Euclid—The Creation of Mathematics

  • Benno Artmann

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Benno Artmann
    Pages 1-2
  3. Benno Artmann
    Pages 3-10
  4. Benno Artmann
    Pages 17-46
  5. Benno Artmann
    Pages 61-71
  6. Benno Artmann
    Pages 79-91
  7. Benno Artmann
    Pages 97-107
  8. Benno Artmann
    Pages 135-149
  9. Benno Artmann
    Pages 161-182
  10. Benno Artmann
    Pages 223-228
  11. Benno Artmann
    Pages 255-265
  12. Benno Artmann
    Pages 271-278
  13. Benno Artmann
    Pages 283-302
  14. Back Matter
    Pages 321-349

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.


Euclid Euclid's elements Geometry Math Volume boundary element method development history of mathematics mathematics metaphysics object philosophy story tool university

Authors and affiliations

  • Benno Artmann
    • 1
  1. 1.GoettingenGermany

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag New York, Inc. 1999
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7134-5
  • Online ISBN 978-1-4612-1412-0
  • Buy this book on publisher's site