See what I mean? That should have been “as you get, etc., etc.”
“Euclidean geometry” as a field (distinct from “a Euclidean geometry” as a structure on a topological space) does indeed go beyond euclid proper, but it is marked by a very formal and austere character. To pick some unit is an arbitrary extra structure imposed for no gain but to call things by numbers rather than the shapes they are. Is there a canonical unit in physics? No, and to afford any unit canonical status would be anathema to the whole point.
Strictly speaking, very little of Newton’s and Leibniz’ (no ‘t’) work is seen in a modern calculus course. No fluxions, no fluents, and definitely no infinitesimals. We at least wave our hands at limits – a hallmark of the Cauchy/Weierstrass era – and go from there. Note that we also don’t call it “Newtonian calculus”.