No, epsilon-delta in the modern form was invented by Karl Weierstrass in 1861. Cauchy's approach was to define an infinitesmal as a sequence approaching 0, and

No, epsilon-delta in the modern form was invented by Karl Weierstrass in 1861. Cauchy's approach was to define an infinitesmal as a sequence approaching 0, and then to use the old infinitesmal definition of a derivative. This almost works. One of the places where it falls apart is defining the chain rule when the inner derivative is 0, because the sequence may wind up with 0/0 infinitely often. But it is from this definition that we get Cauchy sequences today.