PL EN


Journal
2007 | 15 | 2(58) | 95-113
Article title

EUDOXOS VERSUS DEDEKIND

Authors
Title variants
Languages of publication
PL
Abstracts
EN
All through the XXth century it has been repeated that 'there is an exact correspondence, almost coincidence between Euclid's definition of equal ratios and the modern theory of irrational numbers due to Dedekind'. Since the idea was presented as early as in 1908 in Thomas Heath's translation of Euclid's Elements as a comment to Book V, def. 5, we call it in the paper Heath's thesis. Heath's thesis finds different justifications so it is accepted yet in different versions. In the paper its historical and mathematical version is reconstructed. We next reconstruct Eudoxos' theory of proportions in an axiomatic fashion. Finally, we show that Heath's thesis both in the historical and mathematical version is false. To this end a counterexample is given; it is based upon a specific interpretation of the uniform distribution theorem.
Journal
Year
Volume
15
Issue
Pages
95-113
Physical description
Document type
ARTICLE
Contributors
author
  • P. Blaszczyk, Akademia Pedagogiczna w Krakowie, Wydzial Matematyczno-Fizyczny, Instytut Matematyki, ul. Podchorazych 2, 30-084 Krak√≥w, Poland
References
Document Type
Publication order reference
Identifiers
CEJSH db identifier
07PLAAAA03226662
YADDA identifier
bwmeta1.element.8b9156a2-80fe-3c13-89f6-9a4758f95a8d
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