# Lagrange's Theorem as he stated it

In Wikipedia, I found that Lagrange did not state Lagrange's Theorem in its general form. He stated

"If a Polynomial in $$n$$ variables has its variables permuted in all $$n!$$ ways, the number of different polynomials that are obtained is always a factor of $$n!$$."

Where can I find the proof he provided to this statement?

• .-L. Lagrange, « Réflexions sur la résolution algébrique des équations, II », Nouveaux Mémoires de l’Académie Royale des Sciences et Belles-Lettres de Berlin,‎ 1771, p. 138-254 (spéc. p. 202-203), réédité dans Œuvres de Lagrange, t. 3, Paris, 1869, p. 305-421. It's in the French wikipedia ref.4 with links ( gallica.bnf.fr/ark:/12148/bpt6k229222d.image.f370 ), – sand1 Nov 6 '20 at 17:36
• Is there an English translation to it? – Saikat Nov 7 '20 at 3:12