The origins of Euler's early work on continued fractions

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Abstract

In this paper, I examine Euler's early work on the elementary properties of continued fractions in the 1730s, and investigate its possible links to previous writings on continued fractions by authors such as William Brouncker. By analysing the content of Euler's first paper on continued fractions, 'De fractionibus continuis dissertatio' (1737, published 1744) I conclude that, contrary to what one might expect, Euler's work on continued fractions initially arose not from earlier writings on continued fractions, but from a wish to solve the Riccati differential equation. © 2014 Elsevier Inc.

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APA

Cretney, R. (2014). The origins of Euler’s early work on continued fractions. Historia Mathematica, 41(2), 139–156. https://doi.org/10.1016/j.hm.2013.12.004

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