Translating Newton's 'Principia': The Marquise du …...Translating Newton s Principia Figure 1. Pierre Louis Moreau de Maupertuis, one of Du Chatelet's first tutors of mathematics

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Translating Newton's 'Principia': The Marquise du Châtelet's Revisions and Additions for a French Audience Author(s): Judith P. Zinsser Source: Notes and Records of the Royal Society of London, Vol. 55, No. 2 (May, 2001), pp. 227-

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Notes Rec. R. Soc. Lond. 55 (2), 227-245 (2001)

TRANSLATING NEWTON'S PRINCIPIA: THE MARQUISE DU CHATELET'S

REVISIONS AND ADDITIONS FOR A FRENCH AUDIENCE

by

JUDITH P. ZINSSER

History Department, Miami University, Oxford, OH 45056, USA

SUMMARY

In the 1740s, the Marquise du Chatelet translated Newton's Principia (1731, third edition) into French. Hers remains the standard translation. In addition, she wrote an extensive commentary in which she gave her own description of the System of the World, and analytical solutions to key disputed aspects of Newton's theory of universal gravitation. She also included summaries of two mathematical essays that clarified and confirmed Newton's application of his theory to observed phenomena: Alexis-Claude Clairaut's on the shape of the Earth and Daniel Beroulli's on the effects of the Sun and Moon on the tides.

INTRODUCTION

To historians of the Enlightenment, Gabrielle-Emilie le Tonnelier de Breteuil, Marquise du Chatelet (1706-1749), is best known as Voltaire's companion of 15 years, his 'divine Emilie'. Occasionally, these scholars mention her collaboration with Voltaire on his Elemens de laphilosophie de Newton (1738), the first of the popular French accounts of Newton's Optiks and his law of attraction.1 Feminist historians, particularly Carolyn Merchant and Linda Gardiner, worked to prove the originality of Du Chatelet's own description of a unified system of the Universe, the Institutions de physique (1740).

The most eminent scholars of the history and philosophy of science have, with a few exceptions, ignored her altogether, attributed her writings to others or described her work as irrelevant to the grand narrative of modem science.2 Two of the historians of the early modem era, I. Bernard Cohen, a co-editor of the definitive Latin edition of Newton's Principia and of a modem English translation, and Rene Taton, have considered Du Chatelet's translation and the accompanying commentary in some detail. Cohen described differences in editions; Taton, the role of Alexis-Claude Clairaut, F.R.S. (the young mathematician and academician with whom she worked), in the project.3

This 20th-century cacophony of different views of the marquise and her intellectual endeavours makes an interesting topic in the historiography of gender and science.4 In contrast, the views of the learned 18th-century elite are more harmonious. The

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journaux of her day took Du Chatelet's writings seriously and give a uniformly flattering picture of the marquise's abilities. They make it possible to understand why Du Chatelet's male contemporaries, les gens de lettres [men of letters], accepted her as an equal and waited impatiently for the publication of her translation of Newton's Principia and the accompanying commentary.5

To the Journal Universel of 1746, reporting on her election to the Bologna Academy, she was 'notre infatigable Marquise [our indefatigable Marquise]', who had not only mastered 'l'obscurite' of 'la Philosophie', but 'even developed her own, and entered into dispute with the most famous Philosophes of her time'.6 Already in 1741, contemporaries had credited her with introducing and explaining the complexities of Leibniz's metaphysics for a French audience with the publication of her Institutions de physique. In addition, according to the prestigious Jesuit Memoires de Trevoux, she had bested Dortous de Mairan, the renowned scientific author and 'perpetual secretary' of the French Academie Royale des Sciences (Royal Academy of Sciences) in a pamphlet war over the formula for momentum (forces vives).7

These public accolades give some idea of Du Chatelet's qualifications as an interpreter of Newton. They do not explain, however, why in 1744 or 1745, she undertook the project, a translation and commentary on Newton's major work, the project she would later refer to as her 'magnum opus'. By 1744, Du Chatelet seems to have been eager for a new project. She had prepared a third edition of her Institutions de physique, which appeared in 1742, as well as a 1744 collection of essays and 'letters' illustrating her victory over Dortous de Mairan.8

Only one major translation of the Principia had been done: Motte's 1729 English version of Newton's third edition.9 But a translation into English would not make any aspect of the Principia more accessible to continental Europeans. For example, Du Chatelet and Voltaire used English as their secret language when they wished to have discussions that others would not understand. From the perspective of language ability, Du Chatelet was eminently qualified to undertake a French translation. She knew Latin, read English and had already done a very idiosyncratic French version of Bernard Mandeville's acerbic The Fable of the Bees. From the perspective of her knowledge of physics and mathematics, her correspondence, the references throughout her previous scientific works and the inventory of her library done at the time of her death in 1749 all demonstrate her familiarity with the writings of the major astronomers, physicists and mathematicians who had studied and used Newton.'°

As a mathematician, Du Chatelet had the same credentials as many members of the French Academie Royale des Sciences. French universities did not offer lectures in the calculus formulated by Newton and Leibniz to further their investigations of celestial dynamics. Du Chatelet learned analytic geometry, integral and differential calculus from books and from other mathematicians just as her male colleagues had. Though barred from all but the public sessions of the Academie des Sciences, she studied with two of its most illustrious members, Pierre Louis Moreau de Maupertuis (figure 1) in 1733 and 1734, and Alexis-Claude Clairaut (figure 2) in the 1740s. She was essentially an 'autodidact', a figure familiar to women's intellectual historians, but in this case, so were many men. " By the mid-1740s, Du Chatelet had become one

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Translating Newton s Principia

Figure 1. Pierre Louis Moreau de Maupertuis, one of Du Chatelet's first tutors of mathematics. (Royal Society portrait.)

of the few people in Europe, male or female, who could not only read and understand this advanced mathematics, 'le calcul', but also explain its progressions and manipulate its propositions to apply to other cases.

For the work of translation, she used Newton's first and second editions of the Principia, as well as the Latin version of his De Sistemate munde (System of the World, 1731 edn). She also consulted Pere Jacquier's edition (1739-42) with its 'commentaire perpetuel [a continuous commentary included as footnotes]'.2 As for the commentary that accompanied her translation of the Principia, by 1746 when she was well into this part of her project, Du Chatelet had many models to draw from. She refers in her Commentaire to Keill's treatise on astronomy, to Henry Pemberton's popular explication, and to those of other English commentators like J.T. Desaguliers and David Gregory (whose explanations had been published in French as Elements d'astronomie physique in 1702). She also cites the Dutchman Pieter van Musschenbroek's Essai de physique (trans. 1739) and the works of Christian Wolff,

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the German follower of Leibniz. Finally, she drew on the specialized treatises of a number of French and Swiss mathematicians, including Clairaut, Jean le Rond d'Alembert and Daniel Bernoulli. They had created algebraic equivalents to key parts of the Principia in an effort to describe and to prove Newton's hypotheses about the effects of attraction when three, not just two, bodies were involved.

