  As mentioned above, a projective geometry \(\Pi\) may be defined as an  equivalence class of affine geometries, that is, an equivalence class of projectively related affine connections [\(\Gamma\)]. Weyl  presented the details of his approach to projective geometry, which  uses the notion of autoparallelism of direction, in a set of lectures delivered in Barcelona and Madrid in the spring of 1922  (Weyl (1923a); see also Weyl (1921c)). Weyl began with the following  necessary and sufficient condition for the invariance of the  projective structure \(\Pi\) under a transformation  \(\Gamma \rightarrow \overline{\Gamma}\) of the affine  structure: 