The physical problem treated here is to find the equations of motion for a point system subject to auxiliary conditions (constraints). In his analysis, Zermelo refers to a paper of Adolph Mayer (1899), in which the latter uses Gauss's principle to obtain solutions for several cases. Mayer gives uniqueness proofs for some simple cases (two inequalities as constraints). Zermelo both generalizes Mayer's observations and gives his own proof, which he prefaces with a geometric interpretation.