Newton himself wrote two different versions of his own 'commentary'. One constituted Book III of the Principia; the other, Book III in an abbreviated form, appeared posthumously in 1728 as De mundi systemate liber (translated into English as System of the World in the same year). Both explained the application of his mathematical theorems, corollaries, propositions and lemmas on the movement of bodies to the workings of the Universe. However, even the shortened version, De mundi systemate liber, was subject to abrupt shifts in topic, and characterized by the same unfamiliar language and mathematical formulations that filled the Principia itself.'3 For example, after a very brief summary of previous theories about the motions of the planets, and without any explanation to the reader, Newton proceeded to the mathematics for determining the orbits of Jupiter's satellites; his description of the planetary system as a whole comes 23 pages later. In this way, he purposely duplicated the steps by which he had come to his own hypothesis about universal gravitation, but at the expense of clarity.

Given the fact of the language, the style of writing and the method of argumentation, only the most able French 'physiciens [physicists]' and 'geometres [geometricians/mathematicians]' had read either Book III or the 1728 abbreviated version. Most had only a cursory understanding of Newton's 'system', of the law of gravitational attraction, and of the complementary effects of centripetal and centrifugal force in the Universe.

THE TRANSLATION

Once she had begun, Du Chatelet worked rapidly, but sporadically for four years, from 1745 to 1749, on first the translation and then her commentary. In November 1745, she wrote to Jacquier that she did the translation 'quand j'ai du temps [when I have the time]'. Most of her days, however, had to be devoted to what she always referred to as 'mon travail [my job]'. She explained, 'I spend my life in the antechamber of the minister of war to obtain a regiment for my son.' The minister awarded the family the regiment, and, Du Chatelet, by beginning at four or five in the morning, had a draft of the Principia translation to the printers by December.14

Like Voltaire, Du Chatelet wrote and corrected, sent a version of the manuscript to the printer and then worked on the proofs, a preliminary 'impression'.'5 Given the complexities of the subject, she then sent the proofs of her translation and her commentary to Clairaut to review. He grumbled to Jacquier in March 1746 about all that he now had to do, but he had already recommended approval of the project to the royal censors at the end of 1745.16 Meanwhile the printers were doing the engravings for the 'figures' and estimated publication first in six months, and then in a year.17

230




Figure 2. Alexis Claude Clairaut. (Academie des Sciences, Paris.)

The translation that Du Chatelet sent to Clairaut included Newton's prefaces to each of the three editions of the Principia, Cotes's preface (a particularly strong argument against Descartes and his followers' materialist explanation of planetary movement by impulsion),18 the sections entitled 'Definitions' and 'Axioms or Laws of Motion', Books I and II on the Motion of Bodies, and Book III on the System of the World.

The manuscript at the Bibliotheque Nationale indicates that Du Chatelet had translated methodically and carefully.19 Marginal notations in the 12-page 'cahiers', which she favoured, include queries about a particular Latin word or about some aspect of the calculations. She often had written multiple versions of prose sections like Newton's 'Definitions' and the 'Scholie' (the conclusions at the end of a series of propositions, theorems and corollaries). The thoughtfulness of her translation and the extent of her knowledge are evidenced by choices she made for contested passages. For example, the Newtonian scholar Florian Cajori notes that she chose the English mathematician James Jurin's interpretation of Newton's meaning over Henry Pemberton's in her translation of Book I, Section I, lemmas I and XI.20 As in her other

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Judith P Zinsser

scientific writings, the changes, particularly to the prose sections of Book III, make each version of the text clearer and more succinct.2' Most are so characteristic of her practices as a writer and so extensive that they constitute evidence not only of her abilities but also of her exclusive authorship. Some historians have ascribed this kind of editing to Clairaut. Given his other activities from 1745 through the 1750s, it is hard to imagine that he would have had the time or the inclination to work over the language so carefully.22

THE COMMENTARY

This more or less literal rendering of the third Latin edition of the Principia was the first way in which Du Chatelet translated Newton's work. There are other ways as well. All are contained in the five sections of her Commentaire des Principes Mathematiques de la Philosophie Naturelle. Extensive, comprising almost two-thirds of volume II, this commentary was as significant to her contemporaries and to the wide dissemination of Newton's ideas on the Continent as the translation of the text from Latin into French. Here, Du Chatelet offered three different ways to access Newton's celestial mechanics. Each builds on the other in terms of the detail given and the complexity of the mathematics required of the reader.23

First, there is the part of the commentary entitled, 'Exposition abrege du systeme du monde [Abridged exposition of the system of the world]', a wonderfully clear description of the Universe as it was understood in 1749. It is a masterful synthesis of Books I-III of the Principia, of the mathematics of Newton's 1728 De mundi systemate liber and of the principal discoveries that refined or solved problems connected with Newton's applications of his mathematics to observations of the movement of the planets, their satellites and comets.

Overall in her 'Exposition abregee' Du Chatelet made it possible for readers to follow Newton's plan of reasoning in his two Latin versions of the 'System of the World'. Like Newton, in Book III of the Principia, she began with 'ses solutions generales [general solutions]', the definitions and laws. She then proceeded to the many 'applications de ces solutions'. She had no desire, as she explained to Jacquier in July of 1747, to do more than explain this 'system' and its underlying propositions to show 'the route he followed to arrive at [a particular] discovery'.24 As a result, she glibly summarized other sections. Book II of the Principia on 'the motion of bodies in resisting mediums' was dismissed in two sentences and a marginal description: 'M. Newton composed this Book in order to destroy Descartes' tourbillons.'2'

In contrast, however, to Newton's characteristic mixture of prose and mathematical description throughout even De mundi systemate liber, Du Chatelet's language and sequence of thought are so clearly presented and so free of mathematical or scientific jargon that the reader can easily follow her gradual progression from the simplest prose explanations to the most complex algebraic demonstrations. Each of the seven chapters of her 'Exposition abregee' gives not only increasingly detailed descriptions of the 'systeme planetaire', but also the increasingly advanced mathematics needed to apply

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Translating Newton 's Principia 233

the laws governing its motions. For example, she explains how the theory of attraction accounts for the flattening at the Earth's Poles, how this leads to an understanding of the tides and how this, in turn, gave Newton a means to determine the masses of the Earth and the Moon.

