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The use of Cauchy's method in proving the well-known Euler formula is anobject of many controversies. The purpose of this paper is to prove that theCauchy's method applies for convex polyhedra and not only for them, but alsofor surfaces such as the torus, the projective plane, the Klein bottle and thepinched torus.

Uma prova elementar da f\'ormula de Euler usando o m\'etodo de Cauchy