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  • Produktbild: The Evolution of the Euclidean Elements
  • Produktbild: The Evolution of the Euclidean Elements
Band 15

The Evolution of the Euclidean Elements A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry

Aus der Reihe Synthese Historical Library

Fr. 452.00

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

31.10.1980

Abbildungen

XI, 379 p.

Verlag

Springer Netherland

Seitenzahl

379

Maße (L/B/H)

23.5/15.5/2.2 cm

Gewicht

598 g

Auflage

Softcover reprint of the original 1st edition 1975

Sprache

Englisch

ISBN

978-90-277-1192-2

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

31.10.1980

Abbildungen

XI, 379 p.

Verlag

Springer Netherland

Seitenzahl

379

Maße (L/B/H)

23.5/15.5/2.2 cm

Gewicht

598 g

Auflage

Softcover reprint of the original 1st edition 1975

Sprache

Englisch

ISBN

978-90-277-1192-2

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  • Produktbild: The Evolution of the Euclidean Elements
  • Produktbild: The Evolution of the Euclidean Elements
  • 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.