1. A method for the three-dimensional measurement of coordinates (xli, yli, zli) of a set of N predetermined points (Plij) of the surface of a mechanical part to be measured relatively to a predetermined reference system (Ro), and the direction cosines (cxthij, cythij, czthij) of the theoretical normals (Nthij) thereto are known at the theoretical points (Pthij) corresponding to said N predetermined points (Plij), and including: a preparatory phase, in which the coordinates (xoij, yoij, zoij) of N points (Poij), corresponding to said N predetermined points (Plij) of the surface of a first mechanical part taken as a standard part, are measured relatively to the reference system (Ro), an initialization phase, wherein N linear displacement measurements (loij) along said normals (Nthij) are simultaneously and respectively read on said N points (Poij) of said standard part, a measurement phase, wherein N linear displacement measurements (llij), simultaneously and respectively performed on said N points (Plij) of the part to be measured, corresponding to the N points (Poij) of said standard part, are read, a computation phase, in which the three-dimensional coordinates (xlij, ylij, zlij) of the N points of the part to be measured are computed from the three-dimensional coordinates (xoij, yoij, zoij) of the N points of said standard part, from the linear measurements (loij, llij) and from the direction cosines (cxthij, cythij, czthij) of the N theoretical normals at these points.