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1、SelectedworksofGIUSEPPEPEANOTranslatedandedited,withabiographicalsketchandbibliography,byHUBERTC.KENNEDYLondonGEORGEALLEN&UNWINLTDRuskinHouseMuseumStreetFirstpublishedin1973ThisbookiscopyrightundertheBerneConvention.Allrightsarereserved.Apartfromanyfai
2、rdealingforthepurposeofprivatestudy,research,criticismorreview,aspermittedundertheCopyrightAct,1956,nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,electronic,electrical,chemical,mechanical,optical,ph
3、otocopying,recordingorotherwise,withoutthepriorpermissionofthecopyrightowner.Enquiriesshouldbeaddressedtothepublishers.©UniversityofTorontoPress1973TorontoandBuffaloISBN0041640020PrintedintheUnitedStatesofAmericaContentsPrefaceIXLIFEANDWORKSBiographica
4、lsketchofGiuseppePeano3ChronologicallistofthepublicationsofGiuseppePeano11BibliographyonthelifeandworksofGiuseppePeano30TRANSLATIONSOFSELECTEDPUBLICATIONSIOntheintegrabilityoffunctions(1883)3711Differentialcalculusandfundamentalsofintegralcalculus(1884
5、)441Ananalyticexpressionforthefunctionwhichforrationalxequals0,andforirrationalxequals12AcounterexampletoatheoremofAbelonconvergentseries3Ageneralizationofthemeanvaluetheorem4AcounterexampletoacriterionofSerretformaximaandminima5Anexampleofafunctionwho
6、separtialderivativesdonotcommute6Maximaandminimaoffunctionsofseveralvariables7AnewdefinitionofthedefiniteintegralIIIOntheintegrabilityoffirst-orderdifferentialequations(1886)51IVIntegrationbyseriesoflineardifferentialequations(1887)58viCONTENTSvGeometr
7、icalmagnitudes(1887)671Pointsets2Areas3Volumes4IntegralsextendedtopointsetsVIThegeometricalcalculusaccordingtotheAusdehnungslehreofH.Grassmann,precededbytheoperationsofdeductivelogic(1888)751Theoperationsofdeductivelogic2GeometricalformationsVIITheprin
8、ciplesofarithmetic,presentedbyanewmethod(1889)101VIIIAnapproximationformulafortheperimeteroftheellipse(1889)135IXOnthedefinitionoftheareaofasurface1371Onthedefinitionoftheareaofasurface(1890).2Thedefinitionoftheareaofacurvedsurface(1903