For the novice, Du Chatelet defines even the simplest terms, such as 'orbit' and 'ellipse'. She makes analogies to clarify meanings; for example, the glass cover of a watch illustrates the concepts of concave and convex (lenses). She refers to experiments with pendulums and with Boyle's air pump when she explains 'the inverse square law', how differences in mass make bodies turn when affected by attraction. She annotates her explanations with citations to Newton's writings or to the other astronomers, geometricians and physicists upon whose work she had drawn. She even included the occasional anecdote: 'A Jesuit had told his Superior that he had discovered spots on the Sun; the Superior responded in a grave manner, that is impossible, I have read Aristotle two or three times, and Ifound nothing like that in his book'.26

Du Chatelet obviously enjoyed mathematics. Only calculus, 'la methode analytique', she told her readers, could explain a phenomenon like the path of comets, 'ce beau probleme astronomico geometrique [this beautiful astronomical-geometric problem]'.27 Du Chatelet turns to these 'solutions analytique [analytical solutions]', to provide the next form of translation for Newton's Principia, and the second part of her Commentaire. These are algebraic equivalents for the most disputed and complicated sections of the Principia, the key propositions most directly related to the 'problem of three bodies'. In sections I-III of her 'Solution Analytique des Principaux Problemes qui concernent le Systeme du Monde [Analytical Solution to the Principal Problems concerning the System of the World]', Du Chatelet derives the formulae and then, with differential and integral calculus, uses these formulae to work through the specific cases that Newton had only alluded to in his text. For example, on the relationship between increases and decreases in centripetal force on a body moving through space (a useful calculation when considering the path of a comet subject to many gravitational pulls in the course of its orbit).28

Du Chatelet explained her goal in this second part of her Commentaire: 'to show Newton's system in all its glory and to perfect it'.29 To 'perfect' Newton's laws, especially for readers on the Continent, meant yet a third kind of 'translation', descriptions of those works written since Newton's death that extended and elaborated on propositions only given in their most general form in Book I of the Principia. This Du Chatelet did in parts IV and V of the 'Solution analytique'. She chose two topics considered key to the proof of Newton's theories, the relationship between attraction and the shape of the Earth, and the effects of lunar and solar attraction on the tides. She used Clairaut's work to explicate the former, and that of a Swiss mathematician, Daniel Bernoulli, for the latter. Both men's treatises on these questions had been summarized in the 'Exposition abregee'. Now she described their essays in detail, often quoting at length, and giving clear demonstrations of their mathematical proofs of their hypotheses.30

Although familiar with the work of Clairaut and d'Alembert, who both 'seek the system of the world', as she wrote to Jacquier in July of 1747, she preferred



Judith P Zinsser

Figure 3. Cirey. Du Chatelet began her studies of Newton's Principia at the family chateau in Champagne. (Photograph: M.E. Goldby.)

Clairaut's reasoning on the Earth's shape, and used his 'Figure de la terre [Figure of the earth]', the treatise that he had presented to the Academie des Sciences in 1742, for this section of her Commentaire.31 To describe Clairaut's treatise at length also satisfied one of her unspoken goals, to highlight the work of French mathematicians and physicists.32 She continued in the same letter to justify her choice of Beroulli's work. For the tides, no one disputed, as she subsequently explained to her readers, 'la vraie cause [the true cause]', rather 'it only remains to discover what this cause is, to deduce all its consequences, and to calculate the effects'. Of three prize essays on the topic for the 1738 Berlin Academy of Sciences competition, 'I am most attached to ... that of M. [Daniel] Bernoulli, in which he seems to me to have found the most order, clarity and precision.' So she gave her readers an abridgement of his treatise.33

These final two sections of the 'Solution analytique' served as introductions to the most specialized contemporary studies of celestial mechanics. This had been purposeful. At one point, Du Chatelet suggested that those who wished to go beyond these 'extraits', these 'reviews' of Clairaut and Bernoulli, with 'all the help I have given them, by these details that I have introduced them to, will easily understand the same chapter in the work itself'.34 With her summaries of these essays, Du Chatelet completed her 'translations' of Newton's Principia. Having gone from the literal text, through increasingly sophisticated mathematical expositions and demonstrations, she had made Newton's work accessible on many levels.

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Translating Newton s Principia 235

Figure 4. The palace at Luneville. Madame du Chatelet stayed in the Queen's apartments (the corner rooms to the left facing the gardens) where she completed the translation of Newton's

Principia. (©) Ed. Pierron-Sarreguemines, France.)

What is the significance, then, of Du Chatelet's multifaceted 'translation' of Newton's Principia? How did it contribute to the dissemination of Newton's ideas, to the creation of his pre-eminent position at the centre of Enlightenment mathematical and scientific thought? Du Chatelet and Voltaire certainly believed the principal value of her efforts lay in creating a French language version both through her literal rendering and her 'Exposition abregee'. Not only because 'm. Neuton's Latin is one of the difficulties', as she wrote to J. Bernoulli in January of 1746, but also, as Voltaire the non- mathematician explained in his 'Preface historique' to her Principia, because 'it always costs some fatigue to read abstract things in a foreign language'. French, Voltaire continued, was 'Langue courante de l'Europe [the everyday language of Europe]', and continually enriched by the inclusion of all the new and necessary expressions, it is the appropriate language to spread the new knowledge throughout the world'.5

The mathematical part of the Commentaire, the 'Solution analytique', also had its value. As Du Chatelet explained to her readers the complexities of the phenomena that physicists were trying to describe in the 1740s made all previous geometric approaches inadequate. '[L]a mthode analytique', followed by mathematicians like approaches inadequate. ' [L]a methode analytique', followed by mathematicians like



Judith P Zinsser

Figure 5. Frontispiece of the Marquise du Chatelet's Principia. (Royal Society Archives.)

Clairaut, d'Alembert and Bernoulli, the calculus with its ability to consider an infinite number of cases for an infinite number of changing circumstances, 'seems to be the only [method] that could really be satisfactory in research of this nature'.36 For those who doubted its efficacy or were unsure of its application, the first three sections of her 'Solution analytique' would have demonstrated its value.

