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ScienceinMedievalWesternEurope-----HuHepeng•ThebeginningoftheMiddleAgesin476AD,thefalloftheRomanEmpire,abouttheendofthe15thcentury.Thehistoryofthismillenniumcanberoughlydividedintotwosections.Beforetheeleventhcenturyisoftenreferredtoasthedarkages,whenWesternEuropeintheChristiantheologyandphilosophyofdogmatismundertheruleofpeoplelosttheirfreedomofthought,productionrigid,slowtechnologicalprogress,mathematicalstagnation.Thesituationimprovedslightlyaftertheeleventhcentury.so•WesternEuropeanscientificdevelopmentwaslaggingbehindtheIslamicworld,theMediterraneanBasin,China,andIndiaandotherregions,fromthe12thcenturytocatchupagain.Andmainlyinastrology,medicine,mathematics,naturalsciences,socialsciencesandtechnology,etc.,•mathematics•GreekculturethroughtheRomanstothemedievallittle,thisismostlyreflectedinBoisis(about480~524)inthebook.Hisarithmeticprincipleisgenerallyaneo-PythagoreanmathematicianNikoMaosiarithmeticintroductiontranslation,butanumberofbrilliantpropositionsweredeleted.ThegeometryofBoisiswasbasedonEuclid'soriginalgeometry,butitwasnotprovedatallbecausehethoughttheproofwassuperfluous.•In529AD,theemperoroftheEastRomanemperorJustinTimberlakeclosedtheschoolinAthens,forbiddentostudyandspreadmathematics.Onceagain,thedevelopmentofmathematicssufferedaheavyblow.Afterhundredsofyears,commendablemathematicianisnumbered,andmostlyclergy.•AftertheCrusadeexpedition(1096~1291)sothatEuropeansaccesstotheArabcountriestoretaintheancientculturaltreasures.•TheytranslatealargenumberofArabicbooksintoLatin.SothecultureofGreece,IndiaandtheArabs,aswellasChina'sfourmajorinventionswillbespreadtoEurope.Italyislocatedintheeast-westhubofcommunications,hasgraduallybecometheneweconomicandculturalcenter.•12,13centuryEuropeanmathematicalcommunityrepresentativeisFibonacci,heintroducedtotheEuropeansinIndia-Arabiadigitalandbitvaluesystemnotation,andvariousalgorithmsinthecommercialapplication.China'slackofsurplussurgeryandtheSun-countDiophantinesolutionalsoappearsinthebookFibonacci.•The14th-centuryFrenchbishopOrsimintroducedtheideaofasub-indexnotationandacoordinatesystem,whichwasthetransitionfromastronomy,geography,latitudeandlongitudetomoderncoordinategeometry.BritishArchbishopBradWardin'sarithmetic,geometry,mechanicalworksalsohavegreatinfluence.ThefirstEuropeansystemoftrigonometrywaswrittenbyReggioMontanus.•KarlDan•DoctorofMedicine,the16thcenturyRenaissancerepresentativeofhumanism,themostimportantworksofmathematicsispublishedinNuremberg,DaShu(thefullnameofDaShu,oronalgebraiclaw),thebooksystemTherearemanynewconceptsandmethodsinalgebra,withsolutionstocubicandquarticequations(foundbyCalderan'spupilFerrari.Therootoftheequationinthebigtechniqueisusedtodiscusstheproblemofimaginaryrootsencounteredintheequation,forthefirsttimeasageneralnumberofoperations,realizethatifanequationhasavirtualroot,youshouldhaveandOftheconjugateofanothervirtualroot.•Bombelli,hispredecessorshavethisdisciplinetoadevelopmentclimax.PompeythinksthatnobodybutCaldanecangodeepintothesubjectofmathematics,butheisnotsatisfiedwiththeexpressionofKardan,soreadytowriteabook,withitsclearstatementsothatanyonecanDonothavetorelyonotherbooksandgrasptheknowledgeofalgebra,whichispublishedBomberleyalgebrabackground.InthebookBombleyintroducedtheimaginarynumber,formallygivenacleardefinitionofnegative.••TheVedasAppliedtotheMathematicalLawoftheTrianglesystem,describesasphericaltrianglewithallsixtrigonometricfunctions,whichmaybethefirstbookinWesternEurope.Anglesystemofthesphericaltriangleandplanartrigonometry.AstrologyAswetracetheastral-astronomicalbranchoftheancientscientificculture,itisnotdifficulttosenseandgraspthehistoricalcontextfromthesideofthehistoricalfootprintoftheMiddleAges.Becauseastronomicalastronomyitselfisspecial,itiscloselyrelatedtomedicine,literature,politicsandreligion.TheArabsinAstrology-thecontributionofastronomy,itisatouchofbrightlightintheMiddleAges.•Mostscholarsofthetimebelievedthatastrologywasanimportantcomponentofthewholesystemofknowledge,andthatBoitiuswasnoexceptioninhismasterpiece,TheComfortofPhilosophy.Hebelievesthattheplanet'soperationiscontrolledbytheimmortalgods,andfromthecelestialsphereofthestars,youcandeducetheearthlyaffairs.HealsoagreedwithPlato'sviewthateachplanethasitsowncorrespondingscale,constitutetheCelestialMusic,showingtheharmonyoftheuniverse.Therearealsosomedetailsofthecelestialsphere,drawingsomeofthecommonillustrationsintheAstronomicalBook-buttheydonotaddanynewknowledgetoastronomy.ThisphilosophicalworkwiththecontentoftheastrologywaslatertranslatedbytheKingofEngland,Alfred,attheendofthe9thcentury,tobetheAnglo-Saxonlanguage,Inthe14thcentury,whentheEnglishwriterGeorgeChaucertranslatedintoOldEnglish,Chaucerwasalsoascholarwhowasobsessedwithastrology.AstrologyintheRenaissanceInthe15thcentury,thechurch'sattitudetoastrologychangeddramatically.Forthemembersoftheearlychurch,suchasAtanachus,Cyril,Arnobos,GrandGregorian,Basil,andAugustine,allregardedastrologyasapaganpriesthood,Andtobecritical.Ofcourse,sincesomeoftheearlyastrologerwriterswereneo-Platonists,thismadethemawareof