Phantom Theories of pre-Eudoxean Proportion

Bibliographic Data

ID4516234
AuthorsKen Saito (0000-0002-0771-1150, Osaka Prefecture University, corresponding author)
Year2003
Volume16
Issue3
Pages331-347
Publication date2003-09-01
Peer ReviewedYes
Open AccessYes
TypeARTICLE
VenueScience in Context (JOURNAL)
Journal identifiersISSN: 0269-8897 • E-ISSN: 1474-0664
PublisherCambridge University Press (CUP) (PUBLISHER)
DOI10.1017/s0269889703000838
OpenAlexW2087553425
LanguageEN
Citations received2
References cited11

ArgumentThis 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

Archaeology · Epistemology · Extant taxon · Geography · Geometry · Linguistics · Mathematical economics · Computer Science · History and Theory of Mathematics · Mathematics · Mathematics and Applications · Mathematics Education and Teaching Techniques · Philosophy

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