Mentors, the Marquise Du Châtelet and Historical Memory Author(S): Judith P

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Mentors, the Marquise Du Châtelet and Historical Memory Author(s): Judith P. Zinsser Source: Notes and Records of the Royal Society of London, Vol. 61, No. 2 (May 22, 2007), pp. 89-108 Published by: The Royal Society Stable URL: http://www.jstor.org/stable/20462616 . Accessed: 15/11/2013 10:27

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This content downloaded from 75.102.94.107 on Fri, 15 Nov 2013 10:27:53 AM All use subject to JSTOR Terms and Conditions NOTES & RECORDS Notes Rec. R. Soc. (2007) 61, 89-108 -OF THE ROYAL doi: 10.1098/rsnr.2006.0174 SOCIETY Published online 27 March 2007

MENTORS, THE MARQUISE DU CHATELET AND HISTORICAL MEMORY

JUDITH P. ZINSSER*

Department of History, Miami University, Upham Hall, 252 Oxford, OH 45056, USA

When writing a biography, much has to be omitted to keep the life story focused and manageable for the reader. In La Dame d'Esprit: a biography of themarquise Du Chatelet the information about Emilie Du Chatelet's mentors seems, in retrospect, all too brief. This article therefore presents Maupertuis, Clairaut and Dortous de Mairan and describes their interactions with the marquise. It ends with speculations about why this exceptional philosophe is only now gaining the recognition she deserved as a member of France's eighteenth-centuryRepublic of Letters.

Keywords: Emilie Du Chatelet; Dortous de Mairan; Fontenelle; Maupertuis; Clairaut; women's history

Writing a biography means abandoning at least one-third of it:whole sections become just so many rejected pages, parts of files thatneed never be accessed again. To cut La Dame d'Esprit, my biography of Gabrielle Emilie leTonnelier de Breteuil, marquise Du Chatelet (figure 1), to a size thatwould not overwhelm readers proved particularly difficult.Each new decade of her life from her birth in 1706 to her premature death in 1749 had required more background research inFrench eighteenth-century social and intellectual history than I had ever expected. For example, after numerous edits, chapter one, 'The families: daughter and wife', retained only theessentials about hermany relatives and how they functioned in thehierarchies of Louis XIV's court; about the traditional education fora noble's daughter; about hermarriage contract and how it compared to others of a similar class; and about the ingenious ways inwhich the nobility managed their finances. Hard though it is to admit, what felt at times like butchery improved thebiography for the reader and kept the focus clearly on themarquise and her story. When it came to Du Chatelet's writings, the process was even more painful but with a similar result.Du Chatelet worked forprose thatwas simple, clear and concise; so must her biographer. Itmeant, however, that only a part of what I had learned to give context to her books and clandestine texts survived the final cuts; for example, about the controversies over theCartesian versus theNewtonian universe and theways inwhich physiciens (physicists) and geometres (mathematicians) combined aspects of each to explain the cosmos; about Du Chatelet's remarkablymodern understanding of space and time; about her 700-page heretical commentary on theBible; and about the composition of her discourse on personal happiness.

*[email protected]

89 ? 2007 The Royal Society

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Figure 1. Portrait of themarquise Du Chfitelet byMarianne Loir, ca. 174 1. (Supplied courtesy of the collection of the Chaiteau de Breteuil, near Chevreuse, France, and reproduced with permission.)

To make matters worse, thisbiography had a wider purpose: to counter all the half-scholarly, half-popular-romance versions of Du Ch'atelet' s history and to present a balanced and accurate lifeof this remarkable noblewoman who was recognized inher own timenot only because of her liaison with Voltaire-which every previous biography lingersover-but also because of her contemporary reputation as a natural philosopher and as the translatorof and commentator on Newton's Principia. Each paragraph seemed essential to counter yet another stereotype. Fortunately, wise editors knew that the reader caught up in themysteries and challenges of reconstructingthe history of thisunorthodox woman and herworks would go to thebibliography to seek the longer discussions of these issues in articles that I and other scholars had written. If ithad been appropriate tohave a much longerbiography-it is now a relativelymodest 293 pages-what would I have chosen to restore?Given thisopportunity to inaugurate a series on

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Figure 2. Du Chfitelet as she pictured herself for the frontispiece of her 1740 Institutions de physique. (Supplied courtesy of the collection of R. K. Smeltzer, and reproduced with permission.)

life-writing for Notes and Records, what other stories do I wish to tell? Certainly, more information is called for about the ge'ome'tres and physiciens who contributed to her success. Their interactionswith themarquise Du Chatelet are part of the intellectualhistory of Europe, and the gendered evolution of modem science (figure 2). Next I would have added an extended discussion of how and why theaccomplishments of thisexceptional participant in thefirst half of theFrench Enlightenment could have been forgotten,especially when her intellectual and social

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Figure 3. Engraved portrait of Pierre-Louis Moreau de Maupertuis. (Copyright ?D The Royal Society.)

peers accepted her as a genius, and after the publication of her Institutions de physique [Foundations of physics] in 1740 as a philosophe. For history's fascination is as much about the stories thathistorians have allowed us to forgetas those theyhave agreed to tell.

