A unified derivation of the equations of Gauss, Weingarten, and of the affinity transformation is presented in non‐Riemannian geometry. These concepts from differential geometry are obtained here directly from the propagation derivative of the two‐point parallel propagator tensor. In order to measure the deviation of a surface from its tangent plane, the propagation derivative is written in terms of the projection, onto the surface, of the in‐space covariant derivative of the parallel propagator. Consequently, an expression is obtained which involves the unit vector normal to the surface rather than the unit vector tangent to a curve embedded in the surface. The desired concepts are, then, derived directly from this expression in a coherent manner.