Axiom:Playfair's Axiom/Historical Note
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Historical Note on Playfair's Axiom
Playfair's axiom was not actually originated by John Playfair. He merely published it.
However, when he did so, he credited others, specifically William Ludlam, for having used it earlier.
It is a frequently seen alternative presentation of Euclid's Fifth Postulate.
It can easily seen to be equivalent to that given by Euclid, and it can be argued that it is easier to understand.
Texts on analytic geometry often gloss over its intrinsic significance, merely deducing it from the general equation of a straight line and the point of intersection of two such.