After looking for explanations of the Euler's continued fractions to compute exponential on internet and after reading Euler's explanations about, I still don't understand how Euler find this continued fraction :
$$e=2+\dfrac{1}{1+\dfrac{1}{2+\dfrac{1}{1+\dfrac{1}{1+\dfrac{1}{4+\dfrac{1}{1+\dfrac{1}{1+\dfrac{1}{6+\ddots}}}}}}}}$$ I understand how Euler get continued fractions to compute squares but not for exponential. Maybe I have missed something, but I really need to understand. So thanks for your help.