On Systems of Curves on a Ring-Shaped Surface

Poincare, in his paper of 1885 entitled " Sur les courbes definies par les equations differentielles "* has devoted a whole chapter (pp. 137-158 of the Oeuvres) to the study, under certain restrictive assumptions, of the systems of curves defined on a ring-shaped surface by a differential equation of the first order. He makes use of the " method of consequents," which he has also successfully applied to other problems.