The question of significance is complicated by Du Chatelet's sudden death in September of 1749, and the disappearance of all trace of the book until its publication in an incomplete form in 1756. The final version appeared in 1759, 10 years after her death. Hints in her correspondence and in the manuscript indicate that she had finished all of her revisions and probably had sent corrected printer's proofs to Clairaut by the end of the summer of 1749. In May, she wrote from Paris to Madame Boufflers, a leading figure at the Duke of Lorraine's court: '...je ne sors plus, je ne fais que des a et des b, [I don't go out at all, I only make as and bs]'. '[D]es a et des b' suggests that she was then working on parts II and III of Section II of the 'Solution analytique'. A similar reference in a letter to her lover, the Marquis de Saint-Lambert, tentatively dated 10 juin 1749, '...je ne fais ici que des xx [I don't do anything here but make xxs]', could indicate that she had proceeded to her description of Clairaut's 'Figure de la terre', section IV of the 'Solution analytique'.37 But then she died. Clairaut's many other projects and more immediate concerns in relation to his own career must have taken precedence.38 Voltaire, a possible advocate for publication, left France for Prussia.39 Probably the heightened controversy over the correct calculations for the

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Translating Newton ' Principia 237

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return of Halley's comet in the winter of 1758/59 prompted the publishers to finish going through the geometrical 'figures' in the old proofs and to bring out Du Chatelet's translation and commentary.40

The September 1759 'extrait [review]' in the Journal Encyclopedique suggested this as the reason for its appearance in 1759: 'The public has already waited for many years with impatience: but if some difficulties have delayed publication until this moment, it has only been, it seems, to render it more dazzling, contributing to the moment of triumph of the philosophy that it explains and comments on'.41 After praising the translation, the reviewer wrote at length on the value of Du Chatelet's multilevel commentary: 'Thus, one can say of this Commentary that it offers us Newton made accessible to everyone, no less than to all those who can follow philosophical reasoning.' Through her 'Exposition abregee' she transformed 'this magnificent geometric display ... to the level of readers less accustomed to mathematical discussions', and then with the 'solution analytique' introduced 'les jeunes Analystes [young mathematicians]' into 'le sanctuaire de la Philosophy Newtonienne [the sanctuary of Newtonian Philosophy]'.42

In the 1740s, when Du Chatelet had embarked on her project, she hoped that her translation and commentary 'se sera utile [would be useful]'.43 Historians of science acknowledge that it took until the end of the 18th century before Newton's ideas gained universal acceptance from Europe's 'physiciens', 'geometres' and 'philosophes'.44 Du Chatelet certainly played a role in this process. Perhaps the best indication of the utility and significance of her efforts comes from the 1779 edition of the Encyclopedie. The entry on 'Newtonianisme' named Du Chatelet along with Pemberton, 'sGravesande, William Whiston, Jacquier and LeSeur, and Colin Maclauren, as one of seven authors 'who tried to make Newtonian philosophy easier to understand'.45

ACKNOWLEDGEMENTS

Archival research for this project was made possible by grants from Miami University (Bibliotheque National, Bibliotheque de l'Arsenal in Paris, the British Library in London and University Library at Cambridge, 1994, 1997, 1999), and by the Philip and Elaina Hampton Fund (National Public Library in St Petersburg, 1997). A 1995 Mayers fellowship at the Huntington Library in California allowed me to read many of the 18th-century scientific and mathematical works referred to in this essay.

NOTES

1 See, for example, S. Edwards, The divine mistress (London, Cassell, 1971) or the official French biography, Rene Vaillot, Madame du Chdtelet (Paris, Albin Michel, 1978). For the feminist historians of science, see C. Merchant [Iltis], 'Madame du Chatelet's metaphysics and mechanics', Stud. Hist. Phil. Sci. 8, 28-48 (1977); L. Gardiner [Janik], 'Searching for the metaphysics of science: the structure and composition of Madame du Chatelet's Institutions de physique, 1737-1740', Studies on Voltaire and the Eighteenth Century 201, 85-113 (1982).

238




2 See, for example, P. Brunet, L 'Introduction des theories de Newton en France au XVIIIe siecle (ed. Slatkine) (Geneva, 1970); A. Koyre, Newtonian studies (Cambridge, MA, Harvard University Press, 1965); J.L. Heilbron, Elements of early modern physics (Berkeley, University of California Press, 1982); or the more recent D. Gjertsen, The Newton handbook (New York, Routledge & Kegan Paul, 1986), which makes no mention of the Institutions de physique in the list of works on Newton, implies that the translation was a collaborative project and attributes Du Chatelet's commentary to Clairaut. See the entries on 'Chastellet, Gabrielle-Emilie, Marquise du' and on the 'Principia'. I. Bernard Cohen in his own commentary prepared for the new English translation of the Principia, 'A guide to Newton's

Principia', praises her translation as better than Motte's English version, explains that he referred to it when he himself encountered problems with wording and meaning. Even so, he credits Clairaut with exclusive authorship of all of the explanatory sections, her Commentaire. See I. Bernard Cohen, 'A guide to Newton's Principia', The Principia: mathematicalprinciples ofnaturalphilosophy (trans. I. Bernard Cohen and Anne Whitman, assisted by Julia Budenz), pp. 200 (footnote 7), 236, 178 (footnote 30), 21 (footnote 33), 165 (Berkeley, University of California Press, 1999).

3 Cohen compared the 1756 and 1759 editions of the translation, noted considerable differences, and concluded that the 1759 version was the one intended for publication. I believe that the 1756 edition was probably done from a mixture of corrected and uncorrected proofs. For reasons that are unclear, when describing his own translation, Cohen refers only to this 1756

incomplete version. See in his 'Guide', op. cit., note 2, p. 165; I. Bernard Cohen, 'The French translation of Isaac Newton's Philosophiae Naturalis Principia Mathematica (1756, 1759, 1966)'. Archives Internationales d'Histoire des Sciences 21, 261-290 (1968). Taton also endeavoured to establish the chronology for composition of both the translation and the

commentary. See R. Taton, 'Madame du Chatelet, traductrice de Newton'. Archives Internationales d'Histoire des Sciences 22, 185-209 (1969). On the question of chronology, see the more recent and more thorough reconstruction in R. Debever, 'La marquise du Chatelet traduit et commente les Principia de Newton', Bulletin de la Classe des Sciences 73

(5th series), 509-527 (Bruxelles, Palais des Academies, 1987). I am grateful to Olivier Courcelle for this reference.

