Nicole Oresme

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Nicole Oresme
Oresme.jpg
Portrait of Nicole Oresme: Miniature from Oresme's Traité de l'espère, Bibliothèque Nationale, Paris, France, fonds français 565, fol. 1r.
Bornc. 1325
Died11 July 1382
Lisieux, Normandy, France
Alma mater College of Navarre, Paris
Era Medieval philosophy
Region Western philosophy
School Nominalism [1]
Institutions University of Paris
Main interests
Natural philosophy, astronomy, theology, mathematics
Notable ideas
Rectangular co-ordinates, first proof of the divergence of the harmonic series

Nicole Oresme (French:  [nikɔl ɔʁɛm] ; [5] c. 1320–1325 – 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, astrology and 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 14th-century Europe. [6]

Philosopher person with an extensive knowledge of philosophy

A philosopher is someone who practices philosophy. The term "philosopher" comes from the Ancient Greek, φιλόσοφος (philosophos), meaning "lover of wisdom". The coining of the term has been attributed to the Greek thinker Pythagoras.

Middle Ages Period of European history from the 5th to the 15th century

In the history of Europe, the Middle Ages lasted from the 5th to the 15th century. It began with the fall of the Western Roman Empire and merged into the Renaissance and the Age of Discovery. The Middle Ages is the middle period of the three traditional divisions of Western history: classical antiquity, the medieval period, and the modern period. The medieval period is itself subdivided into the Early, High, and Late Middle Ages.

Economics Social science that analyzes the production, distribution, and consumption of goods and services

Economics is the social science that studies the production, distribution, and consumption of goods and services.

Contents

Oresme's life

Nicole Oresme was born c. 1320–1325 in the village of Allemagnes (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 subsidised 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. [7]

Fleury-sur-Orne Commune in Normandy, France

Fleury-sur-Orne is a commune in the Calvados department in the Normandy region in northwestern France.

Caen Prefecture and commune in Normandy, France

Caen, is a commune in northwestern France. It is the prefecture of the Calvados department. The city proper has 108,365 inhabitants, while its urban area has 420,000, making Caen the largest city in former Lower Normandy. It is also the third largest municipality in all of Normandy after Le Havre and Rouen and the third largest city proper in Normandy, after Rouen and Le Havre. The metropolitan area of Caen, in turn, is the second largest in Normandy after that of Rouen, the 21st largest in France.

Normandy Administrative region of France

Normandy is the northwesternmost of the 18 regions of France, roughly referring to the historical Duchy of Normandy.

Oresme studied the "arts" 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. [8]

Paris Capital of France

Paris is the capital and most populous city of France, with an area of 105 square kilometres and an official estimated population of 2,140,526 residents as of 1 January 2019. Since the 17th century, Paris has been one of Europe's major centres of finance, diplomacy, commerce, fashion, science, as well as the arts. The City of Paris is the centre and seat of government of the Île-de-France, or Paris Region, which has an estimated official 2019 population of 12,213,364, or about 18 percent of the population of France. The Paris Region had a GDP of €709 billion in 2017. According to the Economist Intelligence Unit Worldwide Cost of Living Survey in 2018, Paris was the second most expensive city in the world, after Singapore, and ahead of Zurich, Hong Kong, Oslo and Geneva. Another source ranked Paris as most expensive, on a par with Singapore and Hong Kong, in 2018. The city is a major railway, highway, and air-transport hub served by two international airports: Paris-Charles de Gaulle and Paris-Orly. Opened in 1900, the city's subway system, the Paris Métro, serves 5.23 million passengers daily, and is the second busiest metro system in Europe after Moscow Metro. Gare du Nord is the 24th busiest railway station in the world, but the first located outside Japan, with 262 million passengers in 2015.

Jean Buridan medieval philosopher

Jean Buridan was an influential 14th century French philosopher.

Albert of Saxony was a German philosopher known for his contributions to logic and physics. He was bishop of Halberstadt from 1366 until his death.

