An essay on continued fractions

@article{Euler1985AnEO,
  title={An essay on continued fractions},
  author={Leonhard Euler},
  journal={Mathematical systems theory},
  year={1985},
  volume={18},
  pages={295-328}
}
The paper translated here, "De Fractionibus Continuis Dissertatio", represents Euler's first published work on the theory of continued fractions, a subject to which he often returned during his long career. The emphasis is on basic identities and analytic theory, culminating in the development of the continued fraction expansion for e. A discussion of the periodic continued fractions associated with quadratic irrationalities is also included, but applications to number theory come in later… CONTINUE READING