From the physical point of view, Weyl emphasized the roles of light propagation and free (fall) motion in revealing the conformal-causal and the projective structures respectively. However, from the mathematical point of view, Weyl did not use these two structures directly in order to derive from them and their compatibility relation, the metric field. Rather, Weyl regarded the metric and affine structures as fundamental and showed that the conformal and the projective structures respecti