"Euler wrote... Introductio in Analysin infinitorum, 1748, which was intended to serve as an introduction to pure analytical mathematics. ...He ...showed that the trigonometrical and exponential functions are connected by the relation cos\theta + isin\theta = e^{i\theta}. Here too we meet the symbol e used to denote the base of the Naperian logarithms, namely the incommensurable number 2.7182818... The use of the single symbol to denote the incommensurable number 2.7182818... seems to be due to Cotes, who denoted it by M. Newton was probably the first to employ the literal exponential notation, and Euler using the form a'z, had taken a as the base of any system of logarithms. It is probable that the choice of e for a particular base was determined by its being a vowel consecutive to a, or, still more probable because e is the initial of the word exponent."