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 Newton's 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 Bernoulli's approach rather than (...) Newton's. 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. (shrink)

Publiés pour la première fois en 1867 par Giuseppe Canestrini et aujourd’hui offerts en traduction au public français par Florence Courriol, les textes sont ceux de la Consolatoria, de l’Accusatoria et de la Defensoria, rédigés en 1527 par l’homme d’État et historiographe florentin Francesco Guicciardini, peu de temps après la terrible mise à sac de Rome par les lansquenets de l’armée impériale. Principal instigateur de la ligue conclue à Cognac en mai 1526 pour refréner la politique expansio...

The Florentine political philosopher's commentaries on Livy's history of Rome are accompanied by critical and textual notes.

Niccolò Machiavelli's support for what he calls governo largo, or popular government, is usually contrasted with the diffidence towards it of Francesco Guicciardini, the Florentine aristocrat. The article argues that both these authors grounded their vision on Polybius' theory of “mixed government,” though adapting it in different directions. In examining this difference, the article reaches the conclusion that it concerns far less the degree of popular participation in political decision-making and government than the value that Machiavelli and Guicciardini (...) respectively ascribe to it in comparison with that of safety-liberty. In this respect, their theories may be viewed as anticipating the tensions between democracy and the rule of law, the co-presence of which provides the essential foundation of the structure of present-day constitutional democracies. (shrink)

SummaryThis contribution examines the circumstances of composition of the annotated edition of Newton's 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 Newton's 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 Newton's ideas in Europe. (shrink)

Francesco Guicciardini. ciardini uses mind to restrict the force and the effectiveness of Fortune's blows. "Remember this," he warns, "whoever lives a life of chance will in the end find himself a victim of chance. The right way is to think,  ...

The second half of the 17th century is populated by such towering protagonists of the Scientific Revolution as John Wallis, Thomas Hobbes, Robert Boyle, Christiaan Huygens, Robert Hooke, John Flamsteed, Isaac Newton, and Gottfried Wilhelm Leibniz, to name just a few. It is a well-known fact that controversies, issues of intellectual property and priority disputes were very common; and the debates regarding both optics and gravitation, which divided Hooke and Newton, are amongst the most notorious. Most historians of science will (...) have noticed the somewhat morbid interest that some colleagues take in the sexually intemperate and allegedly deformed “mechanic of genius,” who was denied his place in Westminster Abbey by a Puritan tyrant.1 It is not because of such voyeurism that we propose this Open Forum on Hooke. The reason is rather that during the last decade a group of researchers—which is well represented in this fascicle— have shed much new light on Hooke’s contribution to gravitation theory. (shrink)

Este artigo trata de problemas metodológicos tradicionais da história das ideias, partindo da figura do que chamamos de "leitor ideal". Para atingir nossos objetivos procuramos analisar a leitura que Guicciardini fez dos Discorsi de Maquiavel.

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 Newton's mathematical heritage and its reception in the early decades of the eighteenth century. A section devoted to Maclaurin's monumental Treatise of Fluxions describes its attempt to reach a synthesis of the different strands of Newton's 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. (shrink)

The first edition of Newton’s Principia opens with a “Praefatio ad Lectorem.” The first lines of this Preface have received scant attention from historians, even though they contain the very first words addressed to the reader of one of the greatest classics of science. Instead, it is the second half of the Preface that historians have often referred to in connection with their treatments of Newton’s scientific methodology. Roughly in the middle of the Preface, Newton defines the purpose of philosophy (...) as a twofold task: to investigate the forces of the phenomena of nature and, once having established the forces, to demonstrate the remaining phenomena. Newton then introduces a distinction between the first two books, which deal with general propositions, and the third, where the propositions are applied to particular instances of celestial phenomena. From these phenomena, Newton claims, the force of gravity, thanks to which bodies tend toward the Sun, is derived. By assuming this force in mathematical propositions, other motions are deduced: the motions of the planets, the comets, the moon, and the sea. Newton then declares his hope that phenomena relative to small particles will also be explained, as per the celestial ones, thanks to the understanding of attractive forces hitherto unknown to philosophers. The Preface ends with a well-deserved laudatio of Edmond Halley and an apologetic passage concerning certain imperfections in the presentation of advanced subjects, such as the motions of the moon. It is these lines to which historians have given most attention in their various studies. (shrink)