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. In 1382, he died in Lisieux. [9]

Theology Study of the nature of deities and religious belief

Theology is the critical study of the nature of the divine, and more broadly, of religious belief. It is taught as an academic discipline, typically in universities and seminaries. It occupies itself with the unique content of analyzing the supernatural, but also especially with epistemology, and asks and seeks to answer the question of revelation. Revelation pertains to the acceptance of God, gods, or deities, as not only transcendent or above the natural world, but also willing and able to interact with the natural world and, in particular, to reveal themselves to humankind. While theology has turned into a secular field, religious adherents still consider theology to be a discipline that helps them live and understand concepts such as life and love and that helps them lead lives of obedience to the deities they follow or worship.

College of Navarre was one of the colleges of the historic University of Paris

The College of Navarre was one of the colleges of the historic University of Paris, rivaling the Sorbonne and renowned for its library.

Cathedral Christian church that is the seat of a bishop

A cathedral is a church that contains the cathedra of a bishop, thus serving as the central church of a diocese, conference, or episcopate. Churches with the function of "cathedral" are usually specific to those Christian denominations with an episcopal hierarchy, such as the Catholic, Anglican, Orthodox, and some Lutheran and Methodist churches. Church buildings embodying the functions of a cathedral first appeared in Italy, Gaul, Spain and North Africa in the 4th century, but cathedrals did not become universal within the Western Catholic Church until the 12th century, by which time they had developed architectural forms, institutional structures and legal identities distinct from parish churches, monastic churches and episcopal residences.

Oresme's scientific work

Cosmology

A page from Oresme's Livre du ciel et du monde, 1377, showing the celestial spheres Oresme Spheres.jpg
A page from Oresme's Livre du ciel et du monde, 1377, showing the celestial spheres

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. [10] 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. [11] 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. [12] 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. [13] 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." [14]

Celestial spheres Term in ancient times for the heavens

The celestial spheres, or celestial orbs, were the fundamental entities of the cosmological models developed by Plato, Eudoxus, Aristotle, Ptolemy, Copernicus, and others. In these celestial models, the apparent motions of the fixed stars and planets are accounted for by treating them as embedded in rotating spheres made of an aetherial, transparent fifth element (quintessence), like jewels set in orbs. Since it was believed that the fixed stars did not change their positions relative to one another, it was argued that they must be on the surface of a single starry sphere.

Earth is one of the classical elements, in some systems numbering four along with air, fire, and water.

Water is one of the elements in ancient Greek philosophy, in the Asian Indian system Panchamahabhuta, and in the Chinese cosmological and physiological system Wu Xing. In contemporary esoteric traditions, it is commonly associated with the qualities of emotion and intuition.

Critiques of astrology

In his mathematical work, Oresme developed the notion of incommensurate fractions, fractions that could not be expressed as powers of one another, and made probabilistic, statistical arguments as to their relative frequency. [15] From this, he argued that it was very probable that the length of the day and the year were incommensurate (irrational), as indeed were the periods of the motions of the moon and the planets. From this, he noted that planetary conjunctions and oppositions would never recur in quite exactly the same way. Oresme maintained that this disproves the claims of astrologers who, thinking "they know with punctual exactness the motions, aspects, conjunctions and oppositions… [judge] rashly and erroneously about future events." [16]

Irrational number Real number that cannot be expressed as a ratio of integers

In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios of integers. When the ratio of lengths of two line segments is an irrational number, the line segments are also described as being incommensurable, meaning that they share no "measure" in common, that is, there is no length, no matter how short, that could be used to express the lengths of both of the two given segments as integer multiples of itself.

Astrological aspect angle the planets make to each other in the horoscope

In astrology, an aspect is an angle the planets make to each other in the horoscope, also to the ascendant, midheaven, descendant, lower midheaven, and other points of astrological interest. Aspects are measured by the angular distance in degrees and minutes of ecliptic longitude between two points, as viewed from Earth. According to astrological tradition, they indicate the timing of transitions and developmental changes in the lives of people and affairs relative to the Earth.

