Euler's method to compute the number Napier's constant

Question

I am asking about the original way that Euler did to calculate Napier's constant, I heard that he was able to compute its first 23 decimals.

Answer 1

The article Napier's $e$ - $e$ in Leonhard Euler's Introductio says that Euler used the series $$ e=1+{1\over 1}+{1^2\over 1\cdot 2}+{1^3\over 1\cdot 2\cdot 3}+\cdots $$ to obtain $$ e \approx 2.71828182845904523536028\cdots $$

Wikipedia cites Euler's original text, which confirms the story: