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The Evolution of the Euclidean Elements

A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry

  • Book
  • © 1975

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Authors:
  1. Wilbur Richard Knorr
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Part of the book series: Synthese Historical Library (SYHL, volume 15)

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-XI
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  2. Introduction

    • Wilbur Richard Knorr
    Pages 1-20

  3. The Side and the Diameter

    • Wilbur Richard Knorr
    Pages 21-61

  4. Plato’s Account of the Work of Theodorus

    • Wilbur Richard Knorr
    Pages 62-108

  5. A Critical Review of Reconstructions of Theodorus’ Proofs

    • Wilbur Richard Knorr
    Pages 109-130

  6. The Pythagorean Arithmetic of the Fifth Century

    • Wilbur Richard Knorr
    Pages 131-169

  7. The Early Study of Incommensurability: Theodorus

    • Wilbur Richard Knorr
    Pages 170-210

  8. The Arithmetic of Incommensurability: Theaetetus and Archytas

    • Wilbur Richard Knorr
    Pages 211-251

  9. The Geometry of Incommensurability: Theaetetus and Eudoxus

    • Wilbur Richard Knorr
    Pages 252-297

  10. Conclusions and Syntheses

    • Wilbur Richard Knorr
    Pages 298-313

  11. Back Matter

    Pages 314-379
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Keywords

About this book

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 discoveries by fifth-century Pythago­ reans, advancing through the achievements of Theodorus of Cyrene, Theaetetus, Archytas and Eudoxus, and culminating in the formal theory of Elements X; (2) to correlate the stages of this developing theory with the evolution of the Elements as a whole; and (3) to establish that the high standards of rigor characteristic of this evolution were intrinsic to the mathematicians' work. In this third point, we wish to counterbalance a prevalent thesis that the impulse toward mathematical rigor was purely a response to the dialecticians' critique of foundations; on the contrary, we shall see that not until Eudoxus does there appear work which may be described as purely foundational in its intent. Through the examination of these problems, the present work will either alter or set in a new light virtually every standard thesis about the fourth-century Greek geometry. I. THE PRE-EUCLIDEAN THEORY OF INCOMMENSURABLE MAGNITUDES The Euclidean theory of incommensurable magnitudes, as preserved in Book X of the Elements, is a synthetic masterwork. Yet there are detect­ able seams in its structure, seams revealed both through terminology and through the historical clues provided by the neo-Platonist commentator Proclus.

Bibliographic Information

  • Book Title: The Evolution of the Euclidean Elements

  • Book Subtitle: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry

  • Authors: Wilbur Richard Knorr

  • Series Title: Synthese Historical Library

  • DOI: https://doi.org/10.1007/978-94-010-1754-1

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: D. Reidel Publishing Company, Dordrecht, Holland 1975

  • Hardcover ISBN: 978-90-277-0509-9Published: 28 February 1974

  • Softcover ISBN: 978-90-277-1192-2Published: 31 October 1980

  • eBook ISBN: 978-94-010-1754-1Published: 06 December 2012

  • Series ISSN: 0082-111X

  • Edition Number: 1

  • Number of Pages: XI, 379

  • Topics: Classical Philosophy

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