Oresme's critique of astrology in his Livre de divinacions treats it as having six parts. [17] The first, essentially astronomy, the movements of heavenly bodies, he considers good science but not precisely knowable. The second part deals with the influences of the heavenly bodies on earthly events at all scales. Oresme does not deny such influence, but states, in line with a commonly held opinion, [18] that it could either be that arrangements of heavenly bodies signify events, purely symbolically, or that they actually cause such events, deterministically. Mediaevalist Chauncey Wood remarks that this major elision "makes it very difficult to determine who believed what about astrology". [18]

The third part concerns predictiveness, covering events at three different scales: great events such as plagues, famines, floods and wars; weather, winds and storms; and medicine, with influences on the humours, the four Aristotelian fluids of the body. Oresme criticizes all of these as misdirected, though he accepts that prediction is a legitimate area of study, and argues that the effect on the weather is less well known than the effect on great events. He observes that sailors and farmers are better at predicting weather than astrologers, and specifically attacks the astrological basis of prediction, noting correctly that the zodiac has moved relative to the fixed stars (because of precession of the equinoxes) since the zodiac was first described in ancient times. [18] These first three parts are what Oresme considers the physical influences of the stars and planets (including sun and moon) on the earth, and while he offers critiques of them, he accepts that effects exist. The last three parts are what Oresme considers to concern (good or bad) fortune. They are interrogations, meaning asking the stars when to do things such as business deals; elections, meaning choosing the best time to do things such as getting married or fighting a war; and nativities, meaning the natal astrology with birth charts that forms much of modern astrological practice. Oresme classifies interrogations and elections as "totally false" arts, but his critique of nativities is more measured. He denies that any path is predetermined by the heavenly bodies, because humans have free will, but he accepts that the heavenly bodies can influence behaviour and habitual mood, via the combination of humours in each person. Overall, Oresme's skepticism is strongly shaped by his understanding of the scope of astrology. He accepts things a modern skeptic would reject, and rejects some things — such as the knowability of planetary movements, and effects on weather — that are accepted by modern science. [19]

Sense perception

In discussing the propagation of light and sound, Oresme adopted the common medieval doctrine of the multiplication of species, [20] as it had been developed by optical writers such as Alhacen, Robert Grosseteste, Roger Bacon, John Pecham, and Witelo. [21] Oresme maintained that these species were immaterial, but corporeal (i.e., three-dimensional) entities. [22]

Mathematics

Oresme's 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 characteristic 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 as difform. Uniformly varying qualities are represented by a straight line inclined to the axis of the longitude, while he described many cases of nonuniformly varying 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. [23]

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 published what was taught over two centuries prior to Galileo's making it famous. [24] [25] Diagrams of the velocity of an accelerating object against time in On the Latitude of Forms by Jacobus de Sancto Martino (sometimes attributed to Oresme) [26] have been cited to credit Oresme with the discovery of "proto bar charts". [27] [28]

Significantly, Oresme developed the first proof of the divergence of the harmonic series. [29] His proof, requiring less advanced mathematics than current "standard" tests for divergence (for example, the integral test), begins by noting that for any n that is a power of 2, there are n/2 - 1 terms in the series between 1/(n/2) and 1/n. Each of these terms is at least 1/n, and since there are n/2 of them they sum to at least 1/2. For instance, there is one term 1/2, then two terms 1/3+1/4 that together sum to at least 1/2, then four terms 1/5+1/6+1/7+1/8 that also sum to at least 1/2, and so on. Thus the series must be greater than the series 1 + 1/2 + 1/2 + 1/2 + ..., which does not have a finite limit. This proves that the harmonic series must be divergent. This argument shows that the sum of the first n terms grows at least as fast as .

