An approximation technique, and its use by Wallis and Taylor (Q1205949)

A detailed description, analysis, and comparison of Chapters X and XI of \textit{J. Wallis} ``A treatise of algebra'' and \textit{B. Taylor's} ``A new method of computing logarithms''. Wallis deals with Davenant's problem: to approximate a given number as closely as possible by a rational number \(m/n\), where \(m\) and \(n\) are less than a given bound. Taylor's paper, as its title suggests, deals with finding rational numbers to approximate logarithms. The author explores the connections both works have with continued fractions. He argues that Wallis and Taylor, in their respective writings, did not see this connection, even despite Wallis's work on continued fractions. A warning: there are several misprints in the calculations and elsewhere in the author's paper.