Residues arise... naturally in several branches of analysis... Their consideration provides simple and easy-to-use methods, which are applicable to a large number of diverse questions, and some new results...
"Oeuvres completes". Book by Augustin-Louis Cauchy (Serie 2, Tome 6, "Sur un nouveau genre de calcul analogue au Calcul infinitésimal", pp. 23-37, translated), 1826.