Originally written for inclusion in Lesley Cormack, ed. Mathematical practitioners and the transformation of natural knowledge in early modern Europe. This planned volume arose from a double symposium on this topic at the International Congress of the History of Science, Beijing, 2005. The project, pursued in conjunction with University of Chicago Press, fell through but has now been revived with Springer in their Studies in HPS Series. The volume is now edited by Lesley Cormack, Steven Walton and John A. Schuster, to appear later in 2016