Relates Evolutes to single paths in the Calculus of Variations. Proved in the general case by Darboux and Zermelo (1894) and Kneser (1898). It states: ``When a single parameter family of external paths from a fixed point has an Envelope, the integral from the fixed point to any point on the Envelope equals the integral from the fixed point to any second point on the Envelope plus the integral along the envelope to the first point on the Envelope, .''
Kimball, W. S. Calculus of Variations by Parallel Displacement. London: Butterworth, p. 292, 1952.