The article explores the role of the Spartan example in Guicciardini's political thought, giving a particular attention to his early writings. Examining a series of medical metaphors Guicciardini uses in the analysis of the state, the author uncovers Plutarch as their main source. It is argued that Plutarch, and his description of Lacedaemon, exercised a major influence in the formation of Guicciardini's political ideas. The author focuses on the crucial issue of the usage of “Lycurgus’ knife,” while (...) answering two key questions: the feasibility of constituting a republic modelled on Sparta; the legitimacy of the use of force in the cases of extreme necessity. On , Guicciardini's views are compared with Machiavelli's, and the difference in their understanding of necessità pointed out. (shrink)

Newton composed several mathematical tracts which remained in manuscript form for decades. He chose to print some of his mathematical tracts in their entirety only after 1704. In this paper I will give information on the dissemination of Newton’s mathematical manuscripts before the eighteenth-century printing stage. I will not consider another important vehicle of dissemination of Newton’s mathematical discoveries, namely his correspondence with other mathematicians or with intermediaries such as Collins and Oldenburg.In a first stage, Newton’s mathematical manuscripts were rendered (...) available to a group of acolytes, who copied and transmitted them, sometimes in mutilated form. The practice of scribal publication helped Newton to establish his mathematical reputation and to form around himself a group of followers.One can divide Newton’s mathematical activity into two periods: an early analytical and modernist period in which he developed a Cartesian and Wallisian ‘new analysis’, followed by a mature synthetic period, beginning in the 1670s, in which he distanced himself from analysis in favour of geometry, from infinitesimals in favour of limits, from the analysis of the moderns in favour of the geometry of the ancients. Newton came to the conclusion that the ‘new analysis’ was not a mathematical language fit for publication.Newton, however, could not restrict himself to scribal publication of his mathematical manuscripts for too long. The priority dispute with Leibniz, the new status of Newton as undisputed master of British mathematicians and the changing canons of mathematical publication introduced by the funding of scientific academies favoured Newton’s option for the printing of his mathematical manuscripts. However, when Newton decided to print his early analytical mathematical work, he tried to modify and present it to bring it in line with the values that characterise the methodological shift of the 1670s, values that he wished to promote among his followers.Author Keywords: Isaac Newton; Manuscripts; Scribal publication; Analysis; Synthesis. (shrink)

Essay review of William L. Harper, Isaac Newton’s scientific method. Turning data into evidence about gravity & cosmology. Oxford University Press, 2011; Steffen Ducheyne, The main business of natural philosophy. Isaac Newton’s natural-philosophical methodology. Springer, 2012. -/- The years 2011-12 will be regarded as memorable ones for the “Newtonian industry” since they have witnessed the publication of two beautiful and long awaited books devoted to Newton’s method and philosophy. They deserve great attention and praise, and I warmly recommend them to (...) any reader interested in 17th and 18th century science and philosophy. The favorable conjunction of 2011-12 should not come as a surprise for those who have been following the recent trends in Newtonian scholarship. Indeed, after the great generation of H.W. Turnbull, A. Koyré, I.B. Cohen, D.T. Whiteside, B.J.T. Dobbs, A.R. Hall, Mary Boas Hall, and R.S. Westfall, Isaac Newton has continued to be the object of intense historical research. In the 1990s, a new wave of historians of mathematics, who capitalized on the immense riches of Whiteside’s edition of the Mathematical Papers (1967–1981), produced a flood of essays devoted to rather technical aspects of Newton’s oeuvre. An incomplete list includes Michel Blay, Dana Densmore, Herman Erlichson, Bruce Brackenridge, François De Gandt, Bruce Pourciau, and Michael Nauenberg. Now the pendulum seems to be swinging towards philosophy, rather than mathematics, as is immediately apparent from the titles of the two books under review. The focus of Harper and Ducheyne’s books is Newton as the originator of a new method—an alternative and more effective method than the hypothetico-deductive one. In what follows I will not have the space to delve into all the details of the books under review: such a task would require one to exceed even the generous word limit granted by Perspectives on Science. What I will try to do is to provide the reader with an account of the main theses defended in these books by framing them within the context of their respective interpretative traditions. (shrink)