By Imre Tóth

Im Corpus Aristotelicum sind 18 Stellen nachweisbar, an denen Aristoteles dem fundamentalen euklidischen Theorem von der Gleichheit der Dreieckswinkelsumme formal entgegengesetzte Aussagen zitiert. Diese Aussagen entstanden beim Versuch von Geometern der Akademie, den Fundamentalsatz der euklidischen Geometrie auf indirektem Weg zu beweisen. Der Versuch führte jedoch zu keinem Widerspruch und Aristoteles hielt die replacement "euklidisch - nichteuklidisch" für unentscheidbar. In seinen Ethiken führt er sie als einziges Beispiel an, um die Wahlfreiheit des handelnden Subjekts zu illustrieren.

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