Niccolò Guicciardini

Dot-age: Newton's Mathematical Legacy in the Eighteenth Century

According to the received view, eighteenth-century British mathematicians were responsible for a decline of mathematics in the country of Newton; a decline attributed to chauvinism and a preference for geometrical thinking. This paper challenges this view by first describing the complexity of Newtons mathematical heritage and its reception in the early decades of the eighteenth century. A section devoted to Maclaurins monumental Treatise of Fluxions (1742) describes its attempt to reach a synthesis of the different strands of Newtons mathematical legacy, and compares it with contemporary Continental work. It is shown that in the middle of the eighteenth century academic Continental mathematicians such as Euler and Lagrange were driven by local cultural assumptions in directions which sensibly diverged from the ones followed by Maclaurin and his fellow countrymen.

Conceptualism and contextualism in the recent historiography of Newton's Principia

Abstract Recently the Principia has been the object of renewed interest among mathematicians and physicists. This technical interpretative work has remained somewhat detached from the busy and fruitful Newtonian industry run by historians of science. In this paper will advocate an approach to the study of the mathematical methods of Newtons Principia in which both conceptual and contextual aspects are taken into consideration.

Johann Bernoulli, John Keill and the inverse problem of central forces

Summary Johann Bernoulli in 1710 affirmed that Newton had not proved that conic sections, having a focus in the force centre, were necessary orbits for a body accelerated by an inverse square force. He also criticized Newtons mathematical procedures applied to central forces in Principia mathematica, since, in his opinion, they lacked generality and could be used only if one knew the solution in advance. The development of eighteenth-century dynamics was mainly due to Continental mathematicians who followed Bernoullis approach rather than Newtons. The ways of thinking of the British Newtonians have, therefore, been somewhat forgotten. This paper is an attempt to assess what Bernoulli was criticizing and what were the immediate reactions of the Newtonians. In particular, I will concentrate on two papers by John Keill, submitted to the Royal Society in 1708 and 1714, in which the results on central forces achieved by the British were summarized and their methods defended.

Editing Newton in Geneva and Rome: The Annotated Edition of the Principia by Calandrini, Le Seur and Jacquier

Summary This contribution examines the circumstances of composition of the annotated edition of Newtons Principia that was printed in Geneva in 1739–1742, which ran to several editions and was still in print in Britain in the mid-nineteenth century. This edition was the work of the Genevan Professor of Mathematics, Jean Louis Calandrini, and of two Minim friars based in Rome, Thomas Le Seur and François Jacquier. The study of the context in which this edition was conceived sheds light on the early reception of Newtonianism in Geneva and Rome. By taking into consideration the careers of Calandrini, Le Seur and Jacquier, as authors, lecturers and leading characters of Genevan and Roman cultural life, I will show that their involvement in the enterprise of annotating Newtons Principia answered specific needs of Genevan and Roman culture. The publication and reception of the Genevan annotated edition has also a broader European dimension. Both Calandrini and Jacquier were in touch with the French république des lettres, most notably with Clairaut and Du Châtelet, and with the Bernoulli family in Basel. Therefore, this study is also relevant for the understanding of the dissemination of Newtons ideas in Europe.

John Wallis as editor of Newton's mathematical work

This paper explores Walliss role as editor of Newtons mathematical work. My objective is to understand how two mathematicians who held different views concerning mathematical method could nonetheless cooperate with one another quite effectively. Most notably, Wallis and Newton pursued different policies as far as the printing of algebra is concerned. In the 1690s Newton held the view that algebra is a heuristic method ‘not worthy of publication’. Wallis, instead, for all his life was keen on making algebraic methods explicit in print. As the analysis of the correspondence between Wallis, Collins and Newton reveals, the methodological tension between Wallis and Newton was resolved in such a way that Newton agreed to print his heuristic methods in Walliss English Algebra (1685) and Latin Opera (1693–99). Newton wished to guarantee his priority rights on discoveries in algebra and calculus, yet he also sought to avoid any tight authorial commitment towards them. Wallis, in contrast, received from Newton material that turned out to be useful for the fulfilment of a nationalistic programme aimed at eulogizing British mathematicians as well as his own work.

John Wallis. Una vita per un progetto

orientation in relation to modern politics and the new threat to humankind arising from technological warfare. Einstein was attached to the European Enlightenment tradition. This informed his physical thinking, in particular his dissatisfaction with quantum mechanics, and his search for unification in theoretical physics. It also informed his ethical and political outlook, his socialism (p. 284) and his enthusiasm for world government (pp. 74 100). In contrast, Oppenheimer thought that Einstein was attached to a tradition that had failed him, leading to isolation from new developments in physics and also to political positions that marginalized him or were dangerous in the context of Cold War America (pp. 272 273). Oppenheimer’s pragmatic philosophy made him more accepting of paradoxes and uncertainties in physics, but also more willing to adapt himself to prevailing structures of power and to defer to persons of authority and in authority (p. 18). Schweber suggests that Oppenheimer’s pragmatism failed to provide him with a coherent identity and outlook and that his adaptability was indicative of the ‘limitations’ of this philosophical outlook (p. 12). Einstein and Oppenheimer suggests that philosophy was not incidental to, but immanent in, the development of theoretical physics and that for Einstein and Oppenheimer the struggle to reconcile modern physics with a broader philosophical outlook was also related to the struggle to find a philosophical standpoint from which to address human problems of the modern world.

Newton and British Newtonians on the Foundations of the Calculus

As is well known, Newton, working in perfect and splendid isolation while still a young scholar at Trinity, discovered the “new analysis” that is to say, he developed what we recognize today as the basic rules of the calculus. It is not my purpose here to trace the history of this discovery and of its developments in Newton’s published works and manuscripts. At the risk of oversimplifying the complexities of the vast amount of material presented in such an admirable manner by Whiteside in his eight volume edition of Newton’s mathematical papers, I shall outline what seem to me to have been the turning points in Newton’s research into the foundations of the calculus.

Newton o la morte di un eretico

Recent research into Newton’s theology provides the basis for some provisional conjectures on Newton’s ideas concerning death. Here Newton’s views are summarised on mortalism, the relationships between soul and body, Providence, Salvation, and the corruption of Scripture, relevant to the theme to which this issue is devoted.

Geometry, the Calculus and the Use of Limits in Newton’s Principia

Since its publication in 1687 the Prinipia originated much debate. In particular, during the first decades of the eighteenth century the mathematical methods employed by Newton were criticised or defended by the small number of experts who could read the magnum opus with sufficient competence.1 Under its classic facade the Principia hides a panoply of mathematical methods; series, infinitesimals, quadratures, geometric limit procedures, classical theories of conic sections and higher curves, interpolation techniques, and much more. How should the science of motion be mathematized? During Newton’s lifetime this question was still unanswered. It is only in the l730s, mainly thanks to the work of Euler, that the mathematical community became convinced, at first on the Continent, that the calculus, most notably differential equations, was the appropriate language for ‘dynamics’.2 Nowadays, a student of ‘Newtonian mechanics’ will find the language used in the post-Eulerian era somewhat familiar. On the contrary, the language of the Principia, burdened by geometrical diagrams, the theory of proportions, almost devoid of symbolical expressions, leaves our student, even a tenacious one, perplexed.