Zum Stufenaufbau des Parallelenaxioms

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”.