The theorem in question appears in his well-known paper of the year 1894, “Ueber die Elementartheiler der Determinanten.” Save that English takes the place of German, the enunciation of it stands exactly as follows:—

If ξ ≦ r ≦ s < n, and Dξbe any determinant of the nth order in the array

Dξ′ being its complementary minor of the (n − ξ)th order in the determinant of the nth order

then