4 A number of historians of science have written about women scientists and mathematicians in the 17th and 18th centuries. See, for example, A. Cook, 'Ladies in the Scientific Revolution', Notes Rec. R. Soc. Lond. 51, 1-12 (1997) and G. Berti Logan, 'The desire to contribute: an eighteenth-century Italian woman of science [Laura Bassi]', Am. Hist. Rev. 99, 785-812 (1994). Bassi, Du Chatelet's contemporary, held a degree from the University of

Bologna and became Professor of Experimental Physics at the Institute of Sciences in

recognition of her work in fluid mechanics and electricity. No evidence of any contact between the two women has been found. Other historians have explored the relationship between gender and the evolution of French scientific institutions in the 18th century. See in particular, M. Terrall, 'Gendered spaces, gendered audiences: inside and outside the Paris

Academy of Sciences', Configurations 2, 207-232 (1994); and 'Emilie du Chatelet and the

gendering of science', Hist. Sci. 33, 283-310 (1995). Also interesting on this subject, see

chapter 7 of G.V. Sutton, Science for a polite society: gender, culture and the demonstration of enlightenment (Boulder CO, Westview Press, 1995).

5 See the review of her translation and commentary in the Journal Encyclopedique 6, partie 3, p. 4 (September 1759); Arsenal 8oH26260.

6 '...[E]lle fut bientot en etat de les developper elle-meme aux autres, & meme d'entrer en

dispute avec les plus fameux Philosophes de ce tems'. Journal Universel 10, 421 (1746); Arsenal 8oH26346.

7 The Memoires des Trevoux in awarding her these laurels, characteristically, took no side in the argument about physics. Victory came because of 'la finesse de son ironi'. This indicated to the world of the learned that she had, in addition to mastering the literatures of the



Judith P Zinsser

'physiciens' and 'geometres', of her day, achieved the style of an 'honnete homme'. As quoted in K. Kawashima, 'Madame Du Chatelet dans le jouralisme'. LLULL 18, 471 (1995). For the review of the Institutions de physique, see Memoires pour l'Histoire des Sciences & des Beaux Arts [Journal or Memoires de Trevoux], 894-927 (1741); Arsenal 8oH26311.

8 From her letters, it seems that she had considered translating John Keill's Introductio ad veram astronomiae (1718). As one of the most popular explications of the theory of attraction, it would have been a way to make Newton available to a French audience. However, the Royal Astronomer, Le Monnier, sent her the page proofs of his version, and, as she explained to Pere Jacquier, a co-editor of the 'Geneva' edition of the Principia, and one of her learned correspondents: 'Cet ouvrage m'a fait susprendre celui que vous savez que je meditais sur cette matiere [This work made me suspend that which you knew I was planning on this material]'. Du Chatelet to Jacquier, no. 347, 12 November 1745, Lettres de la Marquise du Chdtelet, vol. II (ed. Theodore Besterman), p. 143 (Geneva, Institut et Musee Voltaire, 1958).

9 The third edition of the Principia was 'prepared' by Henry Pemberton. He had planned to do a translation, but concentrated first on completing his description of Newton's work, A View of Sir Isaac Newton s Philosophy (1728). Motte's translation appeared the year after and became the standard version in English. Motte rendered the Latin quite literally and in unnecessarily complex language. Florian Cajori's edition of Motte, was, until Cohen and Whitman's much more readable translation, the most often reprinted version (University of California Press, 1962 edn, 2 vols). Charles Rochedieu mentions an anonymous 1729 translation of Motte's edition into French. (See C.A.E. Rochedieu, Bibliography ofFrench translations of English works 1700-1800 (University of Chicago Press, 1948), p. 229.) The 1759 reviewer of Du Chatelet's Principia and Commentaire attributes a French translation to 'm. [John] Machin' but explains that the English thought it inadequate. Journal Encyclopedique, op. cit., note 5, p. 9. As no such translation exists, these must be references to Machin's 'The Laws of the Moon's Motion according to Gravity', quoted at length in Newton's second Latin edition of the Principia and appended to Motte's 1729 English translation.

10 Du Chatelet scrupulously annotated her scientific treatises and books. Besterman reprints the inventory of her Paris house as Appendix D93, The complete works of Voltaire. correspondence, vol. 95 (ed. Theodore Besterman) (Geneva, Institut et Musee Voltaire, 1968). Descartes's Methode, publications of the Academie Royale des Sciences, some works on geometry and trigonometry, and an edition of Newton are listed. Voltaire's library, which may also contain some of her books, is held by the National Public Library in St Petersburg. It includes a few of the scientific works mentioned by Du Chatelet in her Commentary; for example, an edition of 'sGravesande's Physices elementa mathematica (1721-25), Opere di Galileo Galilei (1656) and Pluche's Le Spectacle de la nature (1732-46)-the last two with marginal notations by Du Chatelet. For a complete list of the Voltaire library, see M.P. Alekseev, Bibliotheque de Voltaire: catalogue des livres (Moscow, Editions de l'Academie des Sciences de l'URSS [sic], 1961).

11 See C.B. Paul, Science and immortality: the eloges of the Paris Academy of Sciences (1699-1791) (Berkeley, University of California Press, 1980). Of the 22 mathematicians, only some spent time at a 'college', or university. Many, including Clairaut and Maupertuis, learned on their own and from a mentor. See pp. 75, 77, and Table 3, p. 76. See also D.J. Sturdy, 'Academicians in the mathematical sciences, 1702-1750'. In Science and social status: the members of the Academie des Sciences, 1666-1750, pp. 375-398 (Rochester, NY, The Boydell Press, 1995).

12 A style of commentary popularized by Samuel Clarke's edition of Jacques Rohault's Traite de physique. The editor wrote at length on the work but through the annotation, not as a separate text. Du Chatelet seems to have considered doing this kind of commentary, but rejected it in favour of a separate set of chapters after the translation. See Du Chatelet to Jacquier, 1 July 1747, no. 361, Du Chatelet Lettres, op. cit., note 8, vol. II, p. 157.

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13 Newton explained that he had modified his original plans for Book III of the Principia. Rather than give an overall prose description of the Universe, he decided on a mathematical presentation of his principles in the order in which they had come to him. He believed that this recreation of his own process of hypothesis and deduction would forestall disputes and force his readers to go beyond their preconceived notions.

14 '[J]e passe ma vie dans l'antichambre du ministre de la guerre pour obtenir un regiment pour mon fils.' Du Chatelet to Jacquier, 12 November 1745, no. 347, Du Chatelet Lettres, op. cit., note 8, vol. II, 144; to Jacquier, 17 December 1745, no. 351, vol. II, p. 148.

15 In her letters Du Chatelet writes of 'epreuves [proofs]' for this project. The manuscript of her Institutions dephysique at the Bibliotheque Nationale (Ffr. 12265) includes pages in her hand, a copyist's, and corrected proofs. Voltaire also worked in this way from numerous drafts and printer's 'impressions'. He even expected his secretaries to correct his spelling, grammar, and phrasing. See P.L. Jacob, 'Le Sottisier de Voltaire', Le Moniteur du Bibliophile 3, 65-75 (1880).

