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the notation e made its first appearance in a letter Euler wrote to Goldbach in 1731. He made various discoveries regarding e in the following years, but it was not until 1748 when Euler published Introductio in Analysin infinitorum that he gave a full treatment of the ideas surrounding e.
Euler gave an approximation for e to 18 decimal places
e = 2.718281828459045235
Tide said:Euler probably chose e for other reasons. He was a very modest man and not at all egotistical (http://www-history.mcs.st-andrews.ac.uk/HistTopics/e.html).