THE MENTORS

The most appealing and interesting of Du Cha'telet's mentors in the new mathematics and physics was Pierre-Louis Moreau de Maupertuis (figure 3). He was 35 years old to her 27

This content downloaded from 75.102.94.107 on Fri, 15 Nov 2013 10:27:53 AM All use subject to JSTOR Terms and Conditions Mentors, themarquise Du Chaitelet and historical memory 93 years in 1733, when she returned to Paris as a young married woman, and had probably already given lessons to her principal women friends, the duchesses de Saint-Pierre and d'Aiguillon. For Maupertuis, with money and the title thathis fatherhad earned as a Breton privateer successfully turnedmerchant and entrepreneur of the Atlantic trade, had taken readily to theworlds of the court and the salon. The elite of Paris appreciated his wit, his amiability, his talent formathematics lessons laced with gallantry.! He had been equally successful with themen of theRepublic of Letters. Having rejected themilitary career his father had arranged for him, he cultivated themembers of one of Paris's most prestigious caf6s, theGradot on the quai du Louvre. He and his friends, such as Charles Marie de La Condamine, the future leader of the expedition to equatorial South America tomeasure the curvature of the Earth, and their young friend, the mathematics prodigy, Alexis-Claude Clairaut, met at the cafe at about noon, and later in the evening after a play, the opera or dinner at one of the noble households they frequented.Maupertuis was so successful in this circle thatwhen the blind and aging librettistof Louis XIV's court, Antoine Houdar de la Motte, died in 1731, themathematician took his place and led the daily conversations. When Du Chatelet became Maupertuis's pupil, he had, in addition, already achieved the status of pensionnaire in geometry, the highest rank for a mathematician among the 42 paid members of the royal Academie des sciences. In his rise,Maupertuis was not atypical of this new learned scientific generation, themen whom Du Chatelet turned to for intellectual instruction and guidance. The average age of members of theAcademie des sciences in the 1720 and 1730s was 28 years. Few among them had a full-fledged university education and formal degrees. Instead, young men's families supported a few years at a college-Maupertuis attended theCollege de laMarche inParis and then arranged for introduction to a member. For example, on his return to Paris, Maupertuis became the protege of important members of the Academie des sciences including its perpetual secretary (executive director), Bernard le Bovier de Fontenelle.2 Perhaps at Fontenelle's suggestion,Maupertuis chose mathematics as his specialty, although some historians have speculated that it had more to do with potential vacancies at the Academie thanwith a particular aptitude.3 However, the renowned Swiss geometre, Johann Bernoulli, with whom Maupertuis studied from September 1729 to July 1730, complimented the younger man to former pupils. Bernoulli wrote to a colleague in Paris at the end of Maupertuis's firstextended stay in July of 1730 about his pupil's 'extraordinary vivacity of mind, understanding things in half a word, and almost as many minutes that I employed hours to find'.4 He imagined that one day Maupertuis would be themaster and he the student. Equally important for Du Chatelet's education and future aspirations, Maupertuis was remarkable for his eclectic interests. He was a 'natural philosopher' in its broadest seventeenth- and eighteenth-century English meaning. His first paper read before the Academie described themathematics of the resonating stringsof musical instruments.He led the polar expedition to Lapland thatwith La Condamine's measurements proved Newton's hypothesis about the oblate shape of the Earth. Later writings, when he had become the director of Frederick of Prussia's Academy in Berlin, concerned themechanics of heredity and reproduction. In addition,Maupertuis, like Fontenelle before him, attained a certain popularity with the men and women of Du Chatelet's circle not only because of his liveliness in theirgatherings but also because he had written on a controversial scientific subject in a style and form that even his novice pupils could follow. In his Discours sur les diffierentesfigures des astres [Discourse on the differentshapes of the stars], published in 1732, he subtly questioned the

