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Euclid—The Creation of Mathematics

  • Book
  • © 1999

Overview

Authors:
  1. Benno Artmann

    1. Goettingen, Germany

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  • Euclid's treatment of mathematics and the presentation of its essential features has set the standard which remains today, and which every mathematician should know

  • Artmann reveals many pieces of beautiful mathematics from the Elements, which are easily accessible and can be studied in detail by anyone with a minimal training in math

  • Each book of the Elements is clearly described in detail, and proofs are given for important results

  • Modernized language is used to make the material more accessible to the reader

  • Includes general remarks about typical mathematical procedures of the day, subjects of historical interest, and connections to philosophy

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Table of contents (31 chapters)

  1. Front Matter

    Pages i-xvi
    Download chapter PDF

  2. General Historical Remarks

    • Benno Artmann
    Pages 1-2

  3. The Contents of the Elements

    • Benno Artmann
    Pages 3-10

  4. The Origin of Mathematics 1: The Testimony of Eudemus

    • Benno Artmann
    Pages 11-16

  5. Euclid Book I: Basic Geometry

    • Benno Artmann
    Pages 17-46

  6. The Origin of Mathematics 2: Parallels and Axioms

    • Benno Artmann
    Pages 47-50

  7. The Origin of Mathematics 3: Pythagoras of Samos

    • Benno Artmann
    Pages 51-60

  8. Euclid Book II: The Geometry of Rectangles

    • Benno Artmann
    Pages 61-71

  9. The Origin of Mathematics 4: Squaring the Circle

    • Benno Artmann
    Pages 73-78

  10. Euclid Book III: About the Circle

    • Benno Artmann
    Pages 79-91

  11. The Origin of Mathematics 5: Problems and Theories

    • Benno Artmann
    Pages 93-95

  12. Euclid Book IV: Regular Polygons

    • Benno Artmann
    Pages 97-107

  13. The Origin of Mathematics 6: The Birth of Rigor

    • Benno Artmann
    Pages 109-111

  14. The Origin of Mathematics 7: Polygons After Euclid

    • Benno Artmann
    Pages 113-120

  15. Euclid Book V: The General Theory of Proportions

    • Benno Artmann
    Pages 121-134

  16. Euclid Book VI: Similarity Geometry

    • Benno Artmann
    Pages 135-149

  17. The Origin of Mathematics 8: Be Wise, Generalize

    • Benno Artmann
    Pages 151-159

  18. Euclid Book VII: Basic Arithmetic

    • Benno Artmann
    Pages 161-182

  19. The Origin of Mathematics 9: Nicomachus and Diophantus

    • Benno Artmann
    Pages 183-191

  20. Euclid Book VIII: Numbers in Continued Proportion, the Geometry of Numbers

    • Benno Artmann
    Pages 193-201
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Keywords

About this book

This book is for all lovers ofmathematics. It is an attempt to under­ stand the nature of mathematics from the point of view of its most important early source. Even if the material covered by Euclid may be considered ele­ mentary for the most part, the way in which he presents it has set the standard for more than two thousand years. Knowing Euclid's Elements may be ofthe same importance for a mathematician today as knowing Greek architecture is for an architect. Clearly, no con­ temporary architect will construct a Doric temple, let alone organize a construction site in the way the ancients did. But for the training ofan architect's aesthetic judgment, a knowledge ofthe Greek her­ itage is indispensable. I agree with Peter Hilton when he says that genuine mathematics constitutesone ofthe finest expressions ofthe human spirit, and I may add that here as in so many other instances, we have learned that language ofexpression from the Greeks. While presenting geometry and arithmetic Euclid teaches us es­ sential features of mathematics in a much more general sense. He displays the axiomatic foundation of a mathematical theory and its conscious development towards the solution of a specific problem. We see how abstraction works and enforces the strictly deductive presentation ofa theory. We learn what creative definitions are and v VI ----=P:. . :re:. ::::fa=ce how a conceptual grasp leads to toe classification ofthe relevant ob­ jects.

Reviews

B. Artmann

Euclid - The Creation of Mathematics

"The author invites the ‘lover of mathematics’ to have a peek, via a gentle introduction and presentation of Euclid’s Elements, with detours to previous Greek geometers, whose work has been incorporated in the Elements. The contents of the Elements are presented book by book . . . with full statements of the definitions, axioms, propositions, and proofs involved. There are . . . notes to subsequent development of Euclidean themes . . . justifications of steps of proof and of the sequence in which results appear . . . An original and pleasing feature of the book consists in the references to Greek architecture, which emphasize the pervasiveness of the concern for proportion in Greek culture, as well as the references to archaeological finds of dodecahedra- and icosahedra-shaped objects."—AMERICAN MATHEMATICAL SOCIETY

Authors and Affiliations

  • Goettingen, Germany

    Benno Artmann

Bibliographic Information

  • Book Title: Euclid—The Creation of Mathematics

  • Authors: Benno Artmann

  • DOI: https://doi.org/10.1007/978-1-4612-1412-0

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1999

  • Hardcover ISBN: 978-0-387-98423-0Published: 10 June 1999

  • Softcover ISBN: 978-1-4612-7134-5Published: 21 October 2012

  • eBook ISBN: 978-1-4612-1412-0Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XVI, 349

  • Topics: Geometry

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