Oresme was the first mathematician to prove this fact, and (after his proof was lost) it was not proven again until the 17th century by Pietro Mengoli. [30]

He also worked on fractional powers, and the notion of probability over infinite sequences, ideas which would not be further developed for the next three and five centuries, respectively. [15]

On local motion

Oresme, like many of his contemporaries such as John Buridan and Albert of Saxony, shaped and critiqued Aristotle’s and Averroes’s theories of motion to their own liking. [31] Taking inspiration from the theories of forma fluens and fluxus formae, Oresme would suggest his own descriptions for change and motion in his commentary of Physics. Forma fluens is described by William of Ockham as "Every thing that is moved is moved by a mover," and fluxus formae as "Every motion is produced by a mover." [32] Buridan and Albert of Saxony each subscribed to the classic interpretation of flux being an innate part of an object, but Oresme differs from his contemporaries in this aspect. [31] Oresme agrees with fluxus formae in that motion is attributed to an object, but that an object is “set into” motion, rather than “given” motion, denying a distinction between a motionless object and an object in motion. To Oresme, an object moves, but it is not a moving object. [31] Once an object begins movement through the three dimensions it has a new “modus rei” or “way of being,” which should only be described through the perspective of the moving object, rather than a distinct point. [31] This line of thought coincides with Oresme’s challenge to the structure of the universe. Oresme’s description of motion was not popular, although it was thorough. [33] A Richard Brinkley is thought to be an inspiration for the modus-rei description, but this is uncertain. [33]

Political thought

Oresme provided the first modern vernacular translations of Aristotle's moral works that are still extant today. Between 1371 and 1377 he translated Aristotle's Ethics , Politics and Economics (nowadays considered to be pseudo-Aristotelian) into Middle French. He also extensively commented on these texts, thereby expressing some of his political views. Like his predecessors Albert the Great, Thomas Aquinas and Peter of Auvergne (and quite unlike Aristotle), Oresme favours monarchy as the best form of government. [34] His criterium for good government is the common good. A king (by definition good) takes care of the common good, whereas a tyrant works for his own profit. A monarch can ensure the stability and durability of his reign by letting the people participate in government. This has rather confusingly and anachronistically been called popular sovereignty. [35] Like Albert the Great, Thomas Aquinas, Peter of Auvergne and especially Marsilius of Padua, whom he occasionally quotes, Oresme conceives of this popular participation as rather restrictive: only the multitude of reasonable, wise and virtuous men should be allowed political participation by electing and correcting the prince, changing the law and passing judgement. [36] Oresme, however, categorically denies the right of rebellion since it endangers the common good. [37] Unlike earlier commentators, however, Oresme prescribes the law as superior to the king's will. [38] It must only be changed in cases of extreme necessity. [39] Oresme favours moderate kingship, [40] thereby negating contemporary absolutist thought, usually promoted by adherents of Roman law. [41] Furthermore, Oresme doesn't comply to contemporary conceptions of the French king as sacred, as promoted by Évrart de Trémaugon in his Songe du vergier or Jean Golein in his Traité du sacre. [42] Although he heavily criticises the Church as corrupt, tyrannical and oligarchical, he never fundamentally questions its necessity for the spiritual well-being of the faithful. [43]

It has traditionally been thought that Oresme's Aristotelian translations had a major impact on King Charles V's politics: Charles' laws concerning the line of succession and the possibility of a regency for an underage king have been accredited to Oresme, as has the election of several high-ranking officials by the king's council in the early 1370s. [44] Oresme may have conveyed Marsilian and conciliarist thought to Jean Gerson and Christine de Pizan. [45]

Economics

With his Treatise on the origin, nature, law, and alterations of money (De origine, natura, jure et mutationibus monetarum), one of the earliest manuscripts devoted to an economic matter, Oresme brings an interesting insight on the medieval conception of money. Oresme’s viewpoints of theoretical architecture are outlined in Part 3 and 4 of his work from De moneta, which he completed between 1356 and 1360. His belief is that humans have a natural right to own property; this property belongs to the individual and community. [46] In Part 4, Oresme provides a solution to a political problem as to how a monarch can be held accountable to put the common good before any private affairs. Though the monarchy rightfully has claims on all money given an emergency, Oresme states that any ruler that goes through this is a “Tyrant dominating slaves”. Oresme was one of the first medieval theorists that did not accept the right of the monarch to have claims on all money as well as “his subjects’ right to own private property.”

