Of course, merely listing a set of constructions is not sufficient to talk about a geometrical theory, so it has to be shown, as it is indeed done by Suppes, that a formal-axiomatic treatment is possible. It suffices to list a set of necessary axioms about the \(B\) and \(D\) operations, so that one can prove that the figure drawn in the example above is indeed a parallelogram. In addition a representation theorem is proven such that points are attributed rational coordinates.