Further to my last question about the history of calculus terms, I am wondering about
- the etymology of differentiate
- the etymology of integrate
- why we speak of a "derivative", but we "differentiate" instead of "derive"
Please note that by "etymology" I mean the mathematical history of these terms.
This may get answered en route, but I am specifically interested in what (if any) relationship there may be between the ideas of "differentiating" (breaking apart) and "integrating" (putting together), and the fact that these two operations do in fact "undo" each other in mathematics, which is the essence of the Fundamental Theorem of Calculus.
EDIT: It just occurred to me that while "derivative" would seem to go with "derive", "differentiate" would go with "difference", and in fact "difference equations" were used by Leibniz when he developed calculus (although I don't know if he called them as such) - can anyone verify this?