Psychology

Oresme was known to be a well rounded psychologist. He practiced the technique of “inner senses” and studied the perception of the world. Oresme contributed to 19th and 20th century psychology in the fields of cognitive psychology, perception psychology, psychology of consciousness, and psychophysics. Oresme discovered the psychology of unconscious and came up with the theory of unconscious conclusion of perception. He developed many ideas beyond quality, quantity, categories and terms which were labeled “theory of cognition”. [47]

English translations

See also

Notes

  1. Hans Blumenberg, The Genesis of the Copernican World, MIT Press, 1987, p. 158.
  2. Marshall Clagett, The Science of Mechanics in the Middle Ages, Madison. 1959, p. 522.
  3. Marshall Clagett (ed.), Critical Problems in the History of Science, University of Wisconsin Press, 1969, p. 95: "[W]hen one asks more specifically what, for example, Galileo or Descartes actually knew and what use they made of the dynamics of impetus or of fourteenth-century Oxford kinematics or of Oresme's graphical methods, the evidence becomes difficult and unsatisfactory."
  4. Dan Burton (ed.), De Visione Stellarum, BRILL, 2007, p. 19 n. 8.
  5. Léon Warnant (1987). Dictionnaire de la prononciation française dans sa norme actuelle (in French) (3rd ed.). Gembloux: J. Duculot, S. A. ISBN   978-2-8011-0581-8.
  6. Wallace, William A. (1981). Prelude to Galileo: essays on medieval and sixteenth-century sources of Galileo's thought. Springer Science & Business. ISBN   978-9027712158.
  7. Edward Grant, ed., De proportionibus proportionum and Ad pauca respicientes, (Madison: University of Wisconsin Pr., 1966), p. 4.
  8. William J. Courtenay, The Early Career of Nicole Oresme, Isis, Vol. 91, No.3 (Sept., 2000), pp 542–548.
  9. Edward Grant, ed., De proportionibus proportionum and Ad pauca respicientes, (Madison: University of Wisconsin Pr., 1966), pp. 4–10.
  10. Edward Grant, The Foundations of Modern Science in the Middle Ages, (Cambridge: Cambridge University Press, 1996), pp. 114–16.
  11. Oresme, Le Livre du ciel et du monde, pp. 521–3
  12. Oresme, Le Livre du ciel et du monde, p. 531
  13. Oresme, Le Livre du ciel et du monde, p. 535
  14. Oresme, Le Livre du ciel et du monde, p. 537
  15. 1 2 James Franklin, The Science of Conjecture, Evidence and Probability before Pascal (Johns Hopkins University Press, 2001), ISBN   0-8018-7109-3 (see chapter 6, pp.140 - 145)
  16. Oresme, Ad pauca respicientes, p. 383.
  17. Coopland, G. W. (1952). Nicole Oresme and the Astrologers: A Study of his Livre de Divinacions. Harvard University Press; Liverpool University Press. pp. 53–57.
  18. 1 2 3 Wood, 1970. p. 9
  19. Wood, 1970. pp. 8–11
  20. Bert Hansen, Nicole Oresme and the Marvels of Nature (Toronto: Pontifical Institute of Mediaeval Studies, 1985), pp. 89-90.
  21. David C. Lindberg, Theories of Vision from al-Kindi to Kepler, (Chicago: University of Chicago Pr., 1976), pp. 78–80, 98, 113–16.
  22. Peter Marshall, "Nicole Oresme on the Nature, Reflection, and Speed of Light," Isis, 72 (1981): 357–374, pp. 360–2.
  23. Clagett, Marshall (1968), 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: Univ. of Wisconsin Press, pp. 177–128, ISBN   0-299-04880-2
  24. Catholic Encyclopedia: "Nicole Oresme"
  25. Clagett, Marshall (1968), 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: Univ. of Wisconsin Press, ISBN   0-299-04880-2
  26. Clagett, Marshall (1968), 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: Univ. of Wisconsin Press, pp. 85–99, ISBN   0-299-04880-2
  27. Beniger, James R.; Robyn, Dorothy L. (1978), "Quantitative Graphics in Statistics: A Brief History", The American Statistician, Taylor & Francis, Ltd., 32 (1): 1–11, doi:10.1080/00031305.1978.10479235, JSTOR   2683467
  28. Der, Geoff; Everitt, Brian S. (2014). A Handbook of Statistical Graphics Using SAS ODS. Chapman and Hall - CRC. ISBN   1-584-88784-2.
  29. Oresme, Nicole (c. 1360). Quaestiones super Geometriam Euclidis[Questions concerning Euclid's Geometry].
