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The mathematical works of Bernard Bolzano PDF

729 Pages·2004·5.358 MB·English
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BernardBolzano:oilpaintingbyHeinrichHollpein(1839–1840) This page intentionally left blank The Mathematical Works of Bernard Bolzano Steve Russ Departmentof ComputerScience, Universityof Warwick,UK 1 3 GreatClarendonStreet,Oxfordox26dp OxfordUniversityPressisadepartmentoftheUniversityofOxford. ItfurtherstheUniversity’sobjectiveofexcellenceinresearch,scholarship, andeducationbypublishingworldwidein Oxford NewYork Auckland CapeTown DaresSalaam HongKong Karachi KualaLumpur Madrid Melbourne MexicoCity Nairobi NewDelhi Shanghai Taipei Toronto Withofficesin Argentina Austria Brazil Chile CzechRepublic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore SouthKorea Switzerland Thailand Turkey Ukraine Vietnam OxfordisaregisteredtrademarkofOxfordUniversityPress intheUKandincertainothercountries PublishedintheUnitedStates byOxfordUniversityPressInc.,NewYork ©OxfordUniversityPress,2004 Themoralrightsoftheauthorhavebeenasserted DatabaserightOxfordUniversityPress(maker) Firstpublished2004 Reprinted2006 Allrightsreserved.Nopartofthispublicationmaybereproduced, storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans, withoutthepriorpermissioninwritingofOxfordUniversityPress, orasexpresslypermittedbylaw,orundertermsagreedwiththeappropriate reprographicsrightsorganization.Enquiriesconcerningreproduction outsidethescopeoftheaboveshouldbesenttotheRightsDepartment, OxfordUniversityPress,attheaddressabove Youmustnotcirculatethisbookinanyotherbindingorcover andyoumustimposethesameconditiononanyacquirer BritishLibraryCataloguinginPublicationData Dataavailable LibraryofCongressCataloginginPublicationData Dataavailable TypesetbyNewgenImagingSystems(P)Ltd.,Chennai,India PrintedinIndia onacid-freepaperbyThomsonPress(India)Ltd. ISBN0198539304(Hbk) 10 9 8 7 6 5 4 3 2 InMemoriam JohnFauvel DavidFowler This page intentionally left blank Contents Listof Illustrations ix Abbreviations x Preface xii NoteontheTexts xx NoteontheTranslations xxiii Introduction 1 GEOMETRY AND FOUNDATIONS 11 ConsiderationsonSomeObjectsof ElementaryGeometry(BG) 25 ContributionstoaBetter-GroundedPresentationof Mathematics(BD) 83 EARLY ANALYSIS 139 TheBinomialTheorem, andasaConsequencefromitthePolynomialThe- orem, and the Series which serve for the Calculation of Logarithmic and ExponentialQuantities,provedmorestrictlythanbefore(BL) 155 PurelyAnalyticProof of theTheorem,thatbetweenanytwoValues,which giveResultsof OppositeSign,thereliesatleastonerealRootof theEquation (RB) 251 The Three Problems of Rectification, Complanation and Cubature, solved without consideration of the infinitely small, without the hypotheses of Archimedesandwithoutanyassumptionwhichisnotstrictlyprovable.This isalsobeingpresentedforthescrutinyof allmathematiciansasasampleof acompletereorganisationof thescienceof space(DP) 279 vii Contents LATER ANALYSIS AND THE INFINITE 345 PureTheoryof Numbers Seventhsection:InfiniteQuantityConcepts(RZ) 355 Theoryof Functions(F) 429 ImprovementsandAdditionstotheTheoryof Functions(F+) 573 Paradoxesof theInfinite(PU) 591 SelectedWorksof BernardBolzano 679 Bibliography 685 NameIndex 691 SubjectIndex 693 viii List of Illustrations Frontispiece i BGTitlepage 24 BGDedicationpage 28 BGDiagramspage 81 BDTitlepage 82 BLTitlepage 154 RBTitlepage 250 DPTitlepage 278 DPDiagramspage 344 TheBolzanofunction 352 RZmanuscriptfirstpage 356 Fmanuscriptfirstpage 436 Fmanuscriptpage 447 PUTitlepage 590 ix

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