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Phantom Theories of pre-Eudoxean Proportion

Published online by Cambridge University Press:  01 September 2003

Ken Saito
Ken Saito
Affiliation:
Osaka Prefecture University, Japan
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Abstract

Argument

This paper proposes an alternative view to Becker’s reconstruction of pre-Eudoxean theory of proportion. No extant document explicitly demonstrates the alleged alternation of theories of proportion before Book V of the Elements. Books V and VI of the Elements are not so complete as a theory of proportion in the abstract, and can be interpreted better as a collection of propositions useful in geometry. It follows then that older theories, if they existed at all, must have been less complete. Prevailing interest in geometry on the part of Greek mathematicians is also visible in some expressions in Book VI for specific ratio and proportion used only in definite geometric context. It is therefore more fruitful to consider the “theory” of proportion before Eudoxus as an aggregate of techniques about proportion that are useful in geometry, rather than as the result of a conscious effort to build a logically consistent set of propositions based on a definition.

Type
Articles
Information
Science in Context , Volume 16 , Issue 3 , September 2003 , pp. 331 - 347
Copyright
2003 Cambridge University Press

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