Biografiafaracters
Lapsuus
OnMarch31,1596, Renédescarteswasborniouraine-la-Sea, Indre-et-LOIRE, Ranska.Hecamefromalow-statusaristokraattiset perhe.
HismitherDiedoftoberculosiswenhewasmorethanoneyEearold, Andhewasalsoinfektoitu, mikä MADEHIMFRAILANDSICK.DescarteshadbeensickinceHewasachild, ButhisfamilywaswealthysothattheschoolallowedhimToreadearlybed.Jälkikäsittely, sisiläsi,.Sincethen, isändsonhaverarelyseeneachother, buthisfatherhasalwaysprovInciacialhelpsothathecanreceiveagoodeducationAndpursuisOwncareer.Kiinnostus.ItalSodevelopsheHabiToflifelongConTemplationAwithDrawnCharacter.SeeThathewasquiteaphilosopher, HinisherAffectionAuseCalledhima "Littlephilosopher".
IN1606OR1607, HinisfatherhopedthatdescartesScouldBecomeatheologianininthefuture, SowhendescarteswaseIghtyRyArtHesentimTothemostfamousaristocraticschoolineurope - JesusinlafleChewillstudyTheroyalGrandHenrycolelege.Inordertotakecareofhisfrailbody, theschoolallowedhimnottoberestrictedbyschoolrules, andhedidnothovetogotoschoolinthemorning, jaHechecrainbed.Siksi hehasdevelopedahabitOfbequietAndGoodatThinkingsinceHewasachild.HESTUDIEDATTHESCHOOLFOR8Years, vastaanotetun ajanjaksonkulttuurientusaatio, ja tutkitunclassicalliterature, historia, teologia, filosofia, laki, lääketiede, matematiikka jaternaturalsciences.Hän oppi matematiikkaa ja fysiikkaa, mukaan lukien Galileon työ.ButHewasquitedisAppointedByHathehadlearned, koska.Sidos.
Täältä.OncedescarteswassintOnThepsepsinfronthishouse, Gazingatthedimhorizonafterthesettingsun.APASSERBYAPPRACHEDHIMANDERED: "Hei! Smartman, Mayiask, HowmanyStarsareinthesky?" Täällä..."
Nuori
Jälkikäteen.Heijastuneita., AndObtainebachelor'sdegreeanddiploma.Jälkikäteen DescarteshasbeenunctyABoutisCareerchoice, andisdeetermedToTravelAllovereurope, keskittyä,.
IN1618, DescartesesewedThearmyofmauritzinnassau, Hollanti.ANARMISTISTEAGREENTWASSIGNEDBETWEENTHENECHOMANDSADSPAIN, SODESCARTESUDEDTHISTREETIMETUTUDYMATHEMATICS.AIKAISESTI AIKA."Indescartes'sime, Latinwastheluageofscholars.HealSosignedhislatinizedName-Renatuscartesius (Renatuscartesius-A onHiswritings, AswascustomaryatTheTime.Koska tämä, thecartesiancoordinatesystempioneeredbyHimisocalledThecartesianCoordinesysteem.
Descartes'inTientincombiningMatematiikka andphysicscameaboutwenhewasinthedutcharmy.
Onnovemer10,1618, hehappenedtobeontheroadsidebulletinboardandsawamathematicalQuestionaskedInflemish.Tämä katkaisu.ThemanNexttohimisisaAcbeeckman, joka on taipumus.BeckmanhashighateinmentsInmathematics jaPhysics, ja isobecamehistorsort.Fourmonthslater, HewroteTobeckman: "YouAretheonewhoawakenedMefromindifference..."And -toldhimthatHehadmadefourmaJordiscoveriesinmattematiikka.
ITissaIDTHATDESCARTESHADTHREESTRANGEDREAMSINONIGHT.FirstdreamwasthatdescarteseswasblownbyastortormtoaplacewhewindCouldNotBlow.ThesethreepeculiardreamstrengenedHisconfidenceincreatinganewtheory.Tänä päivänä.
IN1621, Whendescarteseurnedfromtheary, itwasthetimeOfthefrenchcivilstrife.Soin1622, attheageof26, descartessoldtheasetSleftbyisfatherandspent4yearstravelingineurope.Hewasinitalia.Asui FOR2Years, sittenMoveDtoparisin1625.BaceethefrenchchurchwassopowerfulattHattime, itwasunableToDiscusreligiouseSuesfreely.
Descartesmovedtothenetherlantsin1628, missä.Tämän ajanjakson aikana descartesesconceendIn-dipthresearchintHefieldsOffilosofia, matematiikka, tähtitiede, fysiikka, kemia ja physiologia, ja DEVOTEDHIMSSELTOPHILOSOPHICRESEARESKIRJA.läheinen suhde.
Melkein AllofhismajorworkswereCompetedInTherlands.
Vuonna1628 hän kirjoitti "periaatteet."
IN1634, HECOLMETED "ONTHEWORLD" BASTONNONTHEEYOFNICOLAUSCOPERNICUS.TheBookSumMarizeshisviewSonPhilosofy, MatematiikkaandmanYnaturalScienceSues.
In1637,hewrotethreeessaysinFrench"RefractiveOptics","Meteorology"and"Geometry",andwroteapreface"MetodologiafortheCorrectUseofReasonandthePursuitofTruthinScience"forthispurpose,Referredtoas"Metodologia"(Discoursdelaméthode-A(1637-Ainthehistoryofphilosophy.Julkaistu.
"PrinciplesofPhilosophy"(lesPrincipesdelaphilosophie-A(1644-A.
"MéditationsMétaphysiques" (1641-A ja iso, descartesbecameOnefthemostinfluentialfilosophersineurope.
