Zum Stufenaufbau des Parallelenaxioms
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Euclid's parallel postulate is shown to be equivalent to the conjunction of the following two weaker postulates: “Any perpendicular to one side of a right angle intersects any perpendicular to the other side” and “For any acute angle Oxy, the segmentPQ — whereP is a point onOx, Q a point onOy andPQ ⊥ Oy — grows indefinitely, i. e. can be made longer than any given segment”.
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[5] M. Dehn. Die Legendre'schen Sätze über die Winkelsumme im Dreieck , 1900 .
[6] A. Tarski,et al. Metamathematische Methoden in der Geometrie , 1983 .