This book argues that we can only understand transformations of nature studies in the Scientific Revolution if we take seriously the interaction between practitioners (those who know by doing) and scholars (those who know by thinking). These are not in opposition, however. Theory and practice are end points on a continuum, with some participants interested only in the practical, others only in the theoretical, and most in the murky intellectual and material world in between. It is this borderland where influence, appropriation, and collaboration have the potential to lead to new methods, new subjects of enquiry, and new social structures of natural philosophy and science.

Introduction: Practical Mathematics, Practical Mathematicians, and the Case for Transforming the Study of Nature.- Part 1: Framing The Argument: Theories Of Connection.- Handwork and Brainwork: Beyond the Zilsel Thesis (Lesley B. Cormack).- Consuming and Appropriating Practical Mathematics and the Mixed Mathematical Fields, Or Being "Influenced" by Them: The Case of the Young Descartes (John Schuster).- Part 2: What Did Practical Mathematics Look Like?.- Mathematics for Sale: Mathematical Practitioners, Instrument-makers, and Communities of Scholars in Sixteenth-Century London (Lesley B. Cormack).- Technologies of Pow(d)er: Military Mathematical Practitioners' Strategies and Self-Presentation (Steven A. Walton).- Machines as Mathematical Instruments (Alex G. Keller).- Part 3: What was the Relationship Between Practical Mathematics and Natural Philosophy?.- The Making of Practical Optics: Mathematical Practitioners' Appropriation of Optical Knowledge Between Theory and Practice (Sven Dupré).- Hero of Alexandria and Renaissance Mechanics (Roy Laird).- Duytsche Mathematique and the Building of a New Society: Pursuits of Mathematics in the Seventeenth-Century Dutch Republic (Fokko Jan Dijksterhuis).