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)

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)

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)

En este artículo consideraré los puntos de vista de Newton sobre el método matemático. Newton nunca escribió en extenso sobre este tema, sin embargo, en sus escritos polémicos contra Descartes y Leibniz expresó la idea de que su método era superior a los propuestos por el francés y el alemán. Considerar estos escritos nos puede ayudar a comprender el papel que Newton le atribuyó al álgebra y al cálculo en su pensamiento matemático.

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)

The purpose of this chapter is to give a brief outline of Newton’s methods for “squaring” a curve, which in Leibnizian terms one would call “integrations.” These methods are rarely considered by scholars, even by Newton scholars, with the exception of those, who like George—the dedicatee of this volume—are familiar with the “technical” Newton. My purpose here is not to address the specialists in the history of seventeenth-century mathematics, but rather to offer a reader-friendly primer in Newton’s “quadrature” techniques. I (...) will not help the reader by adapting the notation to our standards: I will strictly adhere to Newton’s notation. But I will try to make things as simple as possible by choosing the most elementary examples. It is often stated that Newton’s mathematical methods were “geometrical.” But once Newton associated an equation to a curve, he could proceed by relying mostly upon symbolic manipulation. This algebraic aspect of Newton’s mathematics should be better known. I hope that the readers non familiar with this side of Newtonian mathematics will derive some instruction, and even some intellectual pleasure, by scratching the surface of the treasure trove of Newton’s algebraic quadrature techniques. (shrink)

Newton devoted some pages of his Opticks to describing an analogy between the color spectrum and the musical scale. Furthermore, in manuscripts penned in the 1690s, the so-called Classical Scholia, he claimed that Pythagoras had used a musical analogy in order to express knowledge of a heliocentric planetary system governed by universal gravitation. On this basis, historians of music and of mathematics have lately claimed that Newton endorsed myths concerning the harmony of the world typical of the neo-Pythagorean tradition. This (...) claim is here critically examined. (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)

This paper examines an annotation in Newton’s hand found by H. W. Turnbull in David Gregory’s papers in the Library of the Royal Society. It will be shown that Gregory asked Newton to explain to him how the trajectories of a body accelerated by an inverse-cube force are determined in a corollary in the Principia: an important topic for gravitation theory, since tidal forces are inverse cube. This annotation opens a window on the more hidden mathematical methods which Newton deployed (...) in his magnum opus. The received view according to which the Principia are written in a geometric style with no help from calculus techniques must be revised. (shrink)

Según la concepción heredada, los matemáticos británicos del siglo XVIII fueron responsables de una decadencia de las matemáticas en el país de Newton; una decadencia atribuida al chovinismo y a una preferencia por el pensamiento geométrico. Este artículo debate este punto de vista describiendo, primero, la complejidad de la herencia matemática de Newton y su recepción durante las primeras décadas del siglo XVIII. Una sección dedicada al monumental Treatise of Fluxions (1742) de Maclaurin describe el intento de lograr una síntesis (...) de las diferentes corrientes de pensamiento del legado matemático de Newton, y lo compara con el trabajo contemporáneo continental. Se demuestra que a mediados del siglo XVIII los matemáticos académicos continentales tales como Euler y Lagrange estaban inspirados por suposiciones culturales locales en direcciones que divergían sensiblemente de las seguidas por Maclaurin y sus seguidores conterráneos. (shrink)

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.

Robert Hooke’s theory of gravitation is a promising case study for probing the fruitfulness of Menachem Fisch’s insistence on the centrality of trading zone mediators for rational change in the history of science and mathematics. In 1679, Hooke proposed an innovative explanation of planetary motions to Newton’s attention. Until the correspondence with Hooke, Newton had embraced planetary models, whereby planets move around the Sun because of the action of an ether filling the interplanetary space. Hooke’s model, instead, consisted in the (...) idea that planets move in the void space under the influence of a gravitational attraction directed toward the sun. There is no doubt that the correspondence with Hooke allowed Newton to conceive a new explanation for planetary motions. This explanation was proposed by Hooke as a hypothesis that needed mathematical development and experimental confirmation. Hooke formulated his new model in a mathematical language which overlapped but not coincided with Newton’s who developed Hooke’s hypothetical model into the theory of universal gravitation as published in the Mathematical Principles of Natural Philosophy (1687). The nature of Hooke’s contributions to mathematized natural philosophy, however, was contested during his own lifetime and gave rise to negative evaluations until the last century. Hooke has been often contrasted to Newton as a practitioner rather than as a “scientist” and unfavorably compared to the eminent Lucasian Professor. Hooke’s correspondence with Newton seems to me an example of the phenomenon, discussed by Fisch in his philosophical works, of the invisibility in official historiography of “trading zone mediators,” namely, of those actors that play a role, crucial but not easily recognized, in promoting rational scientific framework change. (shrink)

During the eighteenth century, several towns located in what is known today as the Suisse romande were extremely receptive toward scientific culture, and most notably Newtonianism. In this paper I deal with a nine-volume publication of Newton’s Opera Omnia that was planned in Geneva and Lausanne during the late 1730s and 1740s. This publication has not received the attention it deserves. To the best of my knowledge, even an awareness of its existence is lacking in the literature devoted to the (...) reception of Newtonianism. This paper examines the circumstances of the publication of a complete set of all of Newton’s works known at the time, and the motivations of the editors, mathematicians, and publishers who were involved in this editorial enterprise. (shrink)

Review of Luigi Maierù, John Wallis (1616-1703), una vita per un progetto. Soveria Mannelli: Rubbettino Editore, 2007. 606 pp.

Review of J.E. Force & S. Hutton (eds.), Newton and Newtonianism: New studies. Dordrecht: Kluwer, 2004. Pp. xvii + 246.