The attempts of geometers to prove Euclid’s Postulate on Parallels have been up till now futile. However, no one can doubt this postulate and the theorems which Euclid deduced from it. Thus the notion of space includes a special property, self-evident, without which the properties of parallels cannot be rigorously established. The idea of a bounded region, e.g., the circle, contains nothing which depends on its absolute magnitude. But if we imagine its radius to diminish, we are brought without