The history of language epsilon-delta from Cauchy up to Weierstrass. Dedicated to Weierstrass 200th anniversary

We shall consider the genesis of ε–δ language in works of mathematicians of the 19th century. Although the symbols ε and δ were initially introduced in 1823 by Cauchy, no functional relationship for δ as a function of ε was ever specified by Cauchy. It was only in 1861 that the epsilon-delta method manifested itself to the full in Weierstrass’ definition of a limit. Bolzano in 1817 and Cauchy in 1821 gave the definition of a limit and a continuous function in the language of increments; Cauchy in 1823 applied the ε and δ in improving evidence Ampere theorem on the average, but Cauchy used the ε and δ as the final error estimate where δ does not depend on ε. The process of understanding the concepts of continuity and uniform continuity of went the hard way in the works of Stokes, Seidel, Riemann, Dirichlet, Raabe and many others. The full method of "epsilon-delta" was formed in the lectures of Weierstrass in 1861. The legend about Cauchy authorship was originated in the early XX century in the work of Lebesgue, and then repeated many times. Appeal to the sources allowed to correct this historic mistake.