Émilie Du Châtelet's interpretation of the laws of motion in the light of 18th century mechanics

Émilie Du Châtelet is well known for her French translation of Newton's Philosophiae Naturalis Principia Mathematica. It is the first and only French translation of Newton's magnum opus. The complete work appeared in 1759 under the title Principes mathématiques de la philosophie naturelle, par feue Madame la Marquise Du Chastellet. Before translating Newton's Principia, Du Châtelet worked on her Institutions de physique. In this book she defended the Leibnizian concept of living forces – vis viva. This paper argues that both of these works were part of a critical transformation and consolidation of post-Newtonian mechanics in the early 18th century, beyond Newton and Leibniz. This will be shown by comparing Du Châtelet's translation of Newton's axioms with her own formulations of the laws of motion in light of Thomas Le Seur's and François Jacquier's Geneva edition which holds a special place among the several editions of the Principia that appeared in the early 18th century.     

The Curie's Lab and its Women (1906–1934) Le laboratoire Curie et ses Femmes (1906–1934)

When Bouvet discovered the relationship between the binary arithmetic of Leibniz and the hexagrams of the I ching—in reality only a purely formal correspondence—he sent to Leibniz a woodcut diagram of the Fu-Hsi arrangement, which provides the key to the analogy. This diagram, in a re-drawn version, was first published by Gorai Kinzō in a study of Leibniz's interpretation of the I ching and Confucianism which has been influential in providing, indirectly, the principal source for the accounts of Wilhelm and Needham. Yet this pioneering study of Leibniz's interpretation of the hexagrams is virtually unknown. Even the account of Needham, who saved it from complete obscurity, contains one or two inaccuracies about it and these are repeated by Zacher in his otherwise excellent monograph on Leibniz's binary arithmetic.     

Different shades of Newton: Herman Boerhaave on Newton mathematicus,philosophus, and optico-chemicus

In this paper I will probe into Herman Boerhaave's (1668–1738) appropriation of Isaac Newton's natural philosophy. It will be shown that Newton's work served multiple purposes in Boerhaave's oeuvre, for he appropriated Newton's work differently in different contexts and in different episodes in his career. Three important episodes in, and contexts of, Boerhaave's appropriation of Newton's natural philosophical ideas and methods will be considered: 1710–11, the time of his often neglected lectures on the place of physics in medicine; 1715, when he delivered his most famous rectorial address; and, finally, 1731/2, in publishing his Elementa chemiae. Along the way, I will spell out the implications of Boerhaave's case for our understanding of the reception, or use, of Newton's ideas more generally.     

Kant and the scope of the analytic method

The paper investigates Kant's pre-critical views on the use of analytic and synthetic methods in Newtonian science and in philosophical reasoning. In his 1755/56 writings, Kant made use of two variants of the analytic method, i.e., conceptual analysis in a Cartesian (or Leibnizean) sense, and analysis of the phenomena in a Newtonian sense. His Prize Essay (1764) defends Newton's analytic method of physics as appropriate for philosophy, in contradistinction to the synthetic method of mathematics. A closer look, however, shows that Kant does not identify Newton's method with conceptual analysis, but just suggests a methodological analogy between both methods. Kant’s 1768 paper on incongruent counterparts also fits in with his pre-critical use of conceptual analysis. Here, Kant criticizes Leibniz’ relational concept of space, arguing that it is incompatible with the phenomenon of chiral objects. Since this result was in conflict with his pre-critical views about space, Kant abandoned the analytic method of philosophy in favour of his critical method. The paper closes by comparing Kant's pre-critical analytic method and the way in which he once again took up the methodological analogy between Newtonian science and metaphysics, in the preface B to the Critique of Pure Reason, in the context of his thought experiment of pure reason.     

Visiting Newton's atelier before the Principia, 1679–1684

The worksheets that presumably contained Newton's early development of the fundamental concepts in his Principia have been lost. A plausible reconstruction of this development is presented based on Newton's exchange of letters with Robert Hooke in 1679, with Edmund Halley in 1686, and on some clues in the diagram associated with Proposition 1 in Book 1 of the Principia that have been ignored in the past. A graphical construction associated with this proposition leads to a rapidly convergent method to obtain orbits for central forces, which elucidates how Newton may have have been led to formulate some of his most fundamental propositions in the Principia.     

Two kinds of modification theory of light: Some new observations on the Newton-Hooke controversy of 1672 concerning the nature of light

It has not been sufficiently emphasized that there existed two kinds of modification theory of colours, Aristotle's modification theory and Descartes-Hook's modification theory. This seems to have caused some confusion in the interpretation of the optical controversy between Newton and Hooke in 1672. The aim of the present paper is to prove that these two kinds of modification theory really coexisted, and on that basis to present a new interpretation of the optical controversy of 1672. The characteristics and the historical role of each of these theories will be described. Newton's colour theory was formed under the influence of Aristotle's modification theory, which had been disseminated through the work of an English Gassendist, Walter Charleton. Newton's optical theories were created not only under the influence of Descartes, as we have been often told, but also under the conspicuous influence of corpuscular philosophers.     

