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. Many of Vater's conclusions – most prominently, his assertion of the late nature of the Pentateuch as compared to the historical books – mirror the independent work of
Wilhelm Martin Leberecht de Wette, whose
Beiträge zur Einleitung in das Alte Testament was published in 1806–7. Against de Wette, though, Vater supposed, based on historical book allusions to Deuteronomy, that at least some parts of Deuteronomy had existed prior to the collection of the Pentateuch. ==Writings==