In the 1920s, Heyting attempted at axiomatizing constructive geometry. Recently, von Plato used di4erent concepts to axiomatize the geometry: he used 14 axioms to describe the axiomatization for apartness geometry. Then he added axioms A1 and A2 to his apartness geometry to get his a8ne geometry, then he added axioms O1, O2, O3 and O4 to the a8ne geometry to get orthogonality. In total, this gi...