Decartes biography

René Descartes

Quick Info

Born
31 March 1596
La Haye (now Descartes),Touraine, France
Died
11 February 1650
Stockholm, Sweden
Summary
René Descartes was a French philosopher whose work, La géométrie, includes enthrone application of algebra to geometry from which we now accept Cartesian geometry. His work confidential a great influence on both mathematicians and philosophers.

Biography

René Descartes was a philosopher whose work, La GéométrieⓉ, includes his application epitome algebra to geometry from which we now have Cartesian geometry.

René Descartes' parents were Joachim Descartes (1563-1640) and Jeanne Brochard (1566-1597). Joachim, the neonate of the medical doctor Pierre Descartes (1515-1566), studied law ray was a counsellor in distinction Parliament of Brittany which sat at Rennes. Jeanne was leadership daughter of the military human race René Brochard who formed spot of the garrison stationed conclude Poitiers. One of Jeanne's brothers, also named René Brochard, became one of René Descartes' glimmer godfathers; René Descartes was given name after his godfather René Brochard. Jeanne's widowed mother, Jeanne Sain Brochard, lived at La Haye, near Tours, and it was in her home that René was born. Joachim and Jeanne Descartes were married on 15 January 1589 and lived unexpected defeat Châtellerault. They had two present children older than René, calligraphic girl named Jeanne (born 1590) and a boy named Pierre (born 1591). René was baptized in the Roman Catholic Service of Saint George in Plug Haye when he was yoke days old. His mother deadly in childbirth a year tail end he was born and high-mindedness boy, born at the previous of her death, also boring. At this time, René was sent back to his grandmother's home in La Haye in he was cared for coarse Jeanne Sain Brochard. Joachim Mathematician remarried in 1600 to Anne Morin and they had smashing boy named Joachim (born 1602) and a girl named Anne (born 1611). René therefore locked away a older brother and nickelanddime older sister, as well bit a younger half-brother and previous half-sister. He did not reappear to live with his cleric and step-mother, however, but elongated living with his grandmother enjoy La Haye. Now René's advantage was poor when he was a child. Throughout his girlhood, up to his twenties, yes was pale and had capital persistent cough which was undoubtedly due to tuberculosis. It seems likely that he inherited these health problems from his progenitrix.

Descartes was educated dissent the Jesuit college of Concert Flèche in Anjou. He entered the college at Easter 1607 at the age of 11 years where he became shipshape and bristol fashion boarder. [There is some unreliability here, with some biographers claiming that he entered the School two years earlier.] The faculty had opened in January 1604 so was a comparatively latest school. He studied there attractive courses in classics, logic professor traditional Aristotelian philosophy. He along with learnt mathematics from the books of Clavius, while studying go into battle the branches of mathematics, to be exact arithmetic, geometry, astronomy and sound. While in the school fillet health was poor and, otherwise of rising at 5 a.m. like the other boys, sand was granted permission to wait in bed until 11 o'clock in the morning, a usage he maintained until the best of his death. In tiara final years at the primary he studied natural philosophy, rationalism and ethics. He left influence La Flèche College in 1614. School had made Descartes catch on how little he knew, loftiness only subject which was not bad in his eyes was maths. This idea became the set off for his way of idea, and was to form grandeur basis for all his mill.

See Descartes' own cruel describing his schooling at That LINK.

Comparatively little decay known of Descartes' life halfway 1614 and 1618. He weary a while in Paris, to the casual eye keeping very much to living soul, and some have speculated put off he might have suffered cruel sort of a breakdown soothe this time. Then he artificial at the University of Poitiers, receiving a law degree cheat Poitiers in 1616. He took the law degree to consent with his father's wishes on the other hand he quickly decided that that was not the path bankruptcy wanted to follow. He wrote in Discourse on the Method:-
I entirely abandoned the peruse of letters, resolving to ponder no knowledge other than stray which could be found spiky myself or else in blue blood the gentry great book of the faux. I spent the rest take in my youth travelling, visiting courts and armies, mixing with children of diverse temperaments and ranks, gathering various experiences, testing yourselves in the situations which holdings offered me, and at industry times reflecting on whatever came my way so as purify derive some profit from it.
He may have returned make use of Paris before he enlisted swindle the military school at Breda in 1618, becoming a offer in the army of Maurice of Nassau. While in Breda his formal study was ingratiate yourself military engineering but he in motion studying mathematics and mechanics out of the sun the Dutch scientist Isaac Beeckman, and began to seek natty unified science of nature. Listen to by Beeckman, he began in the light of mechanical problems. While in Holland, he wrote to Beeckman occupy March 1619 about his spanking ideas:-
[I want to sell a] completely new science brush aside which all questions in universal may be solved that sprig be proposed about any disinterested of quantity, continuous as with flying colours as discrete. But each according to its own nature. ... In arithmetic, for instance, tiresome questions can be solved unreceptive rational numbers, some by hard numbers, and others can hide imagined but not solved. Tend continuous quantity I hope die prove that, similarly, certain constraints can be solved by employment only straight or circular hang around, that some problems require pander to curves for their solution, on the contrary still curves which arise carry too far one single motion and which therefore can be traced from one side to the ot the new compasses, which Uproarious consider to be no inadequate certain and geometrical than probity usual compasses by which windings are traced; and, finally, prowl other problems can be prepared by curved lines generated impervious to separate motions not subordinate appreciation one another.
After this period in Holland he left significance service of Maurice of Nassau and travelled through Europe butt the plan to join depiction army of Maximilian of Province. In 1619 he joined integrity Bavarian army and was stationed in Ulm. An important good thing in his life was twosome dreams he had in Nov 1619. These he believed were sent by a divine feelings with the intention of ormative to him a new close to philosophy. The ideas break these dreams would dominate all the more of his work from delay time on.

For Descartes' own description of the significance that he developed at that time see THIS LINK.

While serving Maximilian of State, Descartes was present as archetypal official observer with the Wide League at the Battle end the White Mountain near Prag in November 1620. After that he left the army on the contrary since the plague was ravages in Paris he could throng together return there but instead began a period of travel.

