In this paper, we describe the genesis of Boscovich’s Sectionum Conicarum Elementa and discuss the motivations which led him to write this work. Moreover, by analysing the structure of this treatise in some depth, we show how he developed the completely new idea of “eccentric circle” and derived the whole theory of conic sections by starting from it. We also comment on the reception of this treatise in Italy, and abroad, especially in England, where—since the late eighteenth century—several authors found (...) inspiration in Boscovich’s work to write their treatises on conic sections. (shrink)

The aim of this paper is twofold: (1) to show the principal aspects of the way in which Newton conceived his mathematical concepts and methods and applied them to rational mechanics in his Principia; (2) to explain how the editors of the Geneva Edition interpreted, clarified, and made accessible to a broader public Newton’s perfect but often elliptic proofs. Following this line of inquiry, we will explain the successes of Newton’s mechanics, but also the problematic aspects of his perfect geometrical (...) methods, more elegant, but less malleable than analytical procedures, of which Newton himself was one of the inventors. Furthermore, we will also consider the way in which Newtonianism was spread before in England and afterwards on continental Europe. In this respect the Geneva Edition plays a fundamental role because of its complete apparatus of notes, and because it appeared only thirteen years after the publication of the third edition of the Principia (1726). Finally, we will also confront some problems connected to the metaphysics of calculus. Therefore, the case of Newton is one of those in which, starting from mathematics applied to physics, it is possible to connect an impressive series of fundamental arguments such as the role of mathematics in science; the comparison between Newton’s geometrical methods and analytical methods; the way in which Newtonianism was spread as well as the philosophical implications of Newton’s mathematical concepts. (shrink)

The causes of tidal motions were widely debated from antiquity up to the eighteenth century. These discussions got a second wind in the early modern period, in the wake of a growing number of cosmological alternatives that challenged the dominant Aristotelian-Ptolemaic stance. The 1687 publication of Isaac Newton’s Principia Mathematica was a defining moment in the discussions and consequently made universal gravitation the most credible and generally accepted explanation. This paper investigates the aftermath of Newton’s discovery and demonstrates how his (...) understanding of tidal motion crowded out competing theories within a broader European context. My main point of reference is Roger Boscovich’s De aestu maris (1747). In his work, the leading Jesuit scholar of the time contrasted Newton’s interpretation to those of other major authorities, namely Johannes Kepler, Galileo Galilei, and René Descartes, and went on to claim the superiority of the British scientist’s achievements over anything written prior to the Principia. As this essay argues, alongside a significant body of literature produced under the umbrella of the Jesuit order, Boscovich’s De aestu maris subsequently contributed to the formation of the popular image of Newton as a “scientific hero.”. (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)