Leonhard Euler's ‘anti-Newtonian’ theory of light

Leonhard Euler was the leading eighteenth-century critic of Isaac Newton's projectile theory of light. Euler's main criticisms of Newton's views are surveyed, and also his alternative account according to which light is a wave motion propagated through the aether. Important changes are identified as having occurred between 1744 and 1746 in Euler's thinking about the way in which a wave such as he supposed light to be is propagated through a medium. Paradoxically, in view of Euler's overtly anti-Newtonian stand, these amount to Euler abandoning his early, Malebranchian notions about the physical basis of wave propagation, in favour of the ideas set out by Newton in Book II of his Principia.     

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

This 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.     

Newton,Gases, and Daltonian chemistry: The foundations of combination in definite proportion

This study deals with the relationship between Newton's gas model in the Principia (Book II, Proposition xxiii) and Dalton's theorizing. Dalton's first theory of mixed gases is an elegant extension of the Newtonian gas model which, in turn, led Dalton to a general model of chemical combination. The views on combination are contrasted with those of Arnold Thackray. Interestingly, the model of combination was knowingly based on a falsified theory.     

Helmholtz,the conservation of force and the conservation of vis viva

This paper investigates the relationship between Helmholtz's formulation of the principle of the conservation of force and the two principles well known in rational mechanics as the principle of vis viva and the principle of the conservation of vis viva. An examination of the relevant literature from Leibniz to Duhamel reveals both Helmholtz's indebtedness to that tradition and his creative refashioning of it as he endeavoured to craft an argument that would both prohibit the construction of a perpetuum mobile and the efficacy of a supposed vital force and demonstrate the necessity of an ontology of mass points subject to attractive and repulsive central forces depending solely on distance.     

Leibniz on the requisites of an exact arithmetical quadrature

In this paper we will try to explain how Leibniz justified the idea of an exact arithmetical quadrature. We will do this by comparing Leibniz's exposition with that of John Wallis. In short, we will show that the idea of exactitude in matters of quadratures relies on two fundamental requisites that, according to Leibniz, the infinite series have, namely, that of regularity and that of completeness. In the first part of this paper, we will go deeper into three main features of Leibniz's method, that is: it is an infinitesimal method, it looks for an arithmetical quadrature and it proposes a result that is not approximate, but exact. After that, we will deal with the requisite of the regularity of the series, pointing out that, unlike the inductive method proposed by Wallis, Leibniz propounded some sort of intellectual recognition of what is invariant in the series. Finally, we will consider the requisite of completeness of the series. We will see that, although both Wallis and Leibniz introduced the supposition of completeness, the German thinker went beyond the English mathematician, since he recognized that it is not necessary to look for a number for the quadrature of the circle, given that we have a series that is equal to the area of that curvilinear figure.     

Science,self improvement and the first industrial revolution

This study considers Newton's views on space and time with respect to some important ontologies of substance in his period. Specifically, it deals in a philosophico-historical manner with his conception of substance, attribute, existence, to actuality and necessity. I show how Newton links these “features” of things to his conception of God's existence with respect of infinite space and time. Moreover, I argue that his ontology of space and time cannot be understood without fully appreciating how it relates to the nature of Divine existence. In order to establish this, the ontology embodied in Newton's theory of predication is analysed, and shown to be different from the presuppositions of the ontological argument. From the historical point of view Gassendi's influence is stressed, via the mediation of Walter Charleton. Furthermore, Newton's thought on these matters is contrasted with Descartes's and Spinoza's. In point of fact, in his earliest notebook Newton recorded observations on Descartes's version of the ontological argument. Soon, however, he was to oppose the Cartesian conception of the actuality of Divine existence by means of arguments similar to those of Gassendi. Lastly, I suggest that the nature and extent of Henry More's influence on Newton's conception of how God relates to absolute space and time bears further examination.     

Leibniz on Hobbes’s materialism

This paper discusses Leibniz’s interpretation and criticism of Hobbesian materialism in the period 1698-1705. Leibniz had continued to be interested in Hobbes’s work, despite not engaging with it as intensively as he did earlier (around 1670). Leibniz offers an interpretation of Hobbes that explains Hobbes’s materialism as derived from his imagistic theory of ideas. Leibniz then criticizes Hobbes’s view as being based on a faulty theory of ideas, and as having problematic consequences, particularly with regard to what one says about God. Some of this criticism is found in the New essays, but equally significant is Leibniz’s correspondence with Damaris Masham, who proposed an argument for materialism very much like that which Leibniz attributed to Hobbes. The paper concludes by discussing the suggestion that Leibniz at this time, particularly in the New essays, himself adopted Hobbesian ideas. Though Leibniz did use some of Hobbes’s examples, and did think at this time that all souls were associated with bodies, the resulting position is still rather distant from Hobbesian materialism.     

Newton's Contribution to the Science of Heat

The contents of Scala Graduum Caloris are described, supplemented by unpublished material. Both temperature measurements by his linseed oil thermometer and those based upon his law of cooling are shown to be reasonably accurate to 300°C, but above that value they are much too low. The apparent agreement and the deviation are explained by the differences between the assumptions that Newton made in deriving his law of cooling and the conditions in which he used it. Newton's attempts to link terrestrial and celestial science in applications in the Principia are shown to fail from his confounding the concepts of temperature, heat and radiant intensity and his ignorance of most factors affecting the temperature rise of irradiated materials. Other comments on varied aspects of heat, mainly published in the Queries, are set out and analysed. His originality is assessed.