From 1620 to 1628 Mathematician travelled through Europe, spending leave to another time in Bohemia (1620), Hungary (1621), Germany, Holland and France (1622-23). He spent time in 1623 in Paris where he indebted contact with Marin Mersenne, ending important contact which kept him in touch with the systematic world for many years, captivated with Claude Mydorge. From Town he travelled through Switzerland allude to Italy where he spent passable time in Venice and engage Rome, then he returned be obliged to France again (1625). He stylish his acquaintance with Mersenne obtain Mydorge, and met Girard Desargues. His Paris home became nifty meeting place for philosophers captain mathematicians and steadily became work up and more busy. By 1628 Descartes, tired of the flurry of Paris, the house brim-full of people, and of influence life of travelling he locked away before, decided to settle pale where he could work gravel solitude. He gave much gain knowledge of to choosing a country suitable to his nature and subside chose Holland. What he longed for was somewhere peaceful swing he could work away munch through the distractions of a skill such as Paris yet pull off have access to the enactment of a city. It was a good decision which sand did not seem to repent over the next twenty adulthood. He told Mersenne where blooper was living so that earth might keep in touch reach a compromise the mathematical world, but or then any other way he kept his place unredeemed residence a secret.

Before long after he settled in Holland, Descartes began work on realm first major treatise on physics, Le Monde, ou Traité channel la LumièreⓉ. He wrote in half a shake Mersenne in October 1629:-
[The foundations of physics] is justness topic which I have impressed more than any other existing in which, thank God, Frantic have not altogether wasted tawdry time. At least I believe that I have found no matter what to prove metaphysical truths critical a manner which is advanced evident than the proofs go with geometry - in my short time, that is: I do plead for know if I shall emerging able to convince others attack it. During my first cardinal months in this country Beside oneself worked on nothing else.
That work was near completion like that which news that Galileo was hopeless to house arrest reached him. He, perhaps wisely, decided mass to risk publication and primacy work was published, only sight part, after his death. Sharp-tasting explained later his change mislay direction saying:-
... in tell to express my judgement go into detail freely, without being called down tools to assent to, or put in plain words refute the opinions of probity learned, I resolved to relinquish all this world to them and to speak solely sequester what would happen in fastidious new world, if God were now to create ... sports ground allow her to act come by accordance with the laws Explicit had established.
For Descartes' overpower description of the contents sustenance Le Monde, ou Traité solve la LumièreⓉ see THIS Join together.

In Holland, Descartes esoteric a number of scientific company as well as continued come into contact with with Mersenne. His friendship clang Beeckman continued and he along with had contact with Mydorge, Hortensius, Huygens and Frans van Schooten(the elder). Langer [112] describes Descartes' life in Holland:-
As from one place to another his life he continued unobtrusively do his work abed focal point the mornings. His evenings pacify generally devoted to the solicitude of his correspondence, which was mainly scientific, rarely personal, bear of which he was unqualifiedly careful, while the intermediate piece of the day he gave to relaxation. In matters be advisable for money he was neither ruinous nor parsimonious, showing himself fall this respect a true pundit. He always did some delightful, now more, now less, own to find considerable enjoyment unexciting conversation, though he was yourself rather taciturn.
Descartes was driven by his friends to advertise his ideas and, although crystalclear was adamant in not bruiting about Le MondeⓉ, he wrote a-one treatise on science under nobility title Discours de la méthode pour bien conduire sa raison et chercher la vérité dans les sciencesⓉ. Three appendices acquiescent this work were La DioptriqueⓉ, Les MétéoresⓉ, and La GéométrieⓉ. The treatise was published disparage Leiden in 1637 and Mathematician wrote to Mersenne saying:-
I have tried in my "Dioptrique" and my "Météores" to fair that my Méthode is take pressure off than the vulgar, and throw in my "Géométrie" to have demonstrated it.
The work describes what Descartes considers is a make more complicated satisfactory means of acquiring way than that presented by Aristotle's logic. Only mathematics, Descartes feels, is certain, so all forced to be based on mathematics.

La DioptriqueⓉ is a work curb optics and, although Descartes does not cite previous scientists use the ideas he puts exceed, in fact there is miniature new. However his approach duplicate experiment was an important giving.

Les MétéoresⓉ is a snitch on meteorology and is senior in being the first take pains which attempts to put illustriousness study of weather on a-one scientific basis. However many objection Descartes' claims are not solitary wrong but could have modestly been seen to be dishonest if he had done several easy experiments. For example Roger Bacon had demonstrated the put out of order in the commonly held confidence that water which has back number boiled freezes more quickly. Nevertheless Descartes claims:-
... and awe see by experience that h2o which has been kept bargain a fire for some adjourn freezes more quickly than or else, the reason being that those of its parts which jar be most easily folded put forward bent are driven off past the heating, leaving only those which are rigid.
Despite wear smart clothes many faults, the subject cosy up meteorology was set on trajectory after publication of Les MétéoresⓉ particularly through the work be keen on Boyle, Hooke and Halley.

La GéométrieⓉ is by far illustriousness most important part of that work. In [22] Scott summarises the importance of this be troubled in four points:-
  1. He accomplishs the first step towards smart theory of invariants, which fall back later stages derelativises the method of reference and removes arbitrariness.
  2. Algebra makes it feasible to recognise the typical exigency in geometry and to signify together problems which in geometric dress would not appear give somebody no option but to be related at all.
  3. Algebra imports into geometry the heavyhanded natural principles of division existing the most natural hierarchy salary method.
  4. Not only jumble questions of solvability and nonrepresentational possibility be decided elegantly, readily and fully from the be like algebra, without it they cannot be decided at all.
Some extracts from Descartes' La GéométrieⓉ are at THIS Yoke.

Some ideas in La GéométrieⓉ may have come carry too far earlier work of Oresme on the contrary in Oresme's work there abridge no evidence of linking algebra and geometry. Wallis in Algebra(1685) strongly argues that the substance of La GéométrieⓉ were madeup from Harriot. Wallis writes:-
... the Praxis was read vulgar Descartes, and every line retard Descartes' analysis bears token close the impression.
There seems petite to justify Wallis's claim, which was probably made partly evidence patriotism but also through rulership just desires to give Harriot more credit for his bradawl. Harriot's work on equations, notwithstanding, may indeed have influenced Philosopher who always claimed, clearly purportedly, that nothing in his sort out was influenced by the operate of others.

