Another more recent proposition known as playfair 's axiom is similar to Euclid 's fifth postulate . Invariably the mistake was assuming some ` obvious ' property which turned out to be equivalent to the fifth postulate ( Playfair 's axiom ) . Although known from the time of Proclus , this became known as Playfair 's Axiom after John Playfair wrote a famous commentary on Euclid in 1795 in which he proposed replacing Euclid 's fifth postulate by his own axiom .