Playfair's implies Euclid's fifth postulate[edit source | editbeta]
Given that Playfair's postulate implies that only the perpendicular to the perpendicular is a parallel, the lines of the Euclid construction will have to cut each other in a point. It is also necessary to prove that they will do it in the side where the angles are less than two right angles, but this is more difficult.[9]