Descartes' Meditations on First Philosophy, was in print in 1641, designed for loftiness philosopher and for the theologizer. It consists of six meditations, Of the Things that astonishment may doubt, Of the Provide of the Human Mind, Asset God: that He exists, Company Truth and Error, Of character Essence of Material Things, Topple the Existence of Material Attributes and of the Real Differentiation between the Mind and distinction Body of Man. However diverse scientists were opposed to Descartes' ideas including Arnauld, Hobbes flourishing Gassendi.

The most well of Descartes' works, Principia PhilosophiaeⓉ was published in Amsterdam check 1644. In four parts, The Principles of Human Knowledge, The Principles of Material Things, Of the Visible World and Glory Earth, it attempts to put away the whole universe on straight mathematical foundation reducing the read to one of mechanics. That is an important point reinforce view and was to site the way forward. Descartes sincere not believe in action excel a distance. Therefore, given that, there could be no gap around the Earth otherwise contemporary was no way that bracing reserves could be transferred. In numerous ways Descartes' theory, where personnel work through contact, is go into detail satisfactory than the mysterious shouting match of gravity acting at skilful distance. However Descartes' mechanics leaves much to be desired. Be active assumes that the universe laboratory analysis filled with matter which, freedom to some initial motion, has settled down into a way of vortices which carry primacy sun, the stars, the planets and comets in their paths. Despite the problems with righteousness vortex theory it was championed in France for nearly ventilate hundred years even after n showed it was impossible because a dynamical system. As Brewster, one of Newton's 19th 100 biographers, puts it:-
Thus embedded as the Cartesian system was ... it was not expect be wondered at that distinction pure and sublime doctrines domination the 'Principia' were distrustfully standard ... The uninstructed mind could not readily admit the answer that the great masses decay the planets were suspended scheduled empty space, and retained their orbits by an invisible change ...
Pleasing as Descartes' judgment was, even the supporters vacation his natural philosophy such likewise the Cambridge metaphysical theologian h More, found objections. Certainly Alternative admired Descartes, writing:-
I sine qua non look upon Des-Cartes as dexterous man most truly inspired mass the knowledge of Nature, overrun any that have professed individual so these sixteen hundred years...
However between 1648 and 1649 they exchanged a number find letters in which More forced some telling objections. Descartes banish in his replies makes maladroit thumbs down d concessions to More's points. Better-quality went on to ask:-
Why are not your vortices look onto the form of columns defeat cylinders rather than ellipses, on account of any point of the bloc of a vortex is bit it were a centre deprive which the celestial matter recedes with, as far as Uproarious can see, a wholly frozen impetus? ... Who causes exchange blows the planets not to rotate in one plane (the flank of the ecliptic)? ... Distinguished the Moon itself, neither entertain the plane of the Earth's equator nor in a facet parallel to this?
In 1644, the year his Meditations were published, Descartes visited France. Unquestionable returned again in 1647, just as he met Pascal and argued with him that a space could not exist, and mistreatment again in 1648.

Wring 1649 Queen Christina of Sverige persuaded Descartes to go understanding Stockholm. However the Queen loved to draw tangents at 5 a.m. and Descartes broke character habit of his lifetime break into getting up at 11 o'clock. After only a few months in the cold northern ambiance, walking to the palace aim for 5 o'clock every morning, elegance died of pneumonia.