16 See the 'Approbation' at the end of volume II of Isaac Newton, Principes mathematiques de la philosophie naturelle (trans. Marquise du Chatelet) (Paris, Jacques Gaby, reprinted 1990) dated 20 December 1745, and Clairaut's letter of 21 March 1746 quoted in Taton, op. cit., note 3, pp. 197-198. Taton speculates that Clairaut made the recommendation to the royal censors on the basis of a preliminary, uncorrected version of the translation and a brief description of the commentary.

17 See Du Chatelet to Jacquier, 17 December 1745, no. 351, Du Chatelet Lettres, op. cit., note 8, vol. II, 148 and to Bernoulli, 8 January 1746, no. 352, vol. II, p. 149. The printing of the engravings for this project continued to hold up publication. See the 'Avertissement sur les Planches de cet Ouvrage' (1756, 1759 edns), which ascribes delay to the 'figures' and to 'd'autres obstacles qu'on ne pouvoit pas prevoir [to other obstacles that one could not have foreseen]', Du Chatelet translation, Principia, vol. I, p. xl. Even with the delays, 'figures' in the final 1759 edition do not always correspond exactly to those of Newton's third edition. See, for example, Book I, section IV, proposition XIX figs 31 32 and 35, where solid and dotted lines differ; Book I, section VIII fig. 85 with two extra lines; Book II, section IX, fig. 56 with all the lines made solid. On the accuracy of printed versions of drawings in the Principia and other works by Newton, see introductory remarks to Isaac Newton, Philosophiae Naturalis Principia Mathematica (ed. A. Koyre and I. Bernard Cohen with the assistance of A. Whitman), vol. I, pp. xxxii-xxxiv (Cambridge, MA, Harvard University Press, 1972) and J.A. Lohne, 'The increasing corruption of Newton's diagrams', Hist. Sci. 6, 69-89 (1967).

18 These are the 'tourbillons', flowing ether-like liquids, that carried the planets in their orbits. Book II of the Principia on the motion of bodies 'in resisting mediums' specifically addresses this hypothesis. Note that Du Chatelet, unlike Motte for his English edition, did not translate the 1728 version of De mundi systemate liber. Her commentary would serve the same purpose. Cohen and Whitman made the same choice in their edition.

19 BN Ffr. 12266 includes Principia: Definitions, Axioms, Book I on Mouvement des Corps, Book III Sisteme du monde; FFr12267 includes Principia: Newton's Prefaces to 1st, 2nd, 3rd editions, Cotes's Preface, Book II.

20 The issue was whether or not 'Newton's variables reach their limits'. Jurin and Du Chatelet said 'yes', Pemberton and later D'Alembert said 'no'. F. Cajori, The Mathematical Gazette 862 (V.2, b), p. 252. Gerard Emch has noted the care with which Du Chatelet translated Book II, propositions XLVIII-L on the speed of sound, a famous example of Newton's efforts to explain a disparity between mathematical and experimental results. G. Emch and A. Emch- Deriaz, 'Is Madame du Chatelet's a fair presentation of Newton's Principia?', International Congress on the Enlightenment, Dublin, 29 July 1999. On this disparity, see also Motte's translation, op. cit., note 9, footnote 38, II, pp. 661-662; and of this and other similar propositions, Cohen, 'Guide', op. cit., note 2, pp. 361-362, 369, 184-186 and R.S. Westfall, 'Newton and the fudge factor', Science 179, 751-758 (1973).

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21 In Book III see, for example, her translation of Newton's introduction, the statement of his rules of reasoning, and the concluding 'Scholie Generale', BN Ffr. 12266, pp. 280-283v, 450v-455v and 480-482. [Note that the cahiers have been bound out of order and thus the pages are out of sequence.] It is probably these longer prose sections that prompted her editor in the 'Avertissement' to suggest that much was 'plus intelligible dans cette traduction que dans l'original; et meme dans la traduction Angloise [more intelligible in this translation than in the original; or even in the English translation]'. See, 'Avertissement de l'Editeur', Du Chatelet Principia, op. cit., note 17, vol. I, p. i. Olivier Courcelle told me of the thesis by Marie-Fran9oise Biarais, 'Les Principia de Newton et "leurs traductions" Francaises au milieu du XVIIIe Siecle' (Paris, 1981). It makes a study of the differences between the manuscript translation and the Latin text of the Principia. I have not yet had the opportunity to consult it.

22 Contemporaries did not question her authorship of the translation and of the commentary, though all mentioned that Clairaut reviewed her work, a fact she readily acknowledged in her letters. Subsequent historians of science and Voltaire scholars, like Ira O. Wade and I. Bernard Cohen, have ascribed the whole commentary to Clairaut in one way or another. See I.O. Wade, The intellectual development of Voltaire (Princeton University Press, 1969), p. 437. As previously mentioned, Gjertsen credits Clairaut with a collaborative role in the translation as well. See note 38 below for more on Clairaut's role and the identity of the author of the 'Avertissement de l'Editeur'. Some literary scholars have hinted that Voltaire might have been the editor, however, he was not knowledgeable enough to have done this. He supplied the 'Preface historique', his 'eloge' for Mme du Chatelet.

23 BN Ffr. 12268 contains the manuscript versions of only part of the Commentaire: the 'Solution analytique' I-IV, and the 'Table des matieres' for each section. The 'Exposition abregee', and section V of the 'Solution analytique' on the tides, are missing.

24 Du Chatelet to Jacquier, 1 July 1747, no. 361, II, Lettres, op. cit., note 8. p. 157; 'le chemin qu'il a suivi pour parvenir a cette decouverte', 'Exposition', Chapter II, XX, II, p. 43.

25 'M. Newton a compose ce Livre pour detruire les tourbillons de Descartes.' The sentences in the text offer more words, but with the same meaning: 'Ce second Livre ... paroit avoir ete destine a detruire le systeme des tourbillons...'. Du Chatelet 'Exposition', Introduction, XVI, II, p. 9.

26 'Ce Jesuite ayant etre dire a son Superieur qu'il avoit decouvert des taches dans le Soleil, celui-ci lui repondit gravement cela est impossible, j'ai li deux ou troisfois Aristote, & je n y ai rein trouve de semblable.' Du Chatelet, 'Exposition', Chapter I, II, footnote p. 21.

