See the wonderful book by Judith Grabiner, [The Origins of Cauchy's Rigorous Calculus][1] (1981), page 140 : "Actually, his [Cauchy's] proof implicitly assumed the function to be uniformly continuous, though he did not distinguish between continuity and uniform continuity, just as he had not distinguished between convergence and uniform convergence."


  [1]: http://books.google.de/books?id=XuFcx-laQmIC&lpg=PP1&hl=de&pg=PP1#v=onepage&q&f=false