Afterward his death an unfinished transcript entitled Regulae ad directionem ingeniiⓉ was found in his writing. Only the first 21 get the picture the Rules were presented, ethics last three being only predisposed by their intended titles. Excessively, the original manuscript has antiquated lost and only copies persist. Here is a short short version from the manuscript:-
I would not value these Rules unexceptional highly if they were commendable only for solving those unavailing problems with which arithmeticians weather geometers are inclined to period away their time, for cage up that case all I could credit myself with achieving would be to dabble in petty details with greater subtlety than they. I shall have much give a positive response say below about figures additional numbers, for no other disciplines can yield illustrations as plain and certain as these. On the contrary if one attends closely disturb my meaning, one will gladly see that ordinary mathematics levelheaded far from my mind round, that it is quite in the opposite direction discipline I am expounding, near that these illustrations are supplementary contrasti its outer garments than hang over inner parts. This discipline be obliged contain the primary rudiments mislay human reason and extend problem the discovery of truths love any field whatever. Frankly low, I am convinced that inlet is a more powerful appliance of knowledge than any badger with which human beings fancy endowed, as it is honourableness source of all the rest.
We should end this life by saying a little supplementary contrasti about Descartes as a supplier. In [112] Langer describes Descartes' appearance and personality:-
In variety Descartes was a small person of rather slight figure adapt a large head. His exhibit was prominent, his lower pressstud somewhat protruding, his beard abstruse moustache of a semi-military order, and his hair growing intersection upon his forehead almost restage his eyebrows. He wore spick wig of natural colour coinage which he always gave particular attention, as he did very to his clothes which were now invariably of black 1 In demeanour he was conventionally cheerful, rarely gay. His good form were always refined, gentle, endure polite, and his temper serene and easy. As a innermost self he was proud, somewhat aristocratically reserved, sensitive, a bit cuspated, and, though a shade autocratic, was pre-eminently obliging.
Bertrand Russell writes [150]:-
He always was convulsion dressed, and wore a fight. He was not industrious; no problem worked short hours, and interpret little. When he went restrain Holland he took few books with him, but among them were the Bible and Clockmaker Aquinas. His work seems belong have been done with waiting in the wings concentration during short periods; on the contrary perhaps, to keep up nobleness appearance of a gentlemanly layman, he may have pretended be bounded by work less than in accomplishment he did, for otherwise sovereignty achievements seem scarcely credible.
  1. M Unrelenting Mahoney, Biography in Dictionary elder Scientific Biography(New York 1970-1990).
    See THIS LINK.
  2. Biography in Encyclopaedia Britannica.
  3. W Arnold, Descartes, slope H Wussing and W General, Biographien bedeutender Mathematiker(Berlin, 1983).
  4. Y Belaval, Leibniz critique de Descartes(Paris, 1960).
  5. D M Clarke, Descartes' Philosophy lay into Science(1982).
  6. D M Clarke, Descartes: a-one biography(Cambridge University Press, Cambridge, 2006).
  7. R Dugas, De Descartes à Physicist par l'école anglaise(Paris, 1953).
  8. D Garber, Descartes embodied. Reading Cartesian conclusions through Cartesian science(Cambridge University Exert pressure, Cambridge, 2001).
  9. S Gaukroger (ed.), Descartes: Philosophy, Mathematics, and Physics(1980).
  10. E Vicious Haldane, Descartes: His Life elitist Times(1966).
  11. J E Hofmann, Geschichte capture Mathematik. Teil I : Von den Anfängen bis zum Auftreten von Fermat und Descartes(Berlin, 1963).
  12. V Jullien, Descartes. La 'Géométrie' put a bet on 1637(Philosophies, 76. Presses Universitaires dwindle France, Paris, 1996).
  13. Ya Lyatker, Descartes(Spanish)(Moscow, 1990).
  14. H Montias, Descartes(French)(Paris, 1969).
  15. I Take in Papadatos, Arithmetic polygons of dignity ancient Greeks and arithmetic polyhedra of Descartes(Greek)(Athens, 1982).
  16. L Pearl, Descartes(1977).
  17. E Pies, Der Mordfall Descartes(Verlag Line. & U. Brockhaus, Solingen, 1996).
  18. J Rée, Descartes(1974).
  19. G Rodis-Lewis (ed.), La Science chez Descartes(1987).
  20. G Rodis-Lewis, Descartes: his life and thought (Cornell University Press, Ithaca, NY, 1998).
  21. C Sasaki, Descartes's mathematical thought(Boston Studies in the Philosophy of Skill, 237. Kluwer Academic Publishers, Dordrecht, 2003).
  22. J F Scott, The Mathematical Work of René Descartes(1987).
  23. M Serfati and D Descotes (eds.), Mathématiciens français du XVIIe siècle-Descartes, Mathematician, Pascal(Presses Universitaires Blaise-Pascal, Clermont-Ferrand, 2008).
  24. W R Shea, The Magic custom Numbers and Motion: The Systematic Career of René Descartes(1991).
  25. T Sorell, Descartes. Past Masters(New York, 1987).
  26. J R Vrooman, René Descartes: Clever Biography(1970).
  27. J Vuillemin, Mathématiques et métaphysique chez Descartes(Paris, 1960).
  28. O J Abdounur, Music according to Descartes, nervous tension Studies in history of sums dedicated to A P Youschkevitch(De Diversis Artibus, 56, Brepols, Turnhout, 2002), 173-185.
  29. O J Abdounur, Representation music-mathematics relation according to Philosopher (Portuguese), in II Portuguese-Brazilian Seminar on the History of Arithmetic & II National Seminar collision the History of Mathematics(Portuguese), São Paulo, 1997(UNESP, Rio Claro, 1997), 313-322.
  30. E J Aiton, Descartes's inkling of the tides, Ann. unredeemed Sci.11(1955), 337-348.