27 Du Chatelet, 'Exposition', Chapter VI, vol. II, p. 110; Chapter VII [Des Cometes], II, p. 112. 28 In Book I of the Principia, Newton gave geometric proofs of all of his basic propositions

concerning the behaviour of bodies, of all kinds of shapes, why and how they moved as a result of the laws of gravity and attraction. As Du Chatelet explained in her 'Exposition abregee', he gave general propositions and then applied them to a number of different cases. This was Newton's own version of Euclidian geometry and Descartes's analytic geometry taken to its highest form. Du Chatelet, in this section of the 'Solution analytique' of her Commentaire, translates these propositions into algebraic equivalents through calculus. Du Chatelet makes specific reference to the sections of Book I of the Principia that match each of her analytic solutions: see especially, Sections II, Determination of centripetal forces; III, Motion of bodies in eccentric conic sections; IV, Determination of elliptic, parabolic and hyperbolic orbits from the focus given; V, Determination of orbits when neither focus is given; VII, Rectilinear ascent and descent of bodies; IX, Motion of bodies in movable orbits and the motion of the apsides. On what Bernard Cohen calls 'the Newtonian style', Newton's use of geometry and calculus, and how to follow his mathematics and method of argument, see Chapter 10, 'How to Read the Principia', 'Guide', op. cit., note 2, pp. 293-368. I am grateful to Sir Alan Cook for his patient explanations of Newton's Principia and to Carson Roberts who helped me puzzle out the correlations between Book I of the Principia and this part of Du Chatelet's Commentaire.

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29 '[M]ettre le systeme de M. Newton dans tout son jour, & da le perfectionner.' Du Chatelet, 'Solution analytique', Section IV, II, p. 260.

30 Although Du Chatelet quotes at length, she gives her own version of both essays, even altering the order of the argument. For example, Bernoulli begins his description of hydrostatics with the Moon, Du Chatelet begins with the Sun. This is unlike the practice followed by Jacquier and LeSeur in their edition of the Principia in which they simply reprinted entire essays as appendices. Note that they also chose Bernoulli's essay, and included those by the other two prize winners of that particular competition, Leonhard Euler, F.R.S., and Colin MacLaurin, F.R.S. Newton, like Du Chatelet, quoted the work of others; see Bernard Cohen's 'Guide', in which he describes Newton's additions, of Machin, and particularly of new observational data, op. cit., note 2, chapters 6, 7 and 8.

31 '[S]ont apres le systeme du monde.' In the same letter, she explained to Jacquier that Clairaut agreed 'qu'il sera de quelque utilite [that it would be somewhat useful for her to write on his essay]' given that 'l'Academie fait attendre bien longtemps ses memoires [the Academy delayed publication of its memoirs for some time]'. Du Chatelet to Jacquier, 1 July 1747, no. 361, Du Chatelet, Lettres, op. cit., note 8, vol. II, p. 157. Note that she focused in her explanation on Clairaut's chapters I-IV, XI, XXIV-XXVIII, XXIX-XLI, XLV. This portion of the manuscript, Section IV of the 'Solution analytique', is the only example of the way in which Clairaut 'checked' her precis of his treatise (or the Commentaire as a whole). In a number of places in the manuscript at the Bibliotheque Nationale, he has extended the calculations, given one or two more sentences of explanation, or added an additional short paragraph. These seem to be the kinds of changes that he made. See, for example, BN Ffr. 12268, 11 bis, 114, 117, 120bis, 123, 129. His notations appear nowhere else. I am grateful to Olivier Courcelle for supplying me with copies of Clairaut's handwriting. Note that Taton seems to have missed this change in handwriting. See Taton, op. cit., note 3, footnote 101, p. 208.

32 See her 'Lettre sur les Elemens de la Philosophie de Newton', Journal des Scavans, 534-541 (Septembre 1738); Arsenal 4oH8909.

33 '[I]l ne reste a present qu'a developper cette cause, a en tirer toutes les consequences, & en calculer les effects'; 'Je me suis sur tout attachee a ... celle de M. [Daniel] Bernoulli, dans laquelle il m'a paru trouver plus d'ordre, de nettete & de precision'. Du Chatelet, 'Solution analytique', Section V, vol. II, pp. 260, 261. Her version of Bernoulli's essay is more descriptive than mathematical, and thus does not exhibit the same obvious similarities as her account of Clairaut's essay. Note that the fullest explanation of the tides came at the end of the 18th century with Joseph-Louis Lagrange's Mecanique analytique (1788).

34 '[L]es personnes qui auront eu tous les secours que je leur ai donne par les details dans lesquels je suis entree, entendront facilement ce Chapitre dans l'ouvrage meme'. Du Chatelet, 'Solution analytique', Section IV, vol. II, p. 259. Note that this was Newton's intention in Book III of the Principia: an explanation of observed phenomena with references back to the geometric modes and analytical solutions of Books I and II for more learned readers to explore. See notes 13 and 28.

35 '[L]e Latin de m. Neuton en est une des difficultes'. Du Chatelet to J. Bernoulli, 8 January 1746, no. 352, Du Chatelet Lettres, op. cit., note 8, vol. II, p. 149; 'il en coute toujours quelques fatiques a lire des choses abstraites dans une langue etrangere...'. 'Le Francais qui est la Langue courante de l'Europe, & qui s'est enrichi de toutes ces expressions nouvelles & necessaires, est beaucoup plus propre que le Latin a repandre dans le monde toutes ces connaissances nouvelles'. 'Preface historique', Du Chatelet, Principia, vol. I, p. ix.

36 '[P]aroit la seule qui puisse vraiment satisfaire dans une recherche de cette nature'. Du Chatelet referring to the problem of three bodies, 'Exposition abregee', chapter VI, vol. II, p. 110. I am grateful to Carson Roberts for a long lesson on Du Chatelet's use of calculus and thus my appreciation of her statement.

