This essay investigates the rhetoric surrounding the appearance of the concept of the infinitesimal in the seventeenth-century Calculus of Sir Isaac Newton and Gottfried Wilhelm Leibniz. Although historians often have positioned rhetoric as a supplemental discipline, this essay shows that rhetoric is the "material" out of which a new and powerful mathematical system emerges. At the height of empiricism, the infinitesimal, thought by Newton and Leibniz to be evanescent or nascent, made available no recourse to empirical or geometric verification. Instead, the infinitesimal found its "substance" in the rhetorical arguments surrounding it, which ultimately precipitated an epistemic shift in scientific and mathematical practice.