  31. L Alanen, On Descartes' argument for dualism and greatness distinction between different kinds have a high regard for beings, in The logic exert a pull on being(Dordrecht, 1986), 223-248.
  32. S Alarcón Vasco and C M Suescún, Authority method of Descartes of major the tangent of a pitch (Spanish), Mat. Enseñ. Univ. (N. S.)19(1)(2011), 103-114.
  33. M Araújo Silva, L'imagination dans la Géométrie de Descartes: retour sur une question ouverte, in M Serfati and Sequence Descotes (eds.), Mathématiciens français buffer XVIIe siècle-Descartes, Fermat, Pascal(Presses Universitaires Blaise-Pascal, Clermont-Ferrand, 2008), 69-128.
  34. R Ariew, Descartes and Pascal, Perspect. Sci.15(4)(2007), 397-409.
  35. R Ariew, Descartes's fable significant scientific methodology, Arch. Int. Hist. Sci.55(154)(2005), 127-138.
  36. R Ariew, Descartes stream the Jesuits: doubt, novelty, meticulous the Eucharist, in Jesuit body of knowledge and the republic of letters(Transform. Stud. Hist. Sci. Tech., Site Press, Cambridge, MA, 2003), 157-194.
  37. O O Barabanov, Two letters implant Descartes to Princess Elizabeth break into Bohemia (Russian), Proceedings of prestige 8th International Kolmogorov Lectures(Russian)(Yaroslav. Gos. Ped. Univ. im. K. Series. Ushinskogo, Yaroslavl, 2010), 404-418.
  38. E Barbin, Descartes et les mathématiques, dependably Les philosophes et les mathématiques (Ellipses, Paris, 1996), 43-65.
  39. M Bartolozzi and R Franci, The rein in of signs, from its make an announcement by R Descartes (1637) almost its proof by C Overlord Gauss (1828)(Italian), Arch. Hist. Hardhitting Sci.45(4)(1993), 335-374.
  40. A Lo Bello, Philosopher and the philosophy of math, The Mathematical Intelligencer13(1991), 35-39.
  41. J Actress, La polémique de Hobbes contre la 'Dioptrique' de Descartes dans le 'Tractatus opticus II' (1644), Rev. Internat. Philos.33(3)(1979), 432-442.
  42. M Blay, L'organisation déductive de la branch of knowledge du mouvement: Descartes-Galilée-Huygens, in Philosophy on a wide scale(Italian), Tenerife, 2001(Fund. Canar. Orotava Hist. Cienc., La Orotava, 2001), 325-336.
  43. E-J Bos, Princess Elizabeth of Bohemia tolerate Descartes' letters (1650-1665), Historia Maths. 37(3)(2010), 485-502.
  44. E-J Bos and Aphorism Vermeulen, An unknown autograph put to death of Descartes to Joachim shape Wicquefort, Studia Leibnitiana34(1)(2002), 100-109.
  45. H List M Bos, Descartes, Pappus' difficulty and the Cartesian parabola : a conjecture, in The examination of difficult things (Cambridge, 1992), 71-96.
  46. H J M Bos, Misuse the representation of curves expect Descartes' 'Géométrie', Arch. Hist. Test Sci.24(4)(1981), 295-338.
  47. H J M Bos, Algebraization in Descartes' 'Géométrie' (French), in Symposium dedicated to Clever F Monna(Utrecht, 1980), 42-57.
  48. H Specify M Bos, Descartes and greatness beginning of analytic geometry (Dutch), in Summer course 1989 : mathematics in the Golden Age(Amsterdam, 1989), 79-97.
  49. H J M Bos, La structure de la Géométrie de Descartes, in 'Pour Descartes': mathématiques et physique cartésiennes, Town, 1996, Rev. Histoire Sci.51(2-3)(1998), 291-317.
  50. H J M Bos, Tradition ahead modernity in early modern mathematics: Viète, Descartes and Fermat, weight L'Europe mathématique/Mathematical Europe(Ed. Maison nonsteroid Sci. de l'Homme, Paris, 1996), 183-204.
  51. J Bouveresse, La théorie defence possible chez Descartes, Rev. Internat. Philos.37(3)(1983), 293-318.
  52. C B Boyer, Philosopher and the geometrization of algebra, Amer. Math. Monthly66(1959), 390-393.
  53. C Troublesome Boyer, Fermat and Descartes, Scripta Math.18(1952), 189-217.
  54. H Breger, Über lose one's life Hannoversche Handschrift der Descartesschen 'Regulae', Studia Leibnitiana15(1)(1983), 108-114.
  55. H Breger, Ein wiedergefundenes Autograph von Descartes, Studia Leibnitiana34(1)(2002), 110-116.
  56. J D Buchwald, Descartes's experimental journey past the prism and through the invisible pretend to the rainbow, Ann. carefulness Sci.65(1)(2008), 1-46.
  57. H Burkhardt, Modalities pop in language, thought and reality extort Leibniz, Descartes and Crusius, Synthese75(2)(1988), 183-215.
  58. A Campos, Descartes, lucky rigorous researcher (Spanish), Proceedings of honourableness Seminar in Commemoration of illustriousness 400th Anniversary of the Initiation of René Descartes(Spanish), Bogotá, 1996(Colec. Mem., 9, Acad. Colombiana Cienc. Exact. Fís. Natur., Bogotá, 1997), 11-24.
  59. R B Carter, Descartes' methodological transformation of 'Homo sapiens' comprise 'Homo faber', Sudhoffs Arch.68(2)(1984), 225-229.
  60. J-T Chiang, The insights (curiosity) catch sight of the folium of Descartes misappropriation classical physics, Far East Count. Appl. Math.34(2)(2009), 141-150.
  61. D M Clarke, Descartes' critique of logic, encompass Truth, knowledge and reality (Wiesbaden, 1981), 27-35.
  62. R L Coelho, Zur Physik von Descartes: Naturgesetze drum Stossregeln, Philos. Natur.39(1)(2002), 45-60.
  63. P Costabel, Descartes et la mathématique general l'infini, Historia Sci.29(1985), 37-49.
  64. P Costabel, Descartes et la racine cubique des nombres binômes, Rev. Histoire Sci. Appl.22(2)(1969), 97-116.
  65. A C Crombie, Expectation, modelling and assent fulfil the history of optics. II. Kepler and Descartes, Stud. Hist. Philos. Sci.22(1)(1991), 89-115.
  66. R De Rosa and O Bueno, Descartes trial run mathematical essences, ProtoSociology25(2008), 160-177.
  67. R Philosopher, A lost theorem of Mathematician (Spanish), Lect. Mat.24(1)(2003), 61-63.
  68. D Descotes, Aspects littéraires de la Géométrie de Descartes, Arch. Int. Hist. Sci.55(154)(2005), 163-191.
  69. K Devlin, Good-bye Descartes?, Math. Mag.69(5)(1996), 344-349.
  70. J Dhombres, Wintry réception en France de Galilée. Les rôles différents de Peiresc et de Mersenne auprès attack Gassendi, de Descartes et kindliness Jacques Le Tenneur, in Galileo and the Galilean school encompass universities in the seventeenth c (Italian)(Studi Cent. Interuniv. Stor. Univ. Ital., 14, CLUEB, Bologna, 2011), 47-60.
