The Geometric Hypothesis of the Meno of Plato

Abstract

This‬‭ translation‬‭ presents,‬‭ for‬‭ the‬‭ first‬‭ time‬‭ in‬‭ English,‬‭ Paul‬‭ Tannery’s‬‭ 1876‬‭ essay‬ L’hypothèse‬‭ géométrique‬‭ du‬‭ Ménon‬‭ de‬‭ Platon‬‭ ,‬‭ published‬‭ in‬‭ Mémoires‬‭ scientifiques‬‭ (vol.‬‭ 3,‬‭ pp.‬ 39–45,‬‭ Paris:‬‭ Gauthier-Villars).‬‭ Tannery,‬‭ one‬‭ of‬‭ the‬‭ most‬‭ important‬‭ French‬‭ historians‬‭ of‬ mathematics,‬‭ here‬‭ attempts‬‭ to‬‭ clarify‬‭ Plato’s‬‭ obscure‬‭ passage‬‭ on‬‭ the‬‭ “geometric‬‭ hypothesis”‬‭ in‬ the‬‭ Meno‬‭ (‬‭ Meno‬‭ 86e–87a),‬‭ situating‬‭ it‬‭ within‬‭ the‬‭ traditions‬‭ of‬‭ Euclidean‬‭ geometry‬‭ and‬‭ the‬  interpretation‬‭ of‬‭ Greek‬‭ mathematical‬‭ language.‬‭ The‬‭ translation‬‭ aims‬‭ to‬‭ remain‬‭ faithful‬‭ to Tannery’s‬‭ technical‬‭ terminology,‬‭ preserving‬‭ key‬‭ Greek‬‭ expressions‬‭ in‬‭ transliteration‬‭ while‬ rendering‬‭ his‬‭ nineteenth-century‬‭ French‬‭ into‬‭ clear‬‭ English,‬‭ thereby‬‭ making‬‭ accessible‬‭ a‬‭ critical‬ investigation into the origins of geometry.‬