 Following Alexander Geddes, he applied the fragmentary hypothesis to the whole of the Pentateuch, treating it as an aggregate of numerous minor documents that had been compiled together.Vater's major work, "Commentar über den Pentateuch" was published in three volumes in Halle between 1802 and 1806.This work's primary purpose was to advance the Supplementary Hypothesis against the earlier Documentarian endeavors of Jean Astruc, Johann Gottfried Eichhorn, and Karl David Ilgen.