"Butch Malahide" <email@example.com> wrote in message news:firstname.lastname@example.org... > On Apr 30, 7:14 pm, "Julio Di Egidio" <ju...@diegidio.name> wrote: >> >> As I gather it, what he says is that from Playfair's axiom and his >> lite-triangle axiom one can prove Pasch's axiom. But the two former >> axioms >> are common to Euclidean and non-Euclidean geometry, while Pasch's axiom >> is >> Euclidean only: hence the contradiction. > > Playfair's axiom? Isn't that the one that says that only one parallel > to a given line can be drawn through a given point not on the line? > That axiom is common to Euclidean and non-Euclidean geometry?
I had misread. Thank you and David Hartley for the feedback, after more reading I see he had nailed it since the beginning.