PL EN


2006 | 51 | 3-4 | 169-203
Article title

Ancient Geometry and Plato's Philosophy on the Base of Pappus' 'Comment on the Xth Book of Elements of Euclid'.

Authors
Title variants
Languages of publication
PL
Abstracts
EN
The article is treating of a new interpretation of ancient geometry (part I) and is willing to explain several mathematical and historical conceptions that were presented in Pappus' 'Comment on the Xth Book of 'Elements' of Euclid' (part II). Euclid's 'Elements' were a kind of 'intuitive model', quite different from the contemporary one, divested of the 'infinite space' notion. Reconstruction of the hermeneutic horizon of the ancient mathematics allows us to explain the structure and mathematics presented in the columns of the Xth book of 'Elements'. The following subjects were handled: (1) reasons for elimination of the Euclid's 'infinite space' notion and substituting it for Plato's Diad in ancient times, (2) basing geometry and searches over the incommensurable magnitudes on one distinguished line together with mathematical consequences, (3) differences in the way of thinking of ancient and contemporary mathematician. Scientific studies allow to qualify from the historical point of view the share in development of the incommensurable magnitudes theories presented by Theaetetus of Athens, Apollonius of Perga, Euclid and Eudoxus. In the article a reconstruction of the mathematical contents of the lost Apollonius' treatise on incommensurable magnitudes is also presented A traditionally established pattern of the development of geometry, according to which Euclidean geometry used to extend as theory basing on relatively unalterable outfit of the fundamental intuition as, for instance, Euclid's infinite space, continuum intuitions and metric intuitions (what is important, the first revolutionary change was a discovery of non–Euclidean geometry in the 19th century) cannot be sustained.
Discipline
Year
Volume
51
Issue
3-4
Pages
169-203
Physical description
Document type
ARTICLE
Contributors
author
  • Z. Krol, Instytut Filozofii i Socjologii PAN, Zaklad Teorii Poznania i Filozofii Nauki, ul. Nowy Swiat 72, 00-330 Warszawa, Poland
References
Document Type
Publication order reference
Identifiers
CEJSH db identifier
07PLAAAA02134501
YADDA identifier
bwmeta1.element.a4f65c65-df49-332d-990e-55074536ac8e
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