Harriot and the Challenge of Projectile Motion

One of the core topics on which the activities of the early modern practical mathematicians centred was the art of gunnery. In the course of the fifteenth and sixteenth centuries, the use of great artillery became increasingly important in European warfare. At the same time, a lack of accuracy in shooting with heavy ordnance was widely perceived. These circumstances made projectile motion a privileged topic of mathematical inquiry, and even though a great part of the mathematicians’ work was of little or no immediate use to practitioners in the field or at sea, it was still useful for attracting patronage by demonstrating the applicability in principle of the mathematical method to practical problems of high political and economic relevance.

Despite enormous differences in the degree of theoretical elaboration, all these sources display fundamental similarities as concerns the basic knowledge they embody, including a common core set of questions. The shared knowledge comprises not only fundamental presumptions on motion, partly reflected in Aristotelian physics, but also the practical experiences of the gunners. A thorough study of the sources with respect to this shared knowledge has yet to be made. Here, this knowledge will only be outlined with particular regard to the role it plays in Harriot’s work on projectile motion (Section 2.1). The different strata of theoretical and practical knowledge clashed in the attempts to describe projectile motion mathematically, in particular in the central quest for a geometrical description of the projectile trajectory (Section 2.2). This quest, in turn, provided a major motivation for studying the relation of time elapsed and space traversed in the motion of free fall (Section 2.3).