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Definition 1. An affine plane is a pair $(X,\mathcal L)$ consisting of a set $X$ and a family $\mathcal L$ of subsets of $X$ called lines which satisfy the following axioms: Any distinct points $x,y\...

There are several well-known axiomatizations of Euclidean plane geometry, the language of which is usually considered to include at least the relations of incidence (point-line, point-segment, or ...