TITLE: Who was the first to prove $\lim_{x \to 0} \frac{\sin{x}}{x}=1 $?
QUESTION [12 upvotes]: Who was the first to prove $\lim_{x \to 0}\frac{\sin{x}}{x}=1$?

REPLY [2 votes]: The first person to set out this limit explicitly, as far as I know, was Cauchy in his Cours d'analyse of 1821, pp. 66-67. See the English translation by Robert E. Bradley and C. Edward Sandifer, p. 45. Cauchy gives the limit again in his Resume des lecons (1823), lesson 1.