Geometrical sense of Newton metods

New geometrical sense of Newton methods for solving the system of nonlinear equations (in infinite-measuring case — nonlinear operational equations) found by us, clarifies completely its inner mechanism. From the point of view of application it enables to explain empirically observed effects, to get a unified characterization of the method and its modification, to get a general theorem on the problem of local convergence and to get a quite clear vision of geometrical-dynamic nature of convergence problem on the whole (both local and global). The results obtained are demonstrated on the model example.