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37 Note, that my picture of the last months of Du Chatelet's life differs from that of other historians, some of whom suggest that she played a minimal role in the translation and either did not write the Commentaire, or was unable to complete it. See note 2 above. I believe that she had, in fact, not only finished the translation and commentary, but also the page proofs of the translation, and probably of the commentary as well, by the time of her death. References in the manuscript texts of both the 'Exposition abregee' and 'Solution analytique' to specific pages as they appeared in the 1759 published translation of the Principia indicate that she must have had proofs of the translation of Books I and II and probably of Book III. She could not have included the pages corresponding to the printed text in any other way. Thus, I believe that she had completed both the draft and the proofs of her translation. A note to abbe Salier (the Royal Librarian) appended to Ffr. 12267 (the translation of Book II, Newton's Prefaces and Cotes's Preface to the Principia), traditionally dated ca. 1 September 1749, confirms this premise. The numbering of the manuscripts could indicate that she had

previously deposited Ffr. 12266 (Books I and III, Definitions, Axioms), perhaps as early as 1747 or 1748. All historians agree that she began writing her Commentaire in 1746. Du Chatelet's letters in the spring and summer of 1749 make it clear that she was determined to finish it before going to Luneville (the court of the Duke of Lorraine) for the birth of her child. On the progress as reflected in her letters, see Du Chatelet to Boufflers, 10 May [1749], no. 467, Du Chatelet, Lettres, op. cit., note 8, vol, II, p. 280; Du Chatelet to Saint-Lambert, [10 June 1749], no. 475, ibid., vol. II, p. 292. A receipt from the Royal Librarian dated 10 September included in the Parisian inventory of Du Chatelet's estate could indicate her completion of the page proofs of the Commentaire. The receipt lists 'trois paquets qui contiennent le commentaire de mad. de sur le livre des principes mathematiques de Neuton'. If the 'trois paquets' were later bound together as Ffr. 12268 (the 'Solution analytique' and the 'Table des Matieres' of the Commentaire), this could mean that she no longer needed the manuscript because she had finished checking the printer's proofs against her handwritten version.

38 The identity of the author of the 'Avertissement de l'Editeur' in volume I of Du Chatelet's translation remains a mystery. Given comments about Clairaut in the 'Avertissement', Simon Schaffer and I believe he is unlikely to have written it. For example, the 'Editeur' notes that nothing has been included of Clairaut's theory of secondary planets, the subject of his prize- winning essay for the St Petersburg Academy of Science for 1751 ['Theorie de la lune deduite d'un seul principe de l'attraction']. Had he been the editor (or the author) he surely would have included this in a 1756/59 explanation of the system of the world. See 'Avertissement'. Du Chatelet, Principia, op. cit., note 17, vol. I, pp. iii-iv. Sir Alan Cook agrees that had Clairaut prepared the 1756/59 editions, he would have made revisions of the 'Exposition abregee' and perhaps additions to the section of the 'Solution analytique' describing his own work. Sir Alan Cook, personal communication, 8 September 2000.

39 Debever quotes Voltaire's letter of 25 June 1751 to Michel Lambert, Du Chatelet's publisher, asking for the book, thus suggesting that he was not involved in the project at that time; Debever, op. cit., note 3, p. 520.

40 The reasons for the delay in publication remain unexplained. The publishers ascribed it to the preparation of the drawings. See note 18. The review of Du Chatelet's work in the Journal Encyclopedique of September 1759 mentioned 'contretems [obstacles]', as the reason it was not published before: Journal Encyclopedique 6, partie 3 (September 1759). I am grateful to Simon Schaffer for alerting me to the coincidence of circumstances and the significance of the translation to the dispute on the comets. Unquestionably, this was the reason it was finally brought out. On the excitement, the rush to finish the calculations before the return of the comet and Clairaut's consciously engineered propaganda campaign in favour of his own work, see C.B. Waff, 'Comet Halley's first expected return: English public apprehensions, 1755-58', J. Hist. Astron. 17 (part 1), 1-37 (1986); S. Schaffer, 'Halley, Delisle, and the making of the comet', and Waff, 'The first international Halley

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watch: guiding the world-wide search for comet Halley, 1755-1759'. In Standing on the shoulders of giants: a longer view of Newton and Halley (ed. N.J.W. Thrower), pp. 373-411, 254-292 (Berkeley, University of California Press, 1990); C. Wilson, 'Clairaut's calculation of the eighteenth-century return of Halley's comet', J. Hist. Astron. 24 (part 1), 1-15 (1993).

41 'Le public l'attendoit deja depuis plusieurs annees avec impatience; mais si quelques contretems en ont retarde jusqu'ici la publication, ce n'a ete, ce semble, que pour le rendre plus eclatante, en la faisant concourir avec le moment du triomphe de la philosophie qui y est expliquee & commentee', Journal Encyclopedique, op. cit., note 5, p. 4. Du Chatelet was aware of the significance of the return of Halley's comet as proof of Newton's 'system of the world', and of the universal application of the law of attraction. See, for example, 'Exposition abregee', Ch. VI, I, pp. 114, 116. Note that she distances herself from the controversy and does not indicate whether she agrees or not.

42 'Ainsi l'on peut dire de ce Commentaire qu'il nous offre Newton, mis a la portee de tout le monde, du moins de tous ceux qui peuvent suive un raisonnement philosophique.' [13] '[S]e faste geometrique ... au niveau les lecteurs les moins accoutumes aux discussions mathematiques.' [9] This is a compilation of quotations from the 'extrait [review]' in Journal

Encyclopedique, op. cit., note 5, pp. 13, 9, 14, 10. The reference to 'mis a la portee de tout le monde' recalls the addition made by the Amsterdam publisher to the title page of Voltaire's Elemens de la philosophie de Newton (1738), an addition that Voltaire objected to strenuously.

43 Du Chatelet to J. Bernoulli, 8 January 1746, no. 352, Du Chatelet, Lettres, op. cit., note 8, vol. II, p. 149.

44 It was possible to agree with parts of Newton's theories, but not the whole, or with the general principle and not all of its applications. Into the 1730s, Rohault's Cartesian explanation with Clarke's notes, a text that could be taught with either emphasis, was used at Cambridge, Newton's own university. Principia, Motte edn, op. cit., note 9, vol. II, footnote 5, pp. 631-632. Euler believed in a resistant ether into the 1760s. Even in 1759, Cesar Fran9ois Cassini of the Paris Observatory, accepted the fact of the return of Halley's comet but continued to explain its movements through impulsion and 'tourbillons'. See Schaffer, op. cit., note 40, p. 260.

45 'Quelques auteurs ont tente de rendre la philosophie newtonienne plus facile a entendre, en mettant a part ce qu'il y avoit de plus sublime dans les recherches mathematiques, & y substituant des raisonnemens plus simples, ou des experiences [and to set aside that which was most sublime of the mathematical investigations, and to put in its place simpler reasoning or experiments].' Encyclopedie, vol. XXII (Lausanne & Berne, Les Societes Typographiques, 1778-82 edn), p. 414.



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Documents

Translating Newton's 'Principia': The Marquise du …...Translating Newton s Principia Figure 1. Pierre Louis Moreau de Maupertuis, one of Du Chatelet's first tutors of mathematics