If P satisfies Huygens' construction, so that the secondary wavefront from P is tangential to W′ at B, then PB is a path of stationary traversal time from W to B. Adding the fixed time from A to W, we find that APB is the path of stationary traversal time from A to B (possibly with a restricted domain of comparison, as noted above), in accordance with Fermat's principle. The argument works just as well in the converse direction, provided that W′ has a well-defined tangent plane at B. Thus Huygens' construction and Fermat's principle are geometrically equivalent.