  30. Pickover, Clifford A. (2009), The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics, Sterling Publishing Company, Inc., p. 104, ISBN   9781402757969, Nicole Oresme ... was the first to prove the divergence of the harmonic series (c. 1350). His results were lost for several centuries, and the result was proved again by Italian mathematician Pietro Mengoli in 1647 and by Swiss mathematician Johann Bernoulli in 1687.
  31. 1 2 3 4 Thijssen, Johannes (2009). "The Debate over the Nature of Motion: John Buridan, Nicole Oresme and Albert of Saxony. With an Edition of John Buridan's 'Quaestiones Super Libros Physicorum, Secundum Ultimam Lecturam', Book III, Q. 7". Early Science and Medicine. 14: 186–210.
  32. "NASC 400 History of Science to 1700 / Mechanics and Motion in the Middle Ages". nasc400.pbworks.com. Retrieved 2018-05-04.
  33. 1 2 Caroti, Stefano (1993). "Oresme on Motion (Questiones Super Physicam, III, 2-7)". Vivarium: Journal for Mediaeval Philosophy and the Intellectual Life of the Middle Ages. 31: 8–36 via EBSCOhost.
  34. Mario Grignaschi: Nicolas Oresme et son commentaire à la «Politique» d'Aristote, in: Album Helen Maud Cam, Louvain 1960 (Studies Presented to the International Commission for the History of Representative and Parliamentary Institutions, 23), 95–151, esp. 99–106.
  35. Shulamith Shahar: Nicolas Oresme, un penseur politique indépendant de l'entourage du roi Charles V, in: L'information historique 32 (1970), 203–209.
  36. Mario Grignaschi: Nicolas Oresme et son commentaire à la «Politique» d'Aristote, in: Album Helen Maud Cam, Louvain 1960 (Studies Presented to the International Commission for the History of Representative and Parliamentary Institutions, 23), 95–151, esp. 111–112; Jacques Krynen: Aristotélisme et réforme de l'Etat, en France, au XIVe siècle, in: Jürgen Miethke (ed.): Das Publikum politischer Theorie im 14. Jahrhundert, München 1992 (Schriften des Historischen Kollegs, 21), 225–236, esp. 231–232; James M. Blythe: Ideal Government and the Mixed Constitution in the Middle Ages, Princeton, New Jersey 1992, 221–225.
  37. Susan M. Babbitt: Oresme's Livre de Politiques and the France of Charles V., in: Transactions of the American Philosophical Society 75,1 (1985), 1–158, esp. 83–84; Ulrich Meier: Molte revoluzioni, molte novità. Gesellschaftlicher Wandel im Spiegel der politischen Philosophie und im Urteil von städtischen Chronisten des späten Mittelalters, in: Jürgen Miethke, Klaus Schreiner (eds.): Sozialer Wandel im Mittelalter. Wahrnehmungsformen, Erklärungsmuster, Regelungsmechanismen, Sigmaringen 1994, 119–176, esp. 127–129.
  38. James M. Blythe: Ideal Government and the Mixed Constitution in the Middle Ages, Princeton, New Jersey 1992, 211–212.
  39. Jacques Krynen: L'empire du roi. Ideés et croyances politiques en France. XIIIe–XVe siècle, Paris 1993, 266–272.
  40. James M. Blythe: Ideal Government and the Mixed Constitution in the Middle Ages, Princeton, New Jersey 1992, 203–242.
  41. Jacques Krynen: L'empire du roi. Ideés et croyances politiques en France. XIIIe–XVe siècle, Paris 1993, 110–124, 343–456.
  42. Shulamith Shahar: Nicolas Oresme, un penseur politique indépendant de l'entourage du roi Charles V, in: L'information historique 32 (1970), 203–209; Vanina Kopp: Der König und die Bücher. Sammlung, Nutzung und Funktion der königlichen Bibliothek am spätmittelalterlichen Hof in Frankreich, Ostfildern 2016 (Beihefte der Fancia, 80).
  43. Susan M. Babbitt: Oresme's Livre de Politiques and the France of Charles V., in: Transactions of the American Philosophical Society 75,1 (1985), 1–158, esp. 98–146.
  44. Albert Douglas Menut: Introduction, in: Transactions of the American Philosophical Society 60,6 (1970), 5–43, esp. 9.
  45. Albert Douglas Menut: Introduction, in: Transactions of the American Philosophical Society 60,6 (1970), 30; Cary J. Nederman: A Heretic Hiding in Plain Sight. The Secret History of Marsiglio of Padua's Defensor Pacis in the Thought of Nicole Oresme, in: John Christian Laursen u.a. (eds.): Heresy in Transition. Transforming Ideas of Heresy in Medieval and Early Modern Europe, London 2005 (Catholic Christendom, 1300–1700), 71–88.
  46. Woodhouse, Adam (2017–18). ""Who Owns the Money?" Currency, Property, and Popular Sovereignty in Nicole Oresme's De moneta". Speculum. 92 (1): 85–116. doi:10.1086/689839. ISSN   0038-7134.CS1 maint: Date format (link)
  47. "Nicole Oresme".