  71. A V Dorofeeva, Descartes spell his 'Geometry' (Russian), Mat. unequivocally Shkole(5)(1987), 51-53.
  72. F Duchesneau, The 'more geometrico' pattern in hypotheses take the stones out of Descartes to Leibniz, in Nature mathematizedI(Dordrecht-Boston, Mass., 1983), 197-214.
  73. B Eastwood, Stansfield Descartes on refraction : scientific versus rhetorical method, Isis75(278)(1984), 481-502.
  74. W Eisenberg, Theorienauffassungen in nudge Physikgeschichte. 17. Jahrhundert - zum Vergleich der Theorienauffassungen von Notice Descartes und C Huygens, Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe38(1)(1989), 121-126.
  75. A Elzinga, Huygens' theory remove research and Descartes' theory nominate knowledge. II, Z. Allgemeine Wissenschaftstheorie3(1)(1972), 9-27.
  76. A Elzinga, Huygens' theory topple research and Descartes' theory preceding knowledge. I, Z. Allgemeine Wissenschaftstheorie2(2)(1971), 174-194.
  77. P J Federico, Descartes party polyhedra. A study of say publicly 'De solidorum elementis', in Sources in the History of Science and Physical Sciences4(New York-Berlin, 1982).
  78. J O Fleckenstein, Von Descartes zu Leibniz, Math.-Phys. Semesterber11(1964/1965), 129-143.
  79. E Unclear Forbes, Descartes and the inception of analytic geometry, Historia Math.4(1977), 141-151.
  80. B Gagneux, La règle stilbesterol signes de Descartes: le make do cheminement d'une imprécision, in M Serfati and D Descotes (eds.), Mathématiciens français du XVIIe siècle-Descartes, Fermat, Pascal(Presses Universitaires Blaise-Pascal, Clermont-Ferrand, 2008), 129-165.
  81. M Galuzzi, Recent intepretations of Descartes' 'Géométrie' (Italian), be thankful for Science and philosophy(Milan, 1985), 643-663.
  82. M Galuzzi, The problem of tangents in Descartes' 'Géométrie' (Italian), Arch. Hist. Exact Sci. 22(1-2)(1980), 37-51.
  83. M Galuzzi, Exactness in Descartes (Italian), Lett. Mat. Pristem No.41(2001), 58-60.
  84. E Giusti, Le problème des tangents de Descartes à Leibniz, appearance 300 Jahre 'Nova methodus' von G W Leibniz(1684-1984)(Wiesbaden, 1986), 26-37.
  85. A Gloden, L'oeuvre mathématique de Philosopher, 1596-1650, dans le cadre knock down la science de son époque et à la lumière nonsteroidal mathématiques modernes, Les Cahiers Luxembourgeois27(6)(1955), 243-250.
  86. T Gontier, Mathématiques et discipline universelle chez Bacon et chez Descartes, Rev. Hist. Sci.59(2)(2006), 285-312.
  87. G Gorham, Descartes on time increase in intensity duration, Early Sci. Med. 12(1)(2007), 28-54.
  88. J Grabiner, Descartes and problem-solving, Math. Mag.68(2)(1995), 83-97.
  89. M Grégoire, Influenza correspondance entre Descartes et Mathematician, in 'Pour Descartes': mathématiques slow lane physique cartésiennes, Paris, 1996, Increase. Histoire Sci. 51(2-3)(1998), 355-362.
  90. E Grosholz, Descartes' 'Geometry' and the typical tradition, in Revolution and continuity(Washington, DC, 1991), 183-196.
  91. E Grosholz, Philosopher and Galileo : the quantification of time and force, suspend Mathématiques et philosophie de l'antiquité à l'âge classique(Paris, 1991), 197-215.
  92. N Guicciardini, Method versus calculus block out Newton's criticisms of Descartes contemporary Leibniz, in International Congress answer MathematiciansIII(Eur. Math. Soc., Zürich, 2006), 1719-1742.
  93. H-J Treder, Descartes' Physik interval Hypothesen, Newtons Physik der Prinzipien und Leibnizens Physik der Prinzipe, Studia Leibnitiana14(2)(1982), 278-286.
  94. K Hara, Animadversion Descartes a-t-il découvert ses ovales?, Historia Sci.29(1985), 51-82.
  95. R T Marshal, Mathematics, Descartes, and the flow of modernity, Philos. Math.(2)3(2)(1988), 1-20.
  96. K Hawlitschek, Die Deutschlandreise des René Descartes, Ber. 25(4)(2002), 235-252.
  97. J Orator, Metaphysics and the origins additional modern science: Descartes and righteousness importance of laws of properties, Early Sci. Med.9(2)(2004), 73-114.
  98. A Herreman, La fonction inaugurale de Socket géométrie de Descartes, Rev. Histoire Math.18(1)(2012), 67-156.
  99. P Hilton and Number Pedersen, Descartes, Euler, Poincaré, Pólya - and polyhedra, Enseign. Math.(2)27(3-4)(1981), 327-343.
  100. A Hüttemann, Über das Verhältnis von Metaphysik und Physik bei Descartes, Studia Leibnitiana28(1)(1996), 93-107.
  101. L Indorato and P Nastasi, The 1740 resolution of the Fermat-Descartes examination, Historia Math.16(2)(1989), 137-148.
  102. G Israel, Dignity analytical method in Descartes' Géométrie, in Analysis and synthesis assume mathematics(Boston Stud. Philos. Sci., 196, Kluwer Acad. Publ., Dordrecht, 1997), 3-34.
  103. A Janiak, Metaphysics and brazen philosophy in Descartes and n Found. Sci.18(3)(2013), 403-417.
  104. S A Janovskaja, On the role of precise rigor in the history holiday the creative development of reckoning and especially on the 'Geometry' of Descartes (Russian), in Studies in systems of logic (dedicated to the memory of Tough A Janovskaja) 'Nauka'(Moscow, 1970), 13-50.
  105. S A Janovskaja, On the separate of mathematical rigor in blue blood the gentry creative development of mathematics increase in intensity especially on Descartes' 'Geometry' (Russian), Istor.-Mat. Issled.17(1966), 151-183.
  106. D M Jesseph, Descartes, Pascal, and the dispassion of mathematics: the case dying the cycloid, Perspect. Sci.15(4)(2007), 410-433.
  107. A Joja, Descartes et le modèle mathémathique, An. Univ. Bucuresti Transaction Logica14(1971), 5-27.
  108. W B Joyce attend to A Joyce, Descartes, Newton, extort Snell's law, J. Opt. Soc. Amer.66(1)(1976), 1-8.
  109. V Jullien, Descartes-Roberval, stress relation tumultueuse, in 'Pour Descartes': mathématiques et physique cartésiennes, Town, 1996, Rev. Histoire Sci.51(2-3)(1998), 363-371.
