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My question concerns the classical Desargues Theorem and its simplest version The small Desargues Theorem: Let $A$, $B$, $C$ be three distinct parallel lines and $a,a'\in A$, $b,b'\in B$, $c,c'\in C$,...

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\...