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Timeline of classical mechanics:

Thomas Bradwardine 14th-century Archbishop of Canterbury and theologian

Thomas Bradwardine was an English cleric, scholar, mathematician, physicist, courtier and, very briefly, Archbishop of Canterbury. As a celebrated scholastic philosopher and doctor of theology, he is often called Doctor Profundus.

Marsilius of Inghen Dutch philosopher

Marsilius of Inghen was a medieval Dutch Scholastic philosopher who studied with Albert of Saxony and Nicole Oresme under Jean Buridan. He was Magister at the University of Paris as well as at the University of Heidelberg from 1386 to 1396.

Bar chart chart

A bar chart or bar graph is a chart or graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally. A vertical bar chart is sometimes called a line graph.

Ernest Addison Moody American philosopher

Ernest Addison Moody (1903–1975) was a noted philosopher, medievalist, and logician as well as a musician and scientist. He served as professor of philosophy at University of California, Los Angeles (UCLA), where he also served as department chair, and Columbia University. He has an annual memorial conference in his name on the subject of medieval philosophy. He was president of the American Philosophical Association from 1963-1964.

<i>On the Heavens</i> work by Aristotle

On the Heavens is Aristotle's chief cosmological treatise: written in 350 BC it contains his astronomical theory and his ideas on the concrete workings of the terrestrial world. It should not be confused with the spurious work On the Universe.

Oxford Calculators group of humans

The Oxford Calculators were a group of 14th-century thinkers, almost all associated with Merton College, Oxford; for this reason they were dubbed "The Merton School". These men took a strikingly logico-mathematical approach to philosophical problems. The key "calculators", writing in the second quarter of the 14th century, were Thomas Bradwardine, William Heytesbury, Richard Swineshead and John Dumbleton. These men built on the slightly earlier work of Walter Burley and Gerard of Brussels.

