Fragmente und Spuren nichteuklidischer Geometrie bei Aristoteles

In the Corpus Aristotelicum there are 18 passages where it can be shown that Aristotle quotes statements that are formally opposite to the fundamental Euclidean theorem of the sum of the angles in a triangle. These statements are the result of the attempt by the geometricians of the Academy to prove the fundamental approach of Euclidean geometry indirectly. However, the attempt did not result in contradiction and Aristotle felt that there was no way of deciding between the alternatives 'Euclidean - non-Euclidean'. In his Ethics this is the only example he uses to illustrate the freedom of choice of the active subject.


Imre Tóth, Universität Regensburg.