Between the cannon and the book: Mathematicians and military culture in sixteenth-century Italy

This dissertation demonstrates how the development of a mechanical world view can be understood as the concerted application of the conceptual tools of books, the physical tools of instruments and machines, and the political tools of social power. The work examines how new uses of mathematics in Cinquecento military technologies led, in part, to the reconceptualization of physical nature on a new mechanical model. Mathematicians of sixteenth-century Italy united the authority of mathematical proof and of artillery demonstration, and provided military men with not only a key to the control of technology and technicians, but also a claim to universal certitude.;This dissertation first explores the sources and themes of sixteenth-century discourse on military engineering in Italy, then focuses on the work of two mathematicians: Niccolo Tartaglia and Guidobaldo del Monte. Cinquecento military writers utilized the traditions of humanism, technology, and mathematics--each of which mediated the divide between texts and action--to draw together military prowess and book-learning. Mathematics emerged in this literature as an authoritative language by which engineers, officers, and state leaders could communicate, and by which men and machines could be organized. It was a language both philosophically certain and generative of new applications of power, and as such, acceptable in the spheres of both arms and letters. Tartaglia and Guidobaldo, mathematicians of vastly different social status, both responded to military developments, and aimed at the capture of the physical world in mathematical measure and geometric representation. This work examines how each fashioned his science in context of military engineering goals, and in accordance with his own vision of the role mechanics could play in his social-political world.