"8th. The mathematical theory of heat includes : first, the exact definition of all the elements of the analysis; next, the differential equations; lastly, the integrals appropriate to the fundamental problems. The equations can be... [obtained] in several ways; the same integrals can also be obtained, or other problems solved, by introducing certain changes in the course of the investigation. ...[T]hese researches do not constitute a method different from our own; but confirm and multiply its results."