On Saturday, February 15, 2014 5:01:05 PM UTC-5, FredJeffries wrote: > On Saturday, February 15, 2014 12:48:52 PM UTC-8, Ken Quirici wrote: > > > > > > I'm beginning to think that Euclid takes a huge number of 'obvious' facts for granted. I'm beginning to think Euclid's elements can only REALLY be made rigorous by making the apparently simple geometry a subset of R^2 real analysis - the whole kit-and-caboodle of calculus, continuity, &c. > > > > The whole kit-and-caboodle of the real numbers is not necessary. > > I believe that most, if not all, of Euclid can be modeled in the "surd plane" >
Cool! I think Pasch's Theorem can be used to prove that 'missing' postulate that figures in Proposition 1.1. However the margin of my editing space is too narrow to hold the truly marvelous proof I have discovered.
But seriously I think it CAN be so used and I'm going to work up a proof.
Film at 11.
Many Thanks FredJeffries!
Ken > (see also "surd field") > > > > See Edwin E Moise's "Elementary Geometry from an Advanced Standpoint" > > > > From what I recall, Euclid missed a bunch of stuff such as order properties. > > > > And Pasch's axiom was not noticed until 1882