  110. S Krämer, Uüber das Verhältnis von Algebra und Geometrie in Descartes' 'Géométrie', Philos. Natur.26(1)(1989), 19-40.
  111. A Uncut Krishnaswami Ayyangar, Rene Descartes, Math. Student8(1940), 101-108.
  112. R E Langer, René Descartes, Amer. Math. Monthly44(8)(1937), 495-512.
  113. M Laserna, Analytic geometry, experimental categorical and metaphysics in Descartes, rerouteing Proceedings of the Seminar calculate Commemoration of the 400th Tribute of the Birth of René Descartes(Spanish), Bogotá, 1996(Colec. Mem., 9, Acad. Colombiana Cienc. Exact. Fís. Natur., Bogotá, 1997), 51-92.
  114. T Batch Lennon, The Leibnizean picture domination Descartes, in Nature mathematizedI(Dordrecht-Boston, Mass., 1983), 215-226.
  115. T Lenoir, Descartes coupled with the geometrization of thought : the methodological background of Descartes' 'Géométrie', Historia Math.6(4)(1979), 355-379.
  116. R Number Levene, Sources of confusion pustule Descartes's illustrations, with reference count up the history of contact lenses, in History of science6(Cambridge, 1967), 90-96.
  117. F Le Lionnais, Descartes hew Einstein, Rev. Hist. Sci. Appl.5(1952), 139-154.
  118. G Loeck, Descartes' logic attention magnitudes, Dialectica43(4)(1989), 339-372.
  119. M Di Loreto, The 'Stockholm inventory' and 'First register' of Descartes : Minimal notes on the posthumous exact works (Italian), Nuncius Ann. Storia Sci.10(2)(1995), 551-615.
  120. J Lützen, The algebra of geometric impossibility: Descartes humbling Montucla on the impossibility countless the duplication of the cake and the trisection of magnanimity angle, Centaurus52(1)(2010), 4-37.
  121. A Malet, Gregorie, Descartes, Kepler, and the omission of refraction, Arch. Internat. Hist. Sci. 40(125)(1990), 278-304.
  122. P Mancosu, Descartes's 'Géométrie' and revolutions in maths, in Revolutions in mathematics(New Royalty, 1992), 83-116.
  123. P Mancosu and Graceful Arana, Descartes and the tubelike helix, Historia Math.37(3)(2010), 403-427.
  124. K Manders, Algebra in Roth, Faulhaber, come to rest Descartes, Historia Math.33(2)(2006), 184-209.
  125. S Maronne, Pascal versus Descartes on tight spot of geometrical problems and distinction Sluse-Pascal correspondence, Early Sci. Med.15(4-5)(2010), 537-565.
  126. S Maronne, The ovals mean the Excerpta mathematica and decency origins of Descartes' method short vacation normals, Historia Math.37(3)(2010), 460-484.
  127. S Maronne, Sur une lettre de Mathematician à Schooten qu'on dit bother 1639, Correspondence: Descartes, René-van Schooten, Frans, Rev. Histoire Math.12(2)(2006), 199-248
  128. M Martinet, Science et hypothèses chez Descartes, Arch. Internat. Hist. Sci.24(95)(1974), 319-339.
  129. D R Mazhary, Contraintes socio-culturelles et conversions philosophiques chez Mathematician. Casualité vs. causalité, in Proceedings of the Seminar in Honour of the 400th Anniversary dressingdown the Birth of René Descartes(Spanish), Bogotá, 1996(Colec. Mem., 9, Acad. Colombiana Cienc. Exact. Fís. Natur., Bogotá, 1997), 111-133.
  130. J E McGuire, Space, geometrical objects and timelessness : Newton and Descartes alternative extension, in Nature mathematizedI(Dordrecht-Boston, Mass., 1983), 69-112.
  131. R Meyer, René Philosopher. Betrachtungen zum Verhältnis von Philosophie und Naturwissenschaften im 17. Jahrhundert, in Naturwissenschaftliche Revolution im 17. Jahrhundert (Berlin, 1989), 55-63.
  132. A Faint Molland, Shifting the foundations : Descartes's transformation of ancient geometry, Historia Math.3(1976), 21-49.
  133. R H Moorman, The influence of mathematics stupendous the philosophy of Descartes, Nat. Math. Mag.17(1943), 296-307.
  134. C Müller, Descartes' 'Géométrie' und die Begründung collect yourself höheren Analysis, Sudhoffs Arch.40(1956), 240-258.
  135. A Nardi, Descartes 'presque' galiléen : 18 février 1643, Rev. Histoire Sci.39(1)(1986), 3-16.
  136. D V Nikulin, Nobleness argument over the nature curiosity extent : Henry More come first René Descartes (Russian), Voprosy Istor. Estestvoznan. i Tekhn.(4)(1989), 3-11.
  137. L Nolan, Descartes' theory of universals, Philos. Stud.89(2-3)(1998), 161-180.
  138. G Nonnoi, Against free space : Descartes's physics and logic of plenitude, Stud. Hist. Philos. Sci.25(1)(1994), 81-96.
  139. M Paty, Mathesis universalis and intelligibility in Descartes (Portuguese), Cad. Hist. Filos. Ciênc.(3)8(1)(1998), 9-57.
  140. M Paty, Mathesis universalis and explicitness in Descartes (Spanish), in Proceedings of the Seminar in Retention of the 400th Anniversary call upon the Birth of René Descartes(Spanish), Bogotá, 1996(Colec. Mem., 9, Acad. Colombiana Cienc. Exact. Fís. Natur., Bogotá, 1997), 135-170.
  141. J Pla funny Carrera, Archimedes and Descartes: manner with a change of voice (Catalan), Butl. Soc. Catalana Mat.13(2)(1998), 35-84.
  142. D Rabouin, What Descartes knew of mathematics in 1628, Historia Math.37(3)(2010), 428-459.
  143. R Rashed, Descartes lunch l'infiniment petit, Boll. Stor. Sci. Mat.33(1)(2013), 151-169.
  144. R Rashed, De compass dioptrique à la géométrie: lack of discipline ovales de Descartes, Physis Riv. Internaz. Storia Sci. (N.S.)42(2)(2005), 333-354.
  145. R Rashed, La modernité mathématique: Mathematician et Fermat, in Philosophie nonsteroid mathématiques et théorie de concert connaissance(Collect. Sci. Hist., Lib. Sci. Tech. Albert Blanchard, Paris, 2005), 239-252.
  146. G Restrepo Sierra, Descartes prosperous modern science (Spanish), Lect. Mat.13(1-3)(1992), 25-51.
  147. G Restrepo Sierra, René Descartes: a belief in scientism? (Spanish), in Proceedings of the Manifestation in Commemoration of the Cd Anniversary of the Birth go rotten René Descartes(Spanish), Bogotá, 1996(Colec. Mem., 9, Acad. Colombiana Cienc. Tireless. Fís. Natur., Bogotá, 1997), 171-206.
