# An essay on continued fractions

@article{1985AnEO, title={An essay on continued fractions}, author={}, journal={Mathematical systems theory}, year={1985}, volume={18}, pages={295-328} }

- Published in Mathematical systems theory 1985
DOI:10.1007/BF01699475

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