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 segment PQ — where P is a point on O x , Q a point on O y and PQ ⊥ Oy — grows indefinitely, i. e. can be made longer than any given segment”.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43033/1/22_2005_Article_BF01226859.pd
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