"In its form, the contents of the memoir [Mémoire sur une propriété générale... (1826)] belongs to the integral calculus. Abelian integrals depend upon an irrational function y which is connected with x by an algebraic equation F((x,y))=0. Abel's theorem asserts that a sum of such integrals can be expressed by a definite number p of similar integrals, where p depends merely on the properties of the equation F((x,y))=0. It was shown later that p is the deficiency of the curve F((x,y))=0. The addition theorems of elliptic integrals are deducible from Abel's theorem. The hyperelliptic integrals introduced by Abel, and proved by him to possess multiple periodicity, are special cases of Abelian integrals whenever p = or > 3. The reduction of Abelian to elliptic integrals has been studied mainly by Jacobi, Hermite, Königsberger, Brioschi, Goursat, E. Picard and O. Bolza..."