Investigation soon showed that certain integrals expressing relations between the motions not only of three but of any number of bodies could be found.
R 1.2 r1.3 r2.3 The theorems of motion just cited are expressed by seven integrals, or equations expressing a law that certain functions of the variables and of the time remain constant.
It is remarkable that although the seven integrals were found almost from the beginning of the investigation, no others have since been added; and indeed it has recently been shown that no others exist that can be expressed in an algebraic form.
Von Zeipel; the expression of definite integrals as determinants by A.
Riemann's results are contained in the memoirs on " Abelian Integrals," &c. (Crelle, t.