Abstract
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 onO x, Q a point onO y andPQ ⊥ Oy — grows indefinitely, i. e. can be made longer than any given segment”.
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Pambuccian, V. Zum Stufenaufbau des Parallelenaxioms. J Geom 51, 79–88 (1994). https://doi.org/10.1007/BF01226859
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DOI: https://doi.org/10.1007/BF01226859