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reigningAcademie view of the universe, Descartes's cosmology. Very diplomatically, he did not insist on any theory, ratherhe planned to leave it 'to the reader to examine if attraction is sufficientlyproved by the facts or it is only an unfounded supposition thatone can pass over'. He set observed phenomena against themathematical calculations and resulting general laws of Descartes and Newton. He asked which author' s hypothesis provided the most correspondence. Apparently with great reluctance, he acknowledged thatNewton's concept of attraction in combination with centrifugal force best explained Kepler's observations of the elliptical paths of the planets and thus confirmed Newton's 'System'.5 Perhaps itwas his example that led Du Chatelet to question both Descartes and Newton in her Institutions de physique and her commentary on Newton's Principia, also destined to appeal to both the learned and the amateur physicien. Du Chatelet's delight inmathematics must have begun when she was child. In La Dame d'Esprit, I have hypothesized thather excitement was rekindled while she awaited thebirth of her second son in Semur, the provincial town where her husband was military governor. Her decision to take lessons with the newly celebrated mathematician followed naturally on the resumption of her life in Paris in 1733. Maupertuis, in turn,must have been flattered and intrigued by Du Chatelet's enthusiasm for the subject. Soon, however, her aptitude and intensity, beyond his usual experience with his noble students, seems to have become a nuisance; he allowed the lessons to become more sporadic. Du Chatelet' s letters to Maupertuis in 1734 and 1735 give only hints about the content of their lessons together.He assigned her the text thathe himself had studied with his mentors, the academician Francois Nicole and Bernoulli: Nicolas Guisnee' sApplication de I 'algebre a' la ge'ometrie [Application of algebra to geometry, 1733 edition]. He also set problems for her to work through.Not surprisingly,Du Chatelet confessed that she preferred learning from her mentor rather than this dry text. She used a recurrenteighteenth-century metaphor: 'You sow the flowers on the path where others find only brambles, your imagination knows how to embellish the driest materials without diminishing their accuracy or theirprecision'.6 Despite his waning interest in her tutelage and a brief period of estrangement later in the 1740s, Du Chatelet described their relationship as one of 'amitie', an eighteenth-centuryword with nuances of affection and respect. As she turned to ever more ambitious studies in mathematics and physics, she continued to seek Maupertuis's counsel and his approbation. Although Maupertuis did not always respond to her queries as rapidly as she hoped, he was in many senses her intellectual model: a man able to navigate the court and theworld of the learned; a philosophe interested in such varied subjects; his writings, as she described them, 'full of wisdom and fine calculations'.7 By 1738 Du Chatelet had moved on to othermentors, but she still felt a special affinitywith him. She described them both as 'heretics in philosophy', a role that each cultivated and enjoyed. Du Chatelet used a seal with Voltaire's profile formany of her letters.To Maupertuis, however, went the singular honour of having the framed engraving of his portrait hung in her bed chamber at the hotel on the rue Traversiere where she completed hermost demanding scientificwritings. Perhaps it gave her inspiration. Clairaut, Du Chatelet' s nextmentor, chose an engraved portrait ofNewton forhis studywith a similar purpose.

Determined to continue her mathematics lessons regardless ofMaupertuis's inattentiveness, as early as the autumn of 1734 Du Chatelet turned to his young protege, Alexis-Claude Clairaut (figure 4). The marquise called her new mentor, 'Petit Clerau [Little Clairaut]', perhaps a reference to his age. Colleagues mention his near-sightedness but not his height. In

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Figure 4. Engraved portrait of Alexis-Claude Clairault. (Supplied courtesy of the Acad6mie des Sciences, Paris.)

1734 he was seven years her junior, just 21 years old, but already recognized as a mathematics genius and already an associate member of theAcadedmie. Clairaut's father,once a pupil of Guisnede and a member of theBerlin Academy, had taught the boy himself. His son excelled.

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Just four months short of his 13th birthday, Clairaut made his firstpresentation to the Academie; the subject, differential calculus. Abbe Bignon, the reformer of theAcademie in the 1690s and later,often itspresiding officer,became his patron.When the young man went to live atMont Valerien, Maupertuis' s country house just on the outskirts of Paris, he became identifiedwith the new generation of Anglophile admirers of Newton. At the same time, as a relative innocent inwhat the elite called 'le usage du monde [theways of theworld]', Clairaut began learning how to negotiate the light-heartedbut politic evenings hosted, for example, by the duchesse de Richelieu, a close friendof themarquise Du Chatelet. Mme de Graffigny, the copious letterwriter of these decades, remarked on Clairaut's youth, his 'lovely, witty pleasantries', but came to find his inability to talk about anything but mathematics with enthusiasm boring. His gift for the subject, however, enabled his rise to the highest level of pensionnaire inMay 1738, after his returnwith Maupertuis from the expedition toLapland. He learned to turn it to lighterpurposes, as well. In 1745, his clever bit ofmathematics, which he called a description of Archimedes' spiral but suggested instead the geometry of a man's erection, merited inclusion in the firstpublished collection ofMlle Quinault and the comte de Caylus's famous literary salon, the 'bout de banc' 8 There are no extant letters between Du Chatelet and Clairaut from the 1730s. Instead the interested biographer must imagine their lessons from another source. Contemporaries assumed that Clairaut's textbooks Elemens de geome'trie [Elements of geometry] (1741) and Elemens d'algebre [Elements of algebra] (1746) had been written forDu Chatelet, and that she used at least one of them when she took over her son's education.9 The tone of both of Clairaut's texts is conversational, almost as if the young geometre and his pupil were discussing the problems and their solutions together. This style made them particularly appealing to their intended audience, 'beginners'. For geometry Clairaut used a commonsense approach, presenting an everyday situation and then guiding the student to its transformation into a general theorem that could be applied inmany situations. As he explained in the preface, geometry began when individuals wanted tomeasure their lands, and thus its literal meaning was 'measurement of the earth'.1? Du Chatelet could easily follow the lessons to survey the fields at Cirey, the chateau where she lived with her family and Voltaire from 1735 to 1739. Obstacles and irregularities in the terrain turned into geometric shapes such as triangles, squares and rectangles, or more complex many-sided figures. By the last section, the lessons had progressed to solid figures and their surfaces, the basic geometry thatDu Chatelet needed when she turned to her studies of Newton's Solar System. Similarly, Clairaut suggested the historical evolution of algebra and began this second text with problems thatDu Chatelet would have recognized from everyday life; for example, her days with theworkmen doing repairs and alterations to the family chateau inChampagne. 'A Workman can do a certain job expressed by a in a time expressed by b; a second does job c in time d, a third job e in time f, one asks how much time would it take for these threemen, working together to complete job g?' She might have found another lesson useful for her experiments with themixing of liquids when she and Voltaire explored the effects of heating and cooling for theirdissertations on the nature of fire for the 1738 Academie des sciences competition. 'Given the specific gravities of twomaterials which have been mixed together, the volume and the totalweight of themixture, findhow much of the twomaterials is in the mixture'. A problem designed to calculate the yearly losses for a businessman unable to remove his money from a failing enterprisewould have been useful to her, given her primary responsibility for her family's finances.'1

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As with thegeometry text, theproblems and theirequations inEle'mens d'algebre increase in complexity, ending with those Clairaut called 'of the thirdand fourthdegree', operations with multiple unknowns and complex operations in the division and multiplication of radicals. With this knowledge Du Chatelet would be able to understandMaupertuis's efforts to transform the geometric analogies of Newton's Principia into an analytical (algebraic) form.When themarquise chose to embark on a similar project herself in the late 1740s, as part of her commentary on Newton's massive work, itwas Clairaut who met with her and checked her calculations. He was thementor who took her aspirations as a geometre seriously and helped her to progress beyond that of an amateur. From their firstlessons he had found her 'altogether remarkable', and after her death it was he who encouraged the Parisian publisher Laurent Francois Prault to bring out her commentary and translation of the Principia and arranged for the completion of the illustrations.12

Jean-Jacques Dortous de Mairan became themarquise Du Chatelet's mentor in 1740 but not in the skills he assumed he would impart. In his eyes, her overt attack on his 1728 Academie Memoire on forces vives (a defense of Descartes's concept of motion) in the last chapter of her Institutions de physique seemed a challenge thathe could not ignore, especially as he was about to succeed Fontenelle as perpetual secretary of theAcademie des sciences. Mairan must have seen this as an opportunity not only to counter thisLeibnizian formula that she favoured for themovement of bodies, but also to remind an errantmarquise of a woman' s proper place. Perhaps Mairan imagined himself as the gallant, learned gentleman of Fontenelle' sEntretiens sur la pluralite des mondes [Conversations on theplurality ofworlds], a perennial best-seller since its publication in 1686. He would instruct and correct this young noblewoman as the fictionalmentor had instructed his. Even ifDu Chatelet resisted his tutelage, by his wit and his superior knowledge he would mock her pretensions and show her to be incapable of serious philosophical and scientific dispute. Mairan, like Maupertuis and Clairaut, came from the provinces. His barrister father planned a military career for his son, and Mairan firstcame to Paris in his twenties for the lessons in riding, fencing and dancing thatwould have completed his education as a future officer.Subsequent service to theKing would, his father assumed, mean advancement to the ranks of theminor nobility for his son.13 However, as Maupertuis would do 20 years later, Mairan turned tomathematics and the new experimental philosophy. The philosophe and academician Nicolas Malebranche became his mentor and continued to correspond with him when, likemany of his contemporaries seeking a reputation in the sciences, Mairan returned to the provinces. There he rose to prominence in the local academy of Bordeaux, finally winning three successive prize medals and a reputation for the difficult task of duplicating Newton's optical experiments.14 Du Chatelet used his Dissertation sur la glace [Dissertation on ice], applauded by the academicians