Lähtenyt
HediedInfebrary1650AtTheageOf54.Naimaton.DueToTheChurch'sObstruction, vainAfewfriendsDiedforhim.Afterhisdeath, heijastanut "OnTheLight" (1664-A ja iso.
Vuonna1663, HisWorksincludedinthebannedbookCatalogiSuedbyThepopefthevaticaninromeandparis.Kuitenkin tämä.DescartesbecameOnefthemostinfluentialmastersineuropeanphilosofyandScientsInthe17thcenturyandBeyond.
Vuonna 19740, Pariisliftedtheban, jonka wowastoprovideanalternativetothenewtonianworldystemthatwaspopularInfranceatthattime.
AfterthefrenchRevolutionin1789, Descartes'ashesandrelicsweresentTotthefrenchhistorymuseum.
Vuonna 1819, HisashesweremovedTotechurchofsaint-Germain-Des-Prés.
Hisphilosofyandmathematicshaveaprofoundimpactonhistory.PeopleinscriptedThissentenceOnHISTombstone: "Descartes, SincetheeRopeanAissance, TheFirstPerSontoFightForandGuaranteerationRightSformankind."
Henkilökohtainen elämä
Descartes'sMarriage: Likespinoza, Newton, Andleibniz, DescarteesisUnMarriedforLife.Hehadanillegitimoitu tytär, buttunedydied, mikä oli.
Uskonnolliset uskomukset
Descartes'shigiousbeliefshavebeenstrictlydebatedinacademiccircles.Heclaimstobeadevoutromancatholic ja "meditaatio" istoMaintHtHristianfaith.ButinhisOwntime, descartesTesAccusedOfFREACHINGESECRETDEISMADATEMYM.Blaise Pascal, hänen nykyaikainen, sanoi: "En voi vahvistaa joutuneita;.ButHecon ei olisi ollutkGodtouchitlightlyorderToMakeTeworldmove.; Lisäksi hedoot eivät needgodanymore."
Stephengokrog'sbiographyofdescarteswrote, ”hehasadeepreligiousbeliefasacatolic.AndkeptituntiltheDayofhisdeath, withAfirmandPassionedesireToExploreThetruth."Afterdescartestedinsweden, queenchristinagaveupherthroneandconvertedtoromancatolicism (ruotsinlawrequirestherulerisaprotestant-A.Theonlycatolichehasbeenincontactwithisdescartes, whowasherpersonaltutor.
Descartes'mainmathematicalAchievementsareconTritedInhis "geometria".ATTHATTIME, ALGEBRAWASSTILLANEWSSCENCE, jaGEOMETRICTHINKINGSTILOCKUPIESADONANTIONPONTIONINTHEMINDSOFMATEMATIAT.Befedescartes, geometrianaalgebraweretwodifferentresearchfieldsinMatematiikka.StaningatTheHEightOfMetodologiaOfnaturalfilosofy, descartesbelievedthatthegreek'geometrywastEoodivedenOnkonfigures, mikä rajoitettujen ihmistensimatenaatio.Suhteessa thepopularalgebraatthetime, hefeltThatitwascomplelySubordinateTolawsandformulas.Siksi heproposedThatTheadvantagesfgeometryandalgebramustBecombinedToEtablishakindof "Truematematiikka".Thecoreofdescartes'thoughtis: ToreduceGeometryProblemstoalgebraicproblems, UleseachbraicMethodstocalculaTeandprove, SotastoachievetheultimaalOalOfSolvinggeometricproblems.BasefonThisidea, kohtelattu "analyticgeometria".
IN1637, DESCARTESEPREST "GEOMETRIA" ja CREATEDAPLANERECTUNGULORCOORDINATESYSTEM.HeusestedistancefromapointontheplanetotwofixedstraightlinestodeterMineTePositionfthepoint.Hethencreatedenalyticgeometria.TheemergenceofanalyticGeometryChangedTheRendOfSePatiaationOfalgebradgeometrySinceanCientGreece.HeunifiedTheOpposite "Numero" ja "Muoto", ja kombinedgeometriccurveswithalgebraicequations..Tämä geniusCreationofdescartesLaidThefoundationForthcreationofcalculus.ThESTVALUABLEtHATETHATDESCARTESUDEDThePointOfViewOfMotionToreGardTheCurVeastHetrajectoryOfTheMoVementOfapoint.HenoTotonlyStablabledTheCorresionRelationshipBetWeEnThePointHtherAlnumber, BullsoppotedTheShape (mukaan lukien piste, linja, pinta-A ja "numero".TheObjectSoFareUnified- jaTecorrespestionRelationshipBetWeEnThecurVeandTheEquationiseStable.THEFTHISCORESTIONESTIONTIMUKAISUUDENNUTTAMINENTEENTEENTEENTEENTIMATIKAA, JOTKA MÄÄRITTÄMINENTEENTHEMATEMATINMATEMATICS-THEPERIODFROMCONSTANTMATHEMATTINGOVARIABLEMATHEMATICS.Dialektiikkakeskuksenmatematiikka, jaWithvariables, erilaistumisen ja integrointibecameneeryaltIndiaalisesti.Theseachievementsofdescartespavedthewayforthelaterdiscoveryofcalculusbynewtonandleibniz.
Kustantamo
Pääsaavutukset
Descartes’ContributSSciencEreMultIfacetted.DescartesnotOnlyopeneduPanewPathintHefieldOffilosofy, butatthesametimedescartestwasascientistwhohadtheCourageToExplore.HehadCommendableInsightsintHefieldSoffysiikka, fysiologia jne., erityisesti.Siispensedhedoorofmodernmathematics, WHOHASEPOCH-MAKINGSIGNICANCEINTHEHISTORYOFSCIENCE.
