IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-031-81414-3_24.html
   My bibliography  Save this book chapter

The Reconstruction of Theaetetus’ Theory of Ratios of Magnitudes

In: Essays on Topology

Author

Listed:
  • Stelios Negrepontis

    (Athens University, Mathematics Department)

  • Dimitrios Protopapas

    (Athens University, Mathematics Department)

Abstract

In the present chapter we obtain the reconstruction of Theaetotus’Theaetetustheory of ratios of magnitudes theory of ratios of magnitudes based, according to Aristotle’s Topics 158b, on the definition of proportion in terms of equal anthyphairesis. Our reconstruction is built on the anthyphairetic interpretation of the notoriously difficult TheaetetusPlatoTheaetetus 147d6-e1 passage on Theaetetus’ mathematicalTheaetetus discovery of quadratic incommensurabilities, itself based on the traces it has left on Plato’sPlato philosophical definition of Knowledge in his dialogues Theaetetus, Sophist and Meno. Contrary to earlier reconstructions by Becker, van der Waerden and Knorr, our reconstruction reveals a theory that (a) applies only to the restricted class of pairs of magnitudes whose anthyphairesis is finite or eventually periodic, and (b) avoids the anachronistic use of Eudoxus’EudoxusDefinition V.4 definition 4 of Book V of Euclid’s Elements.

Suggested Citation

  • Stelios Negrepontis & Dimitrios Protopapas, 2025. "The Reconstruction of Theaetetus’ Theory of Ratios of Magnitudes," Springer Books, in: Louis Funar & Athanase Papadopoulos (ed.), Essays on Topology, chapter 0, pages 593-652, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-81414-3_24
    DOI: 10.1007/978-3-031-81414-3_24
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-031-81414-3_24. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.