Note 56 — APPENDIX II ON ABEL'S PROOF OF THE THEOREM OF V., §11
Reading edition
Bertrand (Calcul intégral, ch. 5) replaces the last step in Abel's argument by the observation that if and are both integrals of then is constant (cf. p. 39, bottom). It follows that the degree of the equation which defines can be decreased, which contradicts the hypothesis that it is irreducible.