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1、EUCLID’SELEMENTSOFGEOMETRYTheGreektextofJ.L.Heiberg(1883–1885)fromEuclidisElementa,ediditetLatineinterpretatusestI.L.Heiberg,inaedibusB.G.Teubneri,1883–1885edited,andprovidedwithamodernEnglishtranslation,byRichardFitzpatrickFirstedition-2007Revisedandcorrected-2008ISBN978-0-615
2、1-7984-1ContentsIntroduction4Book15Book249Book369Book4109Book5129Book6155Book7193Book8227Book9253Book10281Book11423Book12471Book13505Greek-EnglishLexicon539IntroductionEuclid’sElementsisbyfarthemostfamousmathematicalworkofclassicalantiquity,andalsohasthedistinctionofbeingthewor
3、ld’soldestcontinuouslyusedmathematicaltextbook.Littleisknownabouttheauthor,beyondthefactthathelivedinAlexandriaaround300BCE.Themainsubjectsoftheworkaregeometry,proportion,andnumbertheory.MostofthetheoremsappearingintheElementswerenotdiscoveredbyEuclidhimself,butweretheworkofear
4、lierGreekmathematicianssuchasPythagoras(andhisschool),HippocratesofChios,TheaetetusofAthens,andEudoxusofCnidos.However,Euclidisgenerallycreditedwitharrangingthesetheoremsinalogicalmanner,soastodemonstrate(admittedly,notalwayswiththerigourdemandedbymodernmathematics)thattheynece
5、ssarilyfollowfromfivesimpleaxioms.Euclidisalsocreditedwithdevisinganumberofparticularlyingeniousproofsofpreviouslydiscoveredtheorems:e.g.,Theorem48inBook1.ThegeometricalconstructionsemployedintheElementsarerestrictedtothosewhichcanbeachievedusingastraight-ruleandacompass.Further
6、more,empiricalproofsbymeansofmeasurementarestrictlyforbidden:i.e.,anycomparisonoftwomagnitudesisrestrictedtosayingthatthemagnitudesareeitherequal,orthatoneisgreaterthantheother.TheElementsconsistsofthirteenbooks.Book1outlinesthefundamentalpropositionsofplanegeometry,includ-ingt
7、hethreecasesinwhichtrianglesarecongruent,varioustheoremsinvolvingparallellines,thetheoremregardingthesumoftheanglesinatriangle,andthePythagoreantheorem.Book2iscommonlysaidtodealwithgeometricalgebra,sincemostofthetheoremscontainedwithinithavesimplealgebraicinterpretations.Book3i
8、nvestigatescirclesandtheirproperties,andincludestheore
