Method and style in archimedes’ quadrature of the parabola

This article observes and describes distinct stylistic registers that appear in the two main sections of Archimedes’ Quadrature of the Parabola. The correspondence between prose register and mathematical method indicates that in the mechanical propositions of the first section of Quadrature of the Parabola, as well as in several of his other treatises, Archimedes was purposefully deploying a unique style as a kind of rhetorical branding for his most innovative work. This Archimedean register may have been designed to be persuasive to a naturally resistant audience, or to draw mathematical theory into the world of daily experience without compromising its precision. Later authors who took inspiration from Archimedes also imitated his stylistic choices, and the Archimedean register became a signifier of mathematics that pushed the limits of conventional practice.