Christian views on astrology

Astrology had small amounts of support in early Christianity, but support waned during the Middle Ages. Support for it grew again in the West during the Renaissance.

Theory of impetus

The theory of impetus was an auxiliary or secondary theory of Aristotelian dynamics, put forth initially to explain projectile motion against gravity. It was introduced by John Philoponus in the 6th century, and elaborated by Nur ad-Din al-Bitruji at the end of the 12th century. The theory was modified by Avicenna in the 11th century and Hibat Allah Abu'l-Barakat al-Baghdaadi in the 12th century, before it was later established in Western scientific thought by Jean Buridan in the 14th century. It is the intellectual precursor to the concepts of inertia, momentum and acceleration in classical mechanics.

Marshall Clagett was an American historian of science who specialized in medieval science. John Murdoch describes him as "a distinguished medievalist" who was "the last member of a triumvirate [with Henry Guerlac and I. Bernard Cohen, who] … established the history of science as a recognized discipline within American universities" while Edward Grant ranks him "among the greatest historians and scholars of the twentieth century."

Precursorism, called in its more extreme forms precursoritis or precursitis, is a characteristic of that kind of historical writing in which the author seeks antecedents of present-day institutions or ideas in earlier historical periods. This kind of anachronism is considered to be a form of Whig history and is a special problem among historians of science. The French historian of medieval science, Pierre Duhem, exemplifies several of the characteristics of the quest for precursors of modern scientific ideas. Duhem was trained as a physicist, rather than as a historian; he was French and many of the precursors he identified were French or studied at the University of Paris; he was a devout Catholic and many of the precursors of the theologically troubling Italian, Galileo, were members of religious orders. Most striking among them was the French bishop and scholastic philosopher, Nicole Oresme.

Gerard of Brussels was an early thirteenth-century geometer and philosopher known primarily for his Latin book Liber de motu, which was a pioneering study in kinematics, probably written between 1187 and 1260. It has been described as "the first Latin treatise that was to take the fundamental approach to kinematics that was to characterize modern kinematics." He brought the works of Euclid and Archimedes back into popularity and was a direct influence on the Oxford Calculators in the next century. Gerard is cited by Thomas Bradwardine in his Tractatus de proportionibus velocitatum (1328). His chief contribution was in moving away from Greek mathematics and closer to the notion of "a ratio of two unlike quantities such as distance and time", which is how modern physics defines velocity.

Dynamics of the celestial spheres

Ancient, medieval and Renaissance astronomers and philosophers developed many different theories about the dynamics of the celestial spheres. They explained the motions of the various nested spheres in terms of the materials of which they were made, external movers such as celestial intelligences, and internal movers such as motive souls or impressed forces. Most of these models were qualitative, although a few of them incorporated quantitative analyses that related speed, motive force and resistance.

Mean speed theorem

The mean speed theorem, also known as the Merton rule of uniform acceleration, was first discovered in the 14th century by the Oxford Calculators of Merton College, and was proved by Nicole Oresme. It states that a uniformly accelerated body travels the same distance as a body with uniform speed whose speed is half the final velocity of the accelerated body.

European science in the Middle Ages

European science in the Middle Ages comprised the study of nature, mathematics and natural philosophy in medieval Europe. Following the fall of the Western Roman Empire and the decline in knowledge of Greek, Christian Western Europe was cut off from an important source of ancient learning. Although a range of Christian clerics and scholars from Isidore and Bede to Buridan and Oresme maintained the spirit of rational inquiry, Western Europe would see a period of scientific decline during the Early Middle Ages. However, by the time of the High Middle Ages, the region had rallied and was on its way to once more taking the lead in scientific discovery. Scholarship and scientific discoveries of the Late Middle Ages laid the groundwork for the Scientific Revolution of the Early Modern Period.

<i>Livre de Politiques</i>

The Livre de Politiques is an extensively annotated Middle-French translation of Aristotle's Politics by 14th-century scientist and philosopher Nicole Oresme. It is the first extant translation of the Politics into a modern vernacular language.

References