Mathematical Enargeia: The Rhetoric of Early Modern Mathematical Notation

Abstract

This article proposes and explicates a rhetorical model for the function of notational writing in sixteenth- and seventeenth-century European mathematics. Drawing on enargeia's requirement that both author and reader contribute to the full realization of a text, mathematical enargeia enables the transformation of images of mathematical imagination resulting from an encounter with mathematical writing into further written acts of mathematical creation. Mathematical enargeia provides readers with an ability to understand a text as if they created it themselves. Within the period's dominant reading of classical geometry as a synthetic presentation that suppressed, hid, or obscured analytic mathematical reality, notational mathematics found favor as a rhetorically unmediated expression of mathematical truth. Consequently, mathematical enargeia creates an operational and presentational link between mathematics' past and its future.