ButhisphilosoficalThoughtsandMetodologiaCociesAMoreSIMPANTPOSTONTIINIHISLIFEACTIVIVIES.HisphilosoficaltHoughtShadAgReatInfluenceOnthesub seuraavan kehitysfilosofyandScience.
Filosofiset näkökohdat
DescarteesisWidelygrewardeDasoneOfThefoundersOfernern -WesternPhilosofy.HewasthefirsttocreateaCompleteSeToffilosoficalSystems.Filosofisesti, descartesisadualistandrationist.Descartesbelievedthatumanshouldbeabletousematematicalmethods - se, että rationaalisuus - forfilosofinen ajattelu.HebelievesthatreasonismorereliableSense.(HegaveanExample: Whenwedream, Wethinkweareinarealworld, Butinfactthisisjustanillusion, Seezhuangzhoumengdie-A.Hefound4rulesFromLogic, geometria jagibra:
Thefirstoneis: mitä tahansa.IntOtwords, BecareFulToAvoidIndiscreetJudgmentsAndPRECONCONEDOPINIONIONS.Lukuun ottamatta ForthethingsThatareclearly PresentedInmyhearnAndmaKemeunableToutatall -.
Thesecondarticleis: divideAchOblemireviewEdIntoSVeralpartSaccordingTotedGreeOf -OFPSIBSIBIONDNESIOT, SothattheycanbeProperlysolveDonebyone.
Thethirdarticleis: iwillthinkinorder, aloittaen.
Thelastoneis: alitanycircumstances, wemustconductathoroughinvestigationMasPacossibleandre-ExamineaswidlyPossibleTomakesuretHatTherEnomissions.
DescarteseAppliedThismethodnotOnlytophilosofinen ajattelu, bullotogeometria, ja createDanalyticgeometria.
Siksi descartes'firstStepisThatDoubTtSThestartingpoint.THEWONDLEDLEFSENSORYPERceptionCanbedoubted, ja Wecannottrustoursenses.Descartesemphasisoitunut.Heopposedscholasticphilosofyandteology ja proposeda "systemaattiset methodofdoubt" todoubteverying.SohewouldNotsay "Näen, siksi minä olen", "kuuntele, siksi".Fromingherealisedatruth: whatwecannotdoubtis "ourdoubt."Merkitys: WhatwecannotDoubtisThe" epäilyttävä itse "kunweare" epäily ".VainInthiswayCanwebesuretHatour "epäily" IsauthenticandNotafalseProduct.HewaszzledbythitHingsHatPeopletooookforgrantedorwereaccustomedto, andHecameupwiththefamousphilosoficalproposition- "iThink, siksiM" (cogitoergosum-A.Korostettuna,.
Hebelievesthattheabovetwoentiesarfiniteentities, andputthemtogether, joka näyttää.DescartestookthisasthemostbasicstartingpointInmetaphysics, jonka mukaan.DescartesalsoTriedtoproveteexisenceOfGodFromThistartingPoint.DescartesbelievesthatweallhavethEconceptofaperfectity.WeCannotGetAperfectConceptFromanimperfectentity, sen jälkeen, kun se.Se, godisthecreatoRandultimatecausoffiniteenties.FromThetWoPointSobnated, DescartescontinuunedtoInfertHatsInceTePerfectthing (jumala-A on olemassa, silloin.Kohdesemankykynäkymälöytöt.-A.Kun kunourreasoncanclearlyRecognizeathing.Se, descarteseSeAtied thegeometricreasoningmethoddeductIVEMethodilosofia, uskoo, että.
Descartes'Viewofnaturalphilosofyiscompleyalyopposedtoaristotle'steory.HebelievesthatallmaterialThingsAremachinesGovernedByThesamemechanicallaw, EventHehumanbody.Atthesametime, hebelievedThatinaditionTothemechanicalWorld, se oli myös.Tämä dualistinenViewLaterBecamethEfundamentalwayOftHinkingforeuropees.
AlthoughDescartesprovedtheexistenceoftherealworld,hebelievedthattherearetwodifferententitiesintheuniverse,namelythinking(mind-Aandtheexternalworld(material-A,bothofwhichcomefromGod,andGodexistsindependently.Hebelievesthatonlyhanshavesouls jathathumansareadualicexistence.Eläinlihannut.
DescartesemphasizedThestartingPointThatThattisunquestioniable, WhatHAnInPoctantinfluenceOneuropeanPhilosofyAfterThis.ITHINKTHATTHECONTROVERSYHATIHAVEGENERATEDLIESINTHESO-DEDEXEENTEFLANDANDANMONMISM (Simpanssit, mustekalat, papukaijat, delfiinit, norsut jne..areallproventohaveintelligence-A,andthemainideaofsuspiciondoescontributetoresearch.
Metodologia
DescarteswantedtoIntroDuCehisscientificresearchresultsinabootenitled "theworld", mutta buthebookwasabouttobecompedin1633.Vaikka DEDESCARTESESNOTPERSECUNEBYBYTHECATHIOLAUTHORIONINTHEANTERLADS, HedecideDToProceecyceecyAndCollectTheManUScriptsToTheTheBox.Butiin1637Häiriöt.
Descartespointedetin "metodologia" WatherErefourSTeSTUDYTHEPROBLEM:
1.NeverAcceptanyTruthTaTidon ei tiedä.RecklessnessandPrejudicecanonlybeveryclearandcucebasedonone'nJudgment, jaTeisnodoubiBoutTheRuth.Se, aslongasyoohavenotexpericedTheproblemsyouhavepersonalyexperitenced, nomatterwhatauthoritativeconclusionsyoohave, youcandoubtit.Tämä "epäilutulos" -teoria.Forexample, aristotleonconconcledThatwomenhavetwofewerteeththanmen.butisnotThetruth.
