Prove that Euclid's Fifth Postulate is logically equivalent to Axiom P−1. This proof has two parts:
(a) Prove that Euclid's Postulate implies Axiom P−1. (Assume there are two lines through point P parallel to line ℓ in Figure 4.5, drop a perpendicular from P, and gain a contradiction using Euclid's Fifth Postulate.)
(b) Prove that Axiom P−1 implies Euclid's Postulate. (Any of the results of this section can be used because they are logical consequences of Axiom P−1.)
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