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The History of Mathematical Proof in Ancient Traditions /
Explores the nature of mathematical proof in a range of historical settings, providing the first comprehensive history of proof.
| Clasificación: | Libro Electrónico |
|---|---|
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2012.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover ; The History of Mathematical Proof In Ancient Traditions; Title; Copyright; Contents; Figures; Contributors; Note on references; Acknowledgements; Prologue: Historiography and history of mathematical proof: a research programme: ; Part I: Views on The Historiography of Mathematical Proof ; 1: The Euclidean ideal of proof in The Elements and philological uncertainties of Heiberg's edition of the text; Introduction; Reflections on the History of the Text of the Elements; A brief history of the ancient Greek texts; Direct and indirect traditions.
- The textual inventory in the case of the ElementsThe history of the text of the Elements in antiquity; New contributions to the textual inventory; Extent and nature of the textual divergences between versions of the Elements; Typology of deliberate structural alterations; Quantitative aspect; An example of a local variant; Questions of authenticity and the logical architecture of the Elements; The change in the order of vi. 9-13 ; From the substitution of proof to the phenomenon of double proofs: the example of x.105 ; The limits of Knorr's criteria.
- Conclusions: contributions and limitations of the indirect traditionAppendix; Bibliography; Editions and translations of versions of Euclid's Elements; Editions and translations of commentators; 2: Diagrams and arguments in ancient Greek mathematics: lessons drawn from comparisons of the manuscript diagrams with those in modern critical editions: Ken Saito and Nathan Sidoli ; Introduction; Heiberg's edition of Euclid's Elements; Editions of manuscript diagrams; Characteristics of manuscript diagrams; Overspecification; Indifference to visual accuracy; Diagrams in solid geometry.
- One diagram for multiple casesCorrecting the diagrams; Ancient and medieval manuscript diagrams; Diagrams and generality; Bibliography; Manuscripts; Modern scholarship; 3: The texture of Archimedes' writings: through Heiberg's veil; The texture of Archimedes' diagrams; Heiberg goes metrical; Heiberg goes three-dimensional; Heiberg goes iconic; The texture of Archimedes' diagrams: summary; The texture of Archimedes' text: the local level; An overview of Heiberg's practice of excision; Heiberg's practice of excision: close-up on Sphere and Cylinder.
- The texture of Archimedes' text: the global levelThe order of Archimedes' works; The dialect of Archimedes' works; The format of Archimedes' works; A close-up on the Method; The texture of Archimedes' writings: summary; Bibliography; Abbreviations used in this chapter; 4: John Philoponus and the conformity of mathematical proofs to Aristotelian demonstrations: Orna Harari; Philoponus on mathematical demonstrations; Essential predications; Causal demonstrations; Proclus on the conformity between mathematical proofs and Aristotelian demonstrations; Conclusions; Bibliography; Editions; Studies.