Alfred

Alfred North Whitehead makes this claim in his The Axioms of Descriptive Geometry; I found it one of the more brilliant parts (so far) of the book:
"The independence of the Dedekind axiom of the other axioms, combined with the negation of the Euclidean axiom, is proved by considered as in section 12, Descriptive Space to be atetrahedral region in Projective Space, but confining ourselves to the points whose coordinates are algebraic numbers, as in the corresponding proof for Projective Geometry.
   The independence of the Dedekind axiom of the other axioms, combined with the Euclidean axiom, is similarly proved by considering Descriptive Space to be the region in Projective Space found by excluding a particular plane; and further, as before, we confine our consideration the points whose coordinates are algebraic numbers" (14-15).

I don't want to misexplain any of the terminology he uses (which I'm getting a grasp on myself) so I'll be lazy and say that you should look it up. But I want to know what everyone thinks on this statement. He seems pretty logically consistent although I think you'd have to start at the beginning of the book and go through to do sensical logical proofs.