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ISBN: 9789027705099
[ED: Buch], [PU: Springer Nature Singapore], Neuware - The present work has three principal objectives: (1) to fix the chronology of the development of the pre-Euclidean theory of incomme… Meer...

ISBN: 9789027705099
The present work has three principal objectives: (1) to fix the chronology of the development of the pre-Euclidean theory of incommensurable magnitudes beginning from the first discov… Meer...

ISBN: 9789027705099
[ED: Buch], [PU: Springer], Neuware - The present work has three principal objectives: (1) to fix the chronology of the development of the pre-Euclidean theory of incommensurable magnitud… Meer...

ISBN: 9789027705099
Hardback, [PU: Springer], The present work has three principal objectives: (1) to fix the chronology of the development of the pre-Euclidean theory of incommensurable magnitudes beginning… Meer...

ISBN: 9789027705099
The present work has three principal objectives: (1) to fix the chronology of the development of the pre-Euclidean theory of incommensurable magnitudes beginning from the first discoverie… Meer...
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Gedetalleerde informatie over het boek. - The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry W.R. Knorr
EAN (ISBN-13): 9789027705099
ISBN (ISBN-10): 9027705097
Gebonden uitgave
pocket book
Verschijningsjaar: 1974
Uitgever: Springer Netherlands Core >2 >T
385 Bladzijden
Gewicht: 0,712 kg
Taal: eng/Englisch
Boek bevindt zich in het datenbestand sinds 2007-04-18T13:38:19+02:00 (Amsterdam)
Boek voor het laatst gevonden op 2024-11-25T13:21:43+01:00 (Amsterdam)
ISBN/EAN: 9027705097
ISBN - alternatieve schrijfwijzen:
90-277-0509-7, 978-90-277-0509-9
alternatieve schrijfwijzen en verwante zoekwoorden:
Auteur van het boek: knorr wilbur richard, proclus
Titel van het boek: the evolution the euclidean elements study the theory incommensurable magnitudes and its significance for early greek geometry, euclide, the elements euclid
Gegevens van de uitgever
Auteur: W.R. Knorr
Titel: Synthese Historical Library; The Evolution of the Euclidean Elements - A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry
Uitgeverij: Springer; Springer Netherland
379 Bladzijden
Verschijningsjaar: 1974-02-28
Dordrecht; NL
Taal: Engels
374,49 € (DE)
384,99 € (AT)
413,00 CHF (CH)
Available
XI, 379 p.
BB; Hardcover, Softcover / Philosophie/Antike; Antike griechische und römische Philosophie; Verstehen; Plato; bibliography; chronology; construction; dialectic; editing; event; evolution; foundation; interpret; present; reconstruction; structure; style; triangle; Ancient Philosophy / Classical Philosophy; BC; EA
I / Introduction.- I. The Pre-Euclidean Theory of Incommensurable Magnitudes.- II. General Methodological Observations.- III. Indispensable Definitions.- II / The Side and the Diameter of the Square.- I. The Received Proof of the Incommensurability of the Side and Diameter of the Square.- II. Anthyphairesis and the Side and Diameter.- III. Impact of the Discovery of Incommensurability.- IV. Summary of the Early Studies.- III / Plato’s Account of the Work Of Theodorus.- I. Formulation of the Problem: ????µ???.- II. The Role of Diagrams: ???????.- III. The Ideal of Demonstration: ??????????.- IV. Why Separate Cases?.- V. Why Stop at Seventeen?.- VI. The Theorems of Theaetetus.- VII. Theodoras’ Style of Geometry.- VIII. Summary of Interpretive Criteria.- IV / A Critical Review of Reconstructions of Theodorus’ Proofs.- I. Reconstruction via Approximation Techniques.- II. Algebraic Reconstruction.- III. Anthyphairetic Reconstruction.- V / The Pythagorean Arithmetic of the Fifth Century.- I. Pythagorean Studies of the Odd and the Even.- II. The Pebble-Representation of Numbers.- III. The Pebble-Methods Applied to the Study of the Odd and the Even.- IV. The Theory of Figured Numbers.- V. Properties of Pythagorean Number Triples.- VI / The Early Study of Incommensurable Magnitudes: Theodorus.- I. Numbers Represented as Magnitudes.- II. Right Triangles and the Discovery of Incommensurability.- III. The Lesson of Theodorus.- IV. Theodorus and Elements II.- VII / The Arithmetic of Incommensurability: Theaetetus and Archytas.- I. The Theorem of Archytas on Epimoric Ratios.- II. The Theorems of Theaetetus.- III. The Arithmetic Proofs of the Theorems of Theaetetus.- IV. The Arithmetic Basis of Theaetetus’ Theory.- V. Observations on Pre-EuclideanArithmetic.- VIII / The geometry of incommensurability: Theaetetus and Eudoxus.- I. The Theorems of Theaetetus: Proofs of the Geometric Part.- II. Anthyphairesis and the Theory of Proportions.- III. The Theory of Proportions in Elements X.- IV. Theaetetus and Eudoxus.- V. Summary of the Development of the Theory of Irrationals.- IX / Conclusions and Syntheses.- I. The Pre-Euclidean Theory of Incommensurable Magnitudes.- II. The Editing of the Elements.- III. The Pre-Euclidean Foundations-Crises.- Appendices.- A. On the Extension of Theodoras’ Method.- B. On the Anthyphairetic Proportion Theory.- A List of the Theorems in Chapters V-VIII and the Appendices.- Referencing Conventions and Bibliography.- I. Referencing Conventions.- II. Abbreviations used in the Notes and the Bibliography.- III. Bibliography of Works Consulted: Ancient Authors.- IV. Modern Works: Books.- V. Modern Works: Articles.- Index of Names.- Index of Passages Cited from Ancient Works.Andere boeken die eventueel grote overeenkomsten met dit boek kunnen hebben:
Laatste soortgelijke boek:
9789401017541 Evolution of the Euclidean Elements (W.R. Knorr)
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