Gordon Keener % gbn0305181551: Archimedes, Geometrical Solutions Derived from Mechanics. Gordon Keener <gkeener@nc.rr.com>. 1909c. 5/19/2003. ok. \documentclass[12pt]{article} \usepackage[greek,english]{babel} \usepackage{wrapfig} \usepackage{graphicx} \title{Geometrical Solutions Derived from Mechanics} \author{A Treatise of Archimedes} \date{\vspace{\baselineskip} {\small Recently discovered and translated from the Greek by}\\ Dr. J. L. Heiberg\\ {\small Professor of Classical Philology at the University of Copenhagen}\\ \vspace{\baselineskip} {\small with an introduction by}\\ David Eugene Smith\\ {\small President of Teachers College, Columbia University, New York}\\ \vspace{\baselineskip} {\small English version translated from the German by}\\ Lydia G. Robinson\\ {\small and reprinted from ``The Monist,'' April, 1909}\\ \vspace{\baselineskip} {\small Project Gutenberg edition:\\ gbn0305181551: Archimedes, Geometrical Solutions Derived from Mechanics. Gordon Keener $<$gkeener@nc.rr.com$>$. 1909c. 5/19/2003. ok.} } \begin{document} \maketitle \vfill\pagebreak \section*{Introduction} If there ever was a case of appropriateness in discovery, the finding of this manuscript in the summer of 1906 was one. In the first place it was appropriate that the discovery should be made in Constantinople, since it was here that the West received its first manuscripts of the other extant works, nine in number, of the great Syracusan. It was furthermore appropriate that the discovery should be made by Professor Heiberg, \emph{facilis princeps} among all workers in the field of editing the classics of Greek mathematics, and an indefatigable searcher of the libraries of Europe for manuscripts to aid him in perfecting his labors. And finally it was most appropriate that this work should appear at a time when the affiliation of pure and applied mathematics is becoming so generally recognized all over the world. We are sometimes led to feel, in considering isolated cases, that the great contributors of the past have worked in the field of pure mathematics alone, and the saying of Plutarch that Archimedes felt that ``every kind of art connected with daily needs was ignoble and vulgar''\footnote{Marcellus, 17.} may have strengthened this feeling. It therefore assists us in properly orientating ourselves to read another treatise from the greatest mathematician of antiquity that sets clearly before us his indebtedness to the mechanical applications of his subject.