In Grassmann's famous article Ausdehnungslehre from 1844 (the one where he introduces what has come to be famous as Grassmann algebra) he uses the termionology "form" in place of, as he explains in his introduction, "quantity" or really "magnitude" (namely German: Größe). He says that he does so because he finds "quantity"/"magnitude" to be too restrictive to capture what he has in mind.
Indeed, from a modern perspective what he has in mind and what he discusses at length in the bulk of the article is what today we call differential forms on Euclidean space. Maybe what he considers are only the constant differential forms on Euclidean spaces, but anyway.
Certainly one sees from this why he found "magnitude" to be too restrictive. But besides this it seems striking that where he says "form" we still say "form". Or is it again instead of still?
That's my question: is there a continuity of usage from Grassmann's terminology "form" to modern terminology? Or is it a coincidence that when we say "differential form" today, deriving from "linear form", that this happens to use the same word for the same concept as Grassmann did, who seems to have been motivated from more general ideas about "forms of thought".