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1、PETERWOLFFisExecutiveEditorofTheGreatIdeasofToday,anannualsupplementtoGreatBooksoftheWesternWorld,publishedbyEncyclopaediaBritannica,Inc.HeisamagnacumlaudegraduateofSt.John’sCollege,wherehetaughtmathematicswhilecompletinghismaster’sthesis.Mr.Wolffworkedonth
2、eSynopticon,atwo-volume“ideaindex”fortheGreatBooksoftheWesternWorld,andwasAssistantDirectorandaFellowofSanFrancisco’sInstituteofPhilosophicalResearch,setupunderagrantfromtheFordFoundation.COPYRIGHT@1963BYPETERWOLFFAllrightsreservedTheauthorwishestothankthev
3、ariouspublishersandindividualswhopermittedtheselectionsinthisbooktobereprinted.Copyrightnoticesandcreditsaregivenonthefirstpageofeachselection.Thanksalsogototheauthor’sassistant,MaryFlorenceHaugen,forallherhelpandencouragementinconceivingandcompletingthisbo
4、ok.PLUMETRADEMARKREC.U.S.PAT.OFF.ANDFORElGNCO”NTRlESREGlSTERE”TRADEMARK--MARC*REGISTRADAHECHOENCLINTON,MASS.,U.S.A.SIGNET,SIGNETCLASSICS,MENTORANDPLUMEBOOKSarepublishedintheUnitedStatesbyTheNewAmericanLibrary,Inc.,1301AvenueoftheAmericas,NewYork,NewYork1001
5、9,inCanadabyTheNewAmericanLibraryofCanadaLimited,295KingStreetEast,Toronro2,Ontario,intheUnitedKingdombyTheNewEnglishLibraryLimited,Barnard’sInn,Holborn,London,E.C.I,EnglandFIRSTPRINTING,MARCH,1970PRINTEDINTHEUNITEDSTATESOFAMERICAbreakthroughsIn.mathematics
6、PETERWOLFFAPLUMEBOOKfromNEWAMERICANLIBRARYTIMESMlRRORNewYork,TorontoandLondonTOMYWIPB,PatriciaCONTENTSINTRODUCTIONixIGEOMETRYCHAPTERONEE&id-TheBeginningsofGeometry15CHAPTER‘IWOLobachevski-Non-E&deanGeometry63CHAPTERTHREEDescartes-GeometryandAlgebraJoined96I
7、IARITHMETICCHAPTERFOURArchimedes-NumbersandCounting113CHAPTERFIVEDedekind-IrrationalNumbers138CHAPTERSIXRussell-TheDefinitionofNumber161vii...VU1CONTENTSIIIADVANCEDTOPICSCHAPTERSEVENEuler-ANewBranchofMathematics:Topology197CHAPTEREIGHTLaplace-TheTheoryofPro
8、bability218CHAPTERNINEBoole-AlgebraandLogicJoined242SUGGESTIONSFORFURTHERREAIMNG277INDEX279INTRODUCTIONTheninemathematicianswhoseworksarerepresentedinthefollowingpagesareamongthemostfamousinthewholehis
