
Re: Euclid's Elements Book 1 Proposition 1  something Euclid missed?
Posted:
Feb 15, 2014 5:01 PM


On Saturday, February 15, 2014 12:48:52 PM UTC8, 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 kitandcaboodle of calculus, continuity, &c.
The whole kitandcaboodle of the real numbers is not necessary. I believe that most, if not all, of Euclid can be modeled in the "surd plane" (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