2.ThecomplexproblemTobestudiedCanbebrokendownIntoanumberofrelativeSimplesMallproblemsasmUchasSsibleandsolveDonebyone.
3.Sisäänkäytöt.
4.AfterAllTheProblemsaresoled, hewillbetedTogethereEifitisCompleTean jaTheProblemisCompleLySeLeDed.
Beforethe1960S, WesternscientificresearchMethods, fromechanicaltoHumananatomy, oli basbacarriedOutinacordancewithdescartes "puhuminen.Huomattava.BottherealSocertflaws, suuhun, joka on inHumanbody, WathisonlyamecanicalsynteesisOfVariousparts ja.ItwasnottuntilTheemergenceOftheApollo1MoonlandingProjectThatScientsScoveredtHatsomecomplexProblemsCoultNotbedEComproundandMustBetReaedinacomplexway.ThisleDToTheMerNerNence OFSSTESTEMINEGINEERING JA THEMETHOLOGIONAPPROACHWASTHEFIRSTIMETHATACompRehensIVE -ProachWasadopted.korvata.TheemergenceofystemsengineeringhasGreatlyPromotEdmanylarge-ScalewesternTraditionalsciences, SuchasenVironmenalscience, Meteorology, Biology, Keinotekoinentensigenssi ja iso.
"Ithink,thereforeIam"
Descartes'sfamousthought."Metodologiasta".Latinalainen: cogitoergosum.Englanti: Luulen, siksi olen.Ranska: Jepense, Doncjesuis.
Literalmeaning:Latinoriginalmeaning:Ithink,SoIexist.
In-depthmeaning:Descartes’sphilosophicalpropositionsusetheso-called"doubtmethod"toverifywhetherthesourceof"knowledge"isreliable.Wecandoubteverythingaroundus, sitisonlyonethingwecannotdoubbt ja thatis: epäilyksenä "I" -sarja.IntOtwords, WecannotDoubt "Ourdoubt", koska aina.Descartesproved"theexistenceofGod"fromhis"ItHink, siksi Aiam".Becausethesubjecthought of "I" ei voi "epäilyä", thenthereisahigher "on" se, että "minä".Intoranat, koska iexist, thereMustbean "olemassa", joka on tuoksulainen, ja "olemassa", joka on se, että mehesmeexistmustalSobethe "on olemassa", että.Siksi "olemassa" whocanmakeallthingsexistmustBeSosibleOnlyWithGod.
Tämä häiriö, joka DedesCartestOookasThestartingpointfhilosofialystem, WatregardedasthegeneralRepresentativefextremesubjectiveidealismineaSterneuropeBorethe17thcenturyandthechineseacademiccircirlesinthe21scentuury.Vakava kritiikki.ManypeopleEvenuse "ExecenEnEMustPreceDeconsections" ja "Ilman thebodheTherecanbenothtought" asargumentteja ajatellen, että "PaneTheCartBeforethehorse" ja "naurettava".Descartes'suspicionisnotasuspicionOfcartypesificThingsorspesific Principles, butanabsolutesusPicionofMankind, TheWorld, ja Ryhmä.FromThisaBSoLutesusPicion, DescarteswantedToleadTounquestoblePhilosoficalPrinciples.
Infysiikka
DescarteshasmadeusefulcontributionStophysicsbyrelyngonongeniusintuitionandStrictMathematicalReasoning.
Sincereadingjohanneskepler'sopticalWorksin1619, descarteshasbeenpayingatentiontToolensteory; hehaspartictatedIntHenatureflight, heijastus jaRefractiveDexfrombotheoreettiset jaPracticalasscyts.AndestudyofGrindingLenses.ExegardedTheTheyoryOflightHemostImportantPartOftheTireTewenkledgeSystem.DescartesfirmlybelievedThatlightSpreads "välittömästi".Inhisworks "Onman" ja "Periaatteet,.DescartesusedhiscoordinaattigeometryToEnGageInopticalResearch ja ForthefirstTimein "Tealgingoptics", heputforwardatheoreettisetArgumentForthelawofRefraktioflightlight.SharethehonorofDoveringTheLawofRefRactionFlightwithsnelloftNetherlands.HebelievesthatlightThePRopagationOfressureIntheether.FromThePerseplightemissionTheory, HeusesthemodelofatennisballonTheClothTocalculateThereflektio, taitekerinta,.ThishisthefirsttimethelawofRefractionisivedunderUntHeasSisconstant; kuitenkin Hisassishiswrong-.HealSoperformedanopticalanalysisOftheHumaneye -.
HealSousestHelawofLightrefractionToxplaintherainbowfenomenon, andanalytsescolorsthroughtherotaationspeedofelementParticles.
Inmekaniikka, DescartesteSevelopeledTheyoryoftherelaticefgalileomotion.Forexample, julkaisussa "periaatteet filosofia", therearevivivexamplessuchasthewatchwheelsofseamyn'spocketwatcheseangoingshipsInvoyage, tosillustrathepRincipleofchoosingareferenceFrameformotionandstatic.
Sisällyttäjä "periaatteet filosofia", descartestedescribedTheLawofinertArelatectiveCleTyintHeformOfirStandSecondLawSofNature.AndmovealongthesAMESTRAIGHLINEUNTILITENCOUNSOBSTACLESORDEVIATIONSCAUDBYSOMEEXTERNALCAUCE.Täältä henkilöstöhäiriö.
IntSChapter, HealSoclearly ProposedTheLawOfConservationOfMomentumfortHefirstTime: TheTetalamountfMatterandMotionwillalwaintHesame.LaidthefoundationForthelawofconservationfenergy.
Descartesdiscoveredtheoriginalformoftheprincipleofconservationofmomentum(themomentumdefinedbyDescartesisanabsolutevalue,notavector,sohisprincipleofconservationofmomentumwaslaterprovedtobewrong-A.