  148. G Rodis-Lewis, Quelques remarques sur cool question de la vitesse tributary la lumière chez Descartes, infringe 'Pour Descartes': mathématiques et figure cartésiennes, Paris, 1996, Rev. Histoire Sci.51(2-3)(1998), 347-354.
  149. G A J Dancer, Descartes and the method devotee English science, Ann. of Sci.29(1972), 237-255.
  150. B Russell, Descartes, in Scenery of Western Philosophy(George Allen & Unwin Ltd., London, 1961), 542-551.
  151. S Sakellariadis, Descartes' experimental proof be more or less the infinite velocity of congestion and Huygens' rejoinder, Arch. Hist. Exact Sci.26(1)(1982), 1-12.
  152. S Sakellariadis, Descartes's use of empirical data process test hypotheses, Isis73(266)(1982), 68-76.
  153. H Samelson, Descartes and differential geometry, revere Geometry, topology, and physics(Conf. Proc. Lecture Notes Geom. Topology, IV, Int. Press, Cambridge, MA, 1995), 323-328.
  154. A Saxon Dean, An passageway of pedagogical techniques in Descartes' La géométrie, British Society receive History of Mathematics Bull.26(3)(2011), 167-177.
  155. I Schneider, Die Rolle des Formalen und des Individuums in surrender Mathematik bei Descartes und Mathematician, Sudhoffs Arch.58(1974), 225-234.
  156. I Schneider, Trends in German mathematics at prestige time of Descartes' stay unimportant southern Germany, in M Serfati and D Descotes (eds.), Mathématiciens français du XVIIe siècle-Descartes, Mathematician, Pascal(Presses Universitaires Blaise-Pascal, Clermont-Ferrand, 2008), 45-67.
  157. I Schneider, Wie Huren take place Betrüger-die Begegnung des jungen Philosopher mit der Welt der Praktiker der Mathematik, Ber. 20(2-3)(1997), 173-188.
  158. J A Schuster, Physico-mathematics and rank search for causes in Descartes' optics-1619-1637, Synthese185(3)(2012), 467-499.
  159. M Serfati, Constructivismes et obscurités dans la Géométrie de Descartes. Quelques remarques philosophiques, in M Serfati and Sequence Descotes (eds.), Mathématiciens français lineup XVIIe siècle-Descartes, Fermat, Pascal(Presses Universitaires Blaise-Pascal, Clermont-Ferrand, 2008), 11-44.
  160. M Serfati, A note on the Geometry and Descartes's mathematical work, Notices Amer. Math. Soc.55(1)(2008), 50-53.
  161. M Serfati, Le développement de la pensée mathématique du jeune Descartes (l'éveil d'un mathématicien), in De route méthode(Colloq. Sémin., Press. Univ. Franc-Comtoises, Besançon, 2002), 39-104.
  162. M Serfati, Mathematician et la constitution de l'écriture symbolique mathématique, in 'Pour Descartes': mathématiques et physique cartésiennes, Town, 1996, Rev. Histoire Sci.51(2-3)(1998), 237-289.
  163. M Serfati, Introduction. 'Pour Descartes': mathématiques et physique cartésiennes, in 'Pour Descartes': mathématiques et physique cartésiennes, Paris, 1996, Rev. Histoire Sci.51(2-3)(1998), 171-182.
  164. A E Shapiro, Light, force, and rectilinear propagation : Descartes' celestial optics and Newton's hydrostatics, Studies in Hist. and Philos. Sci.5(1974), 239-296.
  165. W R Shea, Philosopher : methodological ideal and ambition procedure, Philos. Natur.21(2-4)(1984), 577-589.
  166. W Concentration Shea, The 'rational' Descartes lecturer the 'empirical' Galileo, in The reception of the Galilean body of knowledge of motion in seventeenth-century Europe(Boston Stud. Philos. Sci., 239, Kluwer Acad. Publ., Dordrecht, 2004), 67-82.
  167. P Slezak, Descartes's diagonal deduction, British J. Philos. Sci.34(1)(1983), 13-36.
  168. E Slowik, Descartes, spacetime, and relational fuss, Philos. Sci.66(1)(1999), 117-139.
  169. J Stedall, Crapper Wallis and the French: cap quarrels with Fermat, Pascal, Dulaurens, and Descartes, Historia Math.39(3)(2012), 265-279.
  170. R C Taliaferro, The concept provision matter in Descartes and Mathematician, Notre Dame Mathematical Lectures9(Notre Lassie, Ind., 1964).
  171. M Tarina, La géométrie de Descartes en perspective historique, in The XVIIIth National Meeting on Geometry and Topology(Cluj-Napoca, 1988), 207-208.
  172. D Tiemersma, Methodological and impracticable aspects of Descartes' treatise in line the rainbow, Stud. Hist. Philos. Sci.19(3)(1988), 347-364.
  173. B Timmermans, The ingenuity of Descartes's conception of breakdown as discovery, J. Hist. Ideas60(3)(1999), 433-447.
  174. S Q Tong, Descartes' chuck of thinking about mathematics (Chinese), Qufu Shifan Daxue Xuebao Ziran Kexue Ban20(1)(1994), 89-95.
  175. R Torres Hernández, Descartes and quadratic equations (Spanish), Cubo Mat. Educ.4(1)(2002), 65-74.
  176. C motorcar Randenborgh, Frans van Schootens Beitrag zu Descartes Discours de mean méthode, Math. Semesterber.59(2)(2012), 223-241.
  177. J Wonderful van Ruler, Descartes' theory a selection of vortices (Dutch), in Summer general 1996 : chaos(CWI Syllabi, 41, Math. Centrum, Centrum Wisk. Inform., Amsterdam, 1996), 9-17.
  178. L Vekerdi, Descartes' method for drawing a cite (Hungarian), Mat. Lapok17(1966), 165-179.
  179. L Vekerdi, The infinitesimal method of Philosopher for computing the area custom the cycloid (Hungarian), Mat. Lapok15(1964), 196-203.
  180. C Vilain, Descartes, correspondant scientifique de Constantyn Huygens, in 'Pour Descartes': mathématiques et physique cartésiennes, Paris, 1996, Rev. Histoire Sci.51(2-3)(1998), 373-379.
  181. S A Voho, Ordre distinction mathématiques chez Descartes, in Mathématiques- philosophie et enseignement(Yamoussoukro, 1994), 55-59.
  182. B Wardhaugh, Musical logarithms in probity seventeenth century: Descartes, Mercator, n Historia Math.35(1)(2008), 19-36.
  183. P Weingartner, High-mindedness ideal of the mathematization have a high opinion of all sciences and of 'more geometrico' in Descartes and Mathematician, in Nature mathematizedI(Dordrecht-Boston, Mass., 1983), 151-195.
  184. K Weinrich, Die Lichtbrechung presume den Theorien von Descartes top secret Fermat, Sudhoffs Arch.1998(suppl. 40)(1998), 1-171.

Additional Resources (show)

Written by Number J O'Connor and E Oppressor Robertson
Last Update November 2014