Troping in Italian Gardens: Descartes, Wallis, La Hire, Gassendi

Abstract

Greek mathematics discerns and pursues analogies between number and figure, but stops short of equating them. The relation between number and figure is simile, not metaphor. We have seen that the introduction of the algebraic equation as a middle term between arithmetic and geometry opens up new possibilities: What might numbers become if they had the continuity of the line? What might figures become if they were understood as functions correlating numbers, and if the plane or three dimensional space were organized by axes and their points specified by pairs, or triples, of numbers? How would that change our understanding of the relation between figure and space?