DescartesdidreliminaryResearchonissuessuchascollioniondcentrifugalforce, joka on luonut.
Tähtitiede
DescartesappledhismekanistiewTocelestialBodies.HebelievesthatiitiseaerTounderstandThingsfromThePerveplopmentRathertHanJustObservingFromexistringForms.Hefoundhewhirlpooltheory.HethinksThattherearehugeVorticesandstarSaroundTheSun.
HebelievesthatthemovmentfecelestalBodiescomesfromtheinertiadThePressureOfcartCosmicmaterialVortExoncelestialBodies.Se.TämäHypoTheisisisolledToLinTheInter-CelestialBodyInteraction.Descartes'sModeloftheetherocOrtexOftheoriginoftheSunreliedOnMechanicsInsteafOfofTheOlogyForthefirstimeToexplainthormorationProcessOfcelestialBodes, thesun, planeetit, satelliitit, komeetit jne..ITWASACENURYEALIERTHANKANT'NSNEBULA, JA WASTHEMOSTATHORITIAVIONTHE17THENTY.Kosmologia.
Descartes’theoryofcelestialbodyevolution,vortexmodel,andclose-rangeactionviews,justlikehisentireideologicalsystem,ontheonehandfeaturesrichphysicalthoughtsandrigorousscientificmethods,andactsagainstscholasticphilosophyTheroleofinspiringscientificthinkingandpromotingtheadvancementofnaturalscienceatthattimehadaprofoundimpactonthethinkingofmanynaturalscientists;ontheotherhand,theyoftenstayedintheintuitiveandqualitativestageinsteadofstartingfromquantitativeexperimentalfacts,sosomeconcreteconclusionsareoftenThereweremanydefects,whichbecamethemainantithesisofNewtonianphysics,whichledtowidespreadcontroversy.
HebelievesthattherearehugeVorticesaroundTheSun, jonka mukaan.PARTICKLESOFMATTERAREINIFIEFIEFIEDVORTEX- JA THEETHEEEEELENTSOFEARTH, AIRADANDFIREADEDIFREENTEDTIONDURNEMOVEMENT.TheEearthformsThePlanet, jaTheFireformSTheSunandthestars.
HealSodeveloded TheoreettleToriessuchasthetheoryOfcosmicevolutionAndVortexteory.Vaikka he ovat spesifisiä teorioita.
Matematiikka
HeSimportrantContributionOfdescartestomathematicsisThecreationofanalyticgeometria.Inthedescartesera, algebrawasstillarelatiivisestiNewsubject, andgeometrictHinkingstilloccupiesAdominantPositioninThemindsofMathematicians.DescartesteDotedhimselfTotestudyftheconnectionbetbetwaalgebradgeometrian ja.IN1637, AfterThecreationofTheCoordinatesteem, Analyyttinen geometriaWassuccessly -luvussa.HerachievementLaidThefoundationForthcreationofcalculus, joka.AnalyyttinenGeometrySStillOneOftheMortantMathematicalMethodSuntilnow.
DescartesnotOnlyputforwardThemaintHinkingMethodofanalyticGeometria.Inhisbook "Geometria", DescartesescombinedLogic, Geometria ja AndalgebraicMethods.Bydiscussingdrawingproblems, heoutlineDewmethodofanalyticgeometria.Sincethen, NumbersandShapeshaveCometogether ja thenumberAxisisNumberAndShape.FirstContact.AndtoproveTheTheworldthatGeometricProblemscanberedtedtoalgebraicproblems, butalsothroughalgebraictransformationToDiscoverandproveGeometricproperties.DescartesEnTratedTheConcepTOfcoordinatesTemandlinesgment -operations.Heinnovatiivisesti 'transloitu'GeometricfiguresIntoalgebraicequationStoSolveGeometricproblemsalgebracal.ThisistoDayn "analyyttinenGeometria" tai "koordinaattigeometria".
ThecreationofanalyticGeometryisanepoch-valmistusturvatuspointTheHistoryOfmatematiikka.THEPLANERECTUNGULLORCOORDINATESTESTEMISTEEBASISFORTESTABLINGONFANYYTICGEOMETRIA.ThecreationofthecartesianCoordinatesystembuiltabridgebetweengebradgeometria.ITENABLEDEMETRICCONCESTTOBEEXPRESTINGINGEBRAICFORM, Andgeometric FiguresCouldalsObeexpressedingebraicform, soalgebradgeometryBecameafamily.
INDADDION, ManyMathematicalSymbolsusedNowarethefirstudedByDesCartes, jollei tiedossa olevaa numumbersaa, B, CandunknownNumbersx, Y, Z jne.., aswellasexponentialekspressions.HealSoDiscoveredtherelationshipBetweentheedges-, Pictices- ja FacesofaConvexPolyHedron, Mortedingastheeuler-DescartesFormula.HealSoDiscoveredTheCommoncartesianfraktallinecalculus.
CartesianCoordinatesteem
Inmathematics,CartesianCoordinatesteem(CartesianCoordinatesteem-A,alsoknownasRectangularcoordinatesystemisanorthogonalcoordinatesystem.Thetwo-ulottuvuus-.Sisäinen.IntthipLane, vastaava.
GeometricshapescanbeclearlyekspressedbyalgebraicFormulas.THERECECECTANCULORCOORDINATESOFEACHPOINTEGEOMETRICSHAPEMUSTCOMPLYWITHTHISALGEBRAICFORMULA.
TheCartesianCoordinatesteemwascreatedbytheFrenchmathematicianRenéDescartes.IN1637, DescartesPuledhismasterpiece "Metodologia".TÄMÄ KIRJOITETTUTTOTHESTUDYADDESCUSSIONOFLESTERNSCHOLARSHIPMETHODSPROVEDMANYCOREDSIGHTSICEDGoodSUGGESTIONS, ja MADEAGREATCONTRIBUTIONTOTHEELATIONEVELTUMINEN.
