The mathematical works of Bernard Bolzano

729 Pages·2004·5.358 MB·English

by  Steve Russ

BernardBolzano:oilpaintingbyHeinrichHollpein(1839–1840)
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The Mathematical
Works of
Bernard Bolzano
Steve Russ
Departmentof ComputerScience,
Universityof Warwick,UK
1
3
GreatClarendonStreet,Oxfordox26dp
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InMemoriam
JohnFauvel
DavidFowler
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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