The tension between geometry and matter, and so between geometry and architecture, has a long philosophical history. This paper traces part of that history, interwoven with the history of rhetoric, where geometry takes on three major roles, as in Robin Evans’ account of that history in his book, The Projective Cast, Architecture and its Three Geometries. More instrumentally, and in Colin Rowe’s essay, ‘The Mathematics of the Ideal Villa’ (1947), draws comparisons between the use of geometry in the work of Palladio and of Le Corbusier. This paper argues that Evans’ final category a ‘signified geometry’, one dependent on its metaphoric properties, is most evidently seen in the writings of Blaise Pascal. In 1657 or 1658, Pascal wrote two short treatises on the rhetorical function of geometry titled De l’esprit géométrique, and L’Art de persuasion. Geometry becomes seen as a species of rhetoric where geometry and rhetoric are paired, but where matter tends to be forgotten. In these writings, Pascal burdens geometry with the demand that the truth of matter be articulate, and persuasively demonstrated. He argued that geometry ‘has explained the art of discovering unknown truths,’ and further, that through geometry the demonstration and proof of truth is ‘invincible [. . .] for this I only have to explain the method that geometry employs; for it teaches it perfectly by its examples.