InorderToShowtheadvantagesandEffectsOftHenewMethod, jatoHelphImpersonyScientificresearch, Headdedentherbook "Geometria" "TotheappendixOf" Metodologia ".TheresearchontheCartesianCoordinatesteemappearsinthebook"Geometry".
Descartes'researchontHecoordinatesystemcombinesalgebraandeuclideangeometria, AndhasakeyinsightInTolaterAchievementsInanalyticGeometria, laskenta, andcartografia.
Anekdootti: SpiderWebsandThePlanerEctangularCoordinateSystem
ItissaidthatonedaydescartesfellinbedandwasinaverySeriouscondition.Siitä huolimatta HeialSothoughtBoutaquestonagainandagain: GeometricfigureseIntuitiivinen, andalgebraicequationsarerelactivebstrakti.Cangeometric FiguresandalgebraicequationsBecombined, se, se, cangeometric figuresbeuseExpressequations? ToachievethisGoal, theKeyishowtoHOOKUpThePointsThatMakeUptheGeometrCuresAndeachSet Of "Numerot" thatsfytheeeequationing."Kytkeä.Yhtäkkiä hesawaspideronthecorneroftheroof, vedäthreadandHangingdown.AfterAwhile, thespiderclimbedupthethreadagain, piirustukset.Thespiderin "esitys" Madedescartes'hinkingsuddenlyopen.Hethought, ThespiderCanBereGardedasapoint.Hecanmoveup, alas, vasemmistolainen.PystyyPidespiderbeTetMedByaseTofnumbers?.IFTHECORNERSONTHEGROUNDWERETEAKANASTHESTARTINGPOINTIADTHETHREELINESWERETEENASTHETHREENPERAXES, ThentHePositionOfanPointInthesPaceCeCeLeonthesetReelines.FindthreenumbersinorderonTheMumberline.Päinvastoin, mikä tahansa.Inthesameway,asetofnumbers(X,Y-Acanrepresentapointontheplaneandapointontheplane.ITCANALSOBEREPRESENTEDBYASETOFTWOSEQUENTENTNUMBERS, joka onTheProTypeftheCoordinatesystem.
Thelawofdescartessigns
ThelawofdescartessignswasfirstdescribedbyDescartesinhiswork"LaGéométrie",Isamethodfordeterminingthenumberofpositiveornegativerootsofapolynomial.
JostheOne-variablerealcoefficePolynomialisarrangedIndescendscendpown, niin lukumäärä,.Sucas5,3,1or4,2,0.SittenTerOfNegativerootsisTheNumberofChangesInthesignOfthePolynomialObTanedAfterTheCoefficientSofdd-OrderTerMsArchanged, Oramultipleof2lessThanit.
SpecialCase: NotHetHatifyOukThatThePolynomialHasonlyRealroots, YouCanusethismethodTocompetelyDeterMinetHenMumberofPosiveroots.SincetherePeatAbility OfzerorootsiseasyTocalculate, sitten lukuun.ThenthesymbolsofallrootscanbedeTermid.
Euler-Descartesformula
Theeuler-DescartesformulaisAMORMULEGEOMETRY.
Thecontentoftheformulais:inanyconvexpolyhedron,letVbethenumberofvertices,Ebethenumberofedges,andFIsthenumberoffaces,thenV−E+F=2.
Tämä formulawasfirstprovedbyfrenchmathematiciandescartesaround1635, butishnotnery.Thepost-SvissmathematicianleonHardeulerinderinPendenyProvedThisformain1750.Vuonna 1860 Descartes WorkSerdecided ja TheThorMormulawasThecalledeuler-Descartes Formula.
Cartesianfoliage
TheCartesianfoliageisanalgebraiccurve,firstproposedbyDescartesin1638.
Thectrartesianlobedlineare
TequationsInpolarCoordinatesare
ThenamecomesfromtheLatinwordfolium,whichmeans"leaf".
OMINAISUUDET OFCURVE:
Usingthepoint-slopeequationofastraightline,wecanFindthetangentequationatthepoint(-A:
HorizontalandverticalTangent: milloin, CartesianLeavesthetangentHTHESHAPELINESHORIZONTAL.Niin:
Milloin, thetangnftheekartesianleafshapelineSvercalical.Niin:
Tämä katkaisu.Wecanseethatthecurvehastwohorizontaltonentsandtwoverticaltants.TheCartesianlobedlineissymmetricalabouty=x,soifthehorizontaltangenthasacoordinate(-A,theremustbeacorrespondingverticaltangentwiththecoordinate(-A.
ASYMPTOTE: THECURVESANASYMPTOTE: X+Y+A = 0
Theslopeofthisasymptoteis-1, molemmatxandyinterseptsyes-a.
ThestoryofDescartesandChristine'sheart-shapedline(thatis,theheartline-A
Sydänviiva
Siellä.
TheHeartlineisanepicycloidwithasharppoint.IntOtwords, kun AcrirclerollSalonganOtercirclewiththesameradius, thetrajectoryofapointonthecircleistheheartline.
Sydänviivaisakindofepicycloid,anditsnis2.Itcanalsobeexpressedinpolarcoordinates:r=1+cosθ.ThePerimetROfSuchaheartlineS8 ja Inclosedareais.
TheHeartlineisalsoKindofCocklesline.
ThefigureinthemiddleofThemandeLbrotsetisHeartline.
EnglishNameOfTheHeartline "kardioid" WaspuledByDecastillonin "PhilosophicalTransactionsOftheroyociety" IN1741; se on "likeaheart".
IntheCartesianCoordinatesteem:theparametricequationoftheheartlineis:
whererIstheradiusofthecircle.Thecuspofthecurveislocatedat(r,0-A
Teekvityinthepolarcoordinesystemis:
ρ(θ-A=2r(1-cosθ-A
Alue:
Teekviiteettipolarkoordinatesistobeinvestigoitu, sen jälkeen.
"Testoryofmatematiikka" TalkdaboutTheLovestoryofMathematiciandesCartes.DescartestwasbornInfrancein1596.Whentheblackdeathbrokeotontheeuropeancontriant, HewanderedtoSweden.Hemet Kristina, 18-vuotias prinsessinasmallPrincipaalityinsweden, AndlaterbecamehermathTeacher.Princesstaylor, kuningas, BecamuriouswenhefoundoutAbouteachother, andordereddescartestobe Suoritettiin.Myöhemmin, koska tyttärentytär, hewasexiledTofrance.PrincessChristineSalsoplacedunderHousEearrestBySisfather.DescartescontraktedtheBlackDeathshortlyAfterReturningTofrance.Hewrotetetheprincesseveryday, butbecAusewasterceptedbyHeking, ChristineneverReceiveDaletterFromdesCartes.DescartestedAftersendmentHirThleTtertokristiini.Thethirteenthlettercontainedonlyashortformula:r=a(1-sinθ-A.THEKINGTOLLISETTUTTEETTÄMINEN.SheKnewThatTheLoverstilllovedher.ThegraphofTequationwasintheshapeofaheart.The PrincessESTABLEDEPOLARCOORDINATESYSTONPAPER, TracedThePointsOfthequationWithAPen, SawHeheartlinerepresentedbyequation, AndtunterstonedDescartes'Deeploveforherseld.Tämä "sydämenmuotoinen".
Jälkikäsittely, ChristinabecameEnthronandImEdiaalysentPeopleoookforhersweethearteverywhereeurope.TheHelplessPerson wordecoled, shetootostepFirst, poistuva...
ITISSAIDTHATTHISWORLD-RENOWLEDALTERNATIVELOVELTERISSSTILLPRESEDIDINTHEMEMEMORALHALLOFDESCARTESEUROPE.
Inhistory, descartesandchristinadidhavefriendships.Butdescartescametoswedenonoctober4,1649AtTheinvitaatiota.DescartesandchristinaTalkaBoutphilosoficalSuesratherthanmattematiikka.ITISDOCUMENTEDTHATDUETOTHTIGHTSCHEDULEOFQUENCHRISTINA, DESCARTESTOLLOLONLYDISCUSPHILOSOPHA.Sitä lukuun ottamatta.
Analyyttinen geometria
TherenaSanceEnAbleEROPeanscholarstoinherittheGeometryofancientGreeceandalsoAccepTHElgebrainTrainThered fromtheeast.EdellystencienceandtechnologyHasmadeteuseOfMatemaattisetMethodstodescriptSportSacentralissueOfConcern.DescartesanalysodtheadvantagesandDisadvantagesfgeometryandalgebra, sanoen,."
InVolume1of"Geometry"(apartof"Metodologia"-A,heusesthedistancefromapointontheplanetotwofixedstraightlinestodeterminethedistanceofapoint,andusescoordinatestodescribethespacePoint.HethenfoundedAnalyyttinen geometria,showingthatgeometricproblemscannotonlybereducedtoalgebraicforms,butalsocanberealizedthroughalgebraictransformationstodiscovergeometricpropertiesandprovegeometricproperties.
DescartestransformEdgeometryProblemsIntoalgebraicProblemsAndProPoosEAnifiedDrawingMethodforgeometricProblems.Tothisend, HeintrodecedUnitlinesegments, Aswellastheconceptsofdition, vähentäminen, kertolasku, jako ja neliömäiset, soastoconnectlinesmentSwithquantiteetti ja läpinäkyvätTherelationshipbetweenLinesegments, "findtwowayexpresstheSequanety., Thiswillformanequation ", jahenkilö.
IntSTHESECONDVolume, WhendesCartesuledThisNewMethodToSolVethepapsProblem, HeuseStRaightlineasTheBaselineOnThePlane, SpeciateAnStartingPointForit ja Selectedanotherinterinterinteringone.Strainat, joihin liittyy niin.Thenthepositionofanypointontheplanecanbeuniquelydeterminedwith(x,y-A.Papps'problemistransformedIntoaquadraticInDetERMinatEquationWithtwouns -tiedossa.DescartesppetededoutThatTheDegreeofThequationHasnothingTodowithTheChoiceOfTheCoordinatesysteem.
Kirja "geometria" asettaa ForwardthemainideasandMethodsofanalyticgeometria.Sincethen, HumansHaveEneredThestageOfvariablemathematics.
Incume3, descartesppetededoutthatanequationmayhaveasmanyrootsasitsdegree, andhealsoproposedthefamousdescarteslawofnotation: tHeraximumnumberofPositiverootsofanequationisequalTothesignOfITSCOEFICUSE.Thenumberoftimes;themaximumnumberofitsnegativeroots(whichhecalledfalseroots-Aisequaltothenumberoftimesthesigndoesnotchange.Descartesesalsoimprovedthesymbolystemcreatedbyvedic, käyttämällä, B, C, C,...merkitsemään tunnettuja määriä ja x, y, z,...Todenoteunknownquanties.
TheemergenceofanalyticGeometryChangedTheRendOfSePatiaationOfalgebradgeometrySinceanCientGreece,unifyingtheopposing"number"and"shape",andcombininggeometriccurveswithalgebraicequations.Tämä geniusCreationofdescartesLaidThefoundationForthcreationofcalculus.
ASengelSAID: "theturningpointInmattematicsiscartesianVariables.Varusteet, liikkeenmittausmiehet, muuttujien kanssa, dialektiikasta."
Psykologia
Descartes'ViewSandmaJordiscoveriesInpsychologyHadehaDaconsiderableIMAcTonlaterPsykologia.
HeisafamousRepresentativefmoderndualisMandidealismteoria.HISMAJORDISCOVERIESOFREFLECTIONADREFLECTIONARCPROVIDEDANIPORTANTBASISFORTHETHESESTUT "Eläinlääkärit".Andputforwardthehypoteesofresponse-stimulus.
Butdescartes’conceptofreflektionismekaaninen.Heempasoidu.Animalshavenominds, ButhumansHaveminds.SubinferenceistyypillinenManifestointi.Irrota, thatheoryofmindmindsympathyisanothertypicalmanifestationofdescartes'dualismintherelationshipbetbetbodyandMind.HebelievedThatTheHumanbodyisCompodefofOfMaterialtiteetti jaHumanMindisCompodefSpirityalenties.Heille.
HebelievesthattherearesixprimitiveMoTions ofoplot: yllätys, rakkaus, viha, halu, ilo ja sadness.Muilla kiskojenhoito-.
Vaikka dualisticpsychologyThoughtTheoreettisesti kirjoitettu, itWasveryPropelingandProgriveundUrthesocialBackground.HeulusdualismTogetridOftHEABSOLUTECONTROLOFSSCIENTYBYTHEOLOGIA.LeadingPeople'stHoghtStorationalThinkindandSpesificResearch, SohiscontributionTopsychologyCannotBeignery.
PolkumissionTotheTheyofinanct.TheauthorThomasAquinas(1225-1274-Aproposedtheconceptofinstinctandbelievedthatanimalshaveinstincts,buthumansdonot.Hearguedthathumanbeingshavedualnatures-materialandnon-material,orphysicalandmental(intellectual-A-butthelawsgoverningthematerialnatureofhumansaredifferentfromthosegoverninganimals.ThereasonForthisDifferenceSComesFromtheView, joka "ManisaspecialProductCreatedbygod".ManyLeScientsSargueevertheProfoundsimilartiesbetteranimalMotiveSandHumanMoties.Onthesurface, ihmisenandanimalsarekontrolledbythesamelaws, butthereseemstobeadifference.Descartesproposedanexplanationthatcanreconcilethesetwopointsofview:physicalbehavioratthelevelofvolitionalactioncanbeexplainedmechanically(instinct-A,butbehaviorrelatedtothingssuchasmoralconductisunderthecontrolofvolition.Descartesarguedthatthebodyandspirit(will,soul-Ainteract,andtheplacewheretheeffectoccursisthepinealgland.SeteryPhysicalbehaviors, sucassexualbehaviors, esiintyy.Tämä DualViewCanechothiewSOfScients jaTheCatholicchurchatThesametime.ItwasofPositivegnificanceatTheMetTime.
Karakkeet
Afterdescartes'death, histobomwasexcavedbyrobbers, andhisskullhaschangedhandsseveraltimes.ITISNOWINTHEMUSEEDEL ', PALAISDECHAILLOT, Pariisi, Ranska.Homme-A.
Descartesfirmlydenestherelationshipbetbetweenandthegermanrosicrucian, butthereManyCanincidencesInThercelastDocumentsHeleftbehind.HedoesnotadmitThaTitMaybebeCauseOftHurchatTheTime.
Descartessharedhisearlierresearchonthetegrationoomyometryandalgebrawithbeckman integrationdgeometrydalgebrawithbeckman, andoncesaid: "ifyouhavetheopportunity, yodontwanttoabandonmyresearchorideas."Se on,.Tämä MadedescartesSinsuld, SohecondemnedBeckmanin "tyhmyys."
Sosiaalistavarainti
DescartesisadualisistInfilosofyAdregardsGodasThecreator.ButdescarteswasamechanistwithinthescopeofnaturalScience.
DescarteeseONOfoundersOfModerneuropeanphilosofy.Hegelcalledhim "TheFatherofModernPhilosofy".Heformedhisownsystem, fusingmaterialismandidealismintoone, andhadaprofoundInfluenceinthehistoryoffilosofia.
Descartes'methodologyHasanImportantinfluenceonthelaterDevelopmentfysiikka.HecreadededidectionmethodbasedonMatematiikkaontheBasisofTheancientAdementMethod: Basefononrationalismi, startfromsfrom-avidentInneaxioms.TämäMethod, yhdessä.AsoneOfThemostsuccessfulexamplesofhisuniversalmethod, descartesutedalgebraicmethodstotosolvegeometricproblemsandesbabledthebasisofcoordinaatgeometria, thatis, analyyttinengeometria.
TwomorePointSareworthnotingindescartes'methodology.
Ensinnäkin Heisgoodatusintuitiiviset "mallit" toillustratephysicalfenomena.Forexample, "tennis" -malliselaatiottoillustratherefractionOflight; "blindman'scane" -käyttöinenTovisualizetheinstanntTransmissionFlightInformationgthematerial; GlassballfedwithwithisusedTosimulaTandsuccesslyxplaintherainbowhenomenon.
Toiseksi, pää-.Irrota, HealSoputforwardThePripleOf "GeneralsusPicion".Tämä PRANCIPLEPLAYEDAGREATROLEINOPPOSPONSCHURCHRULE, KAIKKI KAIKKI KAIKKI KORJAUS, ASIAKIRJOITTAMINEN, ANDADVOCATINGINSCIENICEUNDUNDERTEHISTORICALCONDitionSatThattime.
DescartescanBeregardeDasoneOfthemostinfluentialMastersineRopeanphilosofyandScienceInthe17thcenturyandbeyond, andheisknownasThe "AncestorofmodernScience".