Euler’s De Fractionibus Continuis Dissertatio

Summary: This paper is a faithful presentation of Euler’s proof of the continued fraction expansion of the number e, with more details than in the original memoir E71. As remarked by Sandifer (2006) and Cretney (2014), Euler’s proofs are considerably detailed, and easy to follow by readers familiar with the mathematical literature of the time. Since not many modern readers are familiar with this literature, and requirements for formal details in proofs are stricter now than in Euler’s time, in this article we fill the gaps that a modern reader would likely find in the original source.