Geo-odular axiomatics of affine spaces

The author proves in a purely algebraic way that any flat geo-odular space is an affine space and vice versa. This result gives a new axiomatics of affine spaces based on the concept of vectorization centered at a point (being a vector space) and on two identities describing the relation between vectorizations centered at any two points. par Such an approach admits a useful treatment in the framework of universal algebras.