according to the manuscripts of the imperial Library and Treated monnoie of Copernic, Latin text and French translation , Paris, Guillaumin, 1864, Geneva, Slatkine Reprints, 1976
- Traité hopes for , McCarthy, Lillian, 1943,1974
- Traité monetary currencies and other writings of (Jean Buridan, Bartole de Sassoferrato): texts, Claude Dupuy and Al , Lyon, Manufacture; 1989
- Lord Frãçois Petracque of the different moon remedies fortune, thrives aduerse , Paris, Denis Ianot, 1534,1523
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