Willem Jacob ’s Gravesande is widely remembered as a leading advocate of Isaac Newton’s work. In the first half of the eighteenth century, ’s Gravesande was arguably Europe’s most important proponent of what would become known as Newtonian physics. ’s Gravesande himself minimally described this discipline, which he called «physica», as studying empirical regularities mathematically while avoiding hypotheses. Commentators have as yet not progressed much beyond this view of ’s Gravesande’s physics. Therefore, much of its precise nature, its methodology, and (...) its relation to Newton’s actual work remains unclear. This article discusses one particular methodological element that ’s Gravesande himself often stressed in detail, namely the use of mathematics in philosophy and physics. In doing so, it takes exception to the claim that mathematics played only a minor role in ’s Gravesande’s work, a view put forward in recent historiography. Besides that, this article casts new light on the interpretation of ’s Gravesande’s philosophical notion of «mathematical reasoning», a notion that has remained somewhat obscure thus far. (shrink)

In 1730, the Dutch cartographer and meteorological observer Nicolaas Samuel Cruquius constructed a spectacular map of the river Merwede. Cruquius’s map is celebrated as one of the earliest to use lines of equal depth—or indeed any type of contour lines. So far, however, the secondary literature has paid no attention to why Cruquius created these lines or to the knowledge involved in his innovation. This essay makes three related points. First, Cruquius intentionally used lines representing equal depth in an entirely (...) new way: whereas earlier maps had used similar lines to represent a river’s navigability, for Cruquius they visualized river flow. Second, different technical and epistemic practices grounded the making of the map: Cruquius built on his expertise in surveying but also on practices from both natural history and mathematical physics, with which he was familiar through contacts at Leiden University and the Royal Society of London. Third, Cruquius’s case does not fit with the way work cutting across different fields of expertise is usually conceptualized. Cruquius did not just straddle different fields. Instead, he gave new meaning to lines of equal depth by integrating specific practices from different fields of expertise and omitting others; through this integration, Cruquius created a way to visualize water flows and gave shape to possible new ways of acting on the river and its environment. (shrink)

This article discusses the quest for the mechanical advantage of the wedge in the eighteenth century. As a case study, the wedge enlightens our understanding of eighteenth-century mechanics in general and the controversy over “force” or vis viva in particular. In this article, I show that the two different approaches to mechanics, the one that favoured force in terms of velocities and the one that primarily used displacements—known as the ‘Newtonian’ and ‘Leibnizian’ methods, respectively—were not at all on par in (...) their ability to solve the problem of the wedge. In general, only those who used the Leibnizian concept of force or some related notion were able to get to the conventional results. This article thus rebuts the received view that the vis viva controversy was merely a semantic one. Instead, it shows that different understandings of “force” led to real and pragmatic differences in eighteenth-century mechanics. (shrink)

This article challenges the scholarly consensus on Willem Jacob 's Gravesande’s philosophy, namely the view that it was predominantly influenced by Newton, Locke, and Descartes. More generally, it opposes the tendency to read the work of eighteenth-century natural philosophers as being part of well-defined strands of Newtonianism. I argue that we will understand the intellectual history of the early eighteenth century better if we let go of essentialist taxonomic views and instead pay attention to the historical trajectories of various actors (...) and ideas. In the case of 's Gravesande (1688–1742), it has often been assumed that he used a particular form of Newtonianism to combat rationalist metaphysics, particularly Spinozism. Here I show that this view is not tenable when we take account of 's Gravesande’s metaphysical writings. On topics such as liberty, necessity, and theodicy, these writings deviate from what Newtonianism is usually taken to stand for. Instead, 's Gravesande’s views on such matters correspond more closely to certain interpretations of Leibniz’s Théodicée. (shrink)