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Tableofcontents
Fromtheauthor.
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Introduction
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ChapterI
Theflyingarrow•Aristotle3sviewoftheaporiaofZeno•Itsinfluenceonthe
evolutionofgeometryandonthescienceofmotion•Democritus3sversion
ofthisaporia•Onmathematicalatomism.
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ChapterII
Aporiaofthewanderer•TheArchimedeanpostulate•TheEudoxianexhaustion
lemma•Non-Archimedeancontinua•AnotherZeno3sdifficulty:Stadium.
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ChapterIII
Number•Onidealisminmathematics•Itstwovarieties:Pythagoreism
andPlatonism•Discoveryofincommensurablesegments•TheEuclidean
algorithm•Onsomepossiblemeaningsoftheproportionofsegments
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ChapterIV
Ongeometricmagnitudes•Comparisonofpolygonsfromthepointofview
ofarea•Comparisonthroughcomplementation•Comparisonthroughfinite
decomposition•TheroleofArchimedeanpostulate•Onquadratures
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ChapterV
TheEudoxiantheoryofproportions•TheroleinitoftheArchimedeanpostulate•The
theoremoninterchangingtermsinaproportion•OnTales3stheorem•Comparison
withDedekindtheory•Inequalityofproportions•Ontheareaofacircle•On
Greekgeometricalgebra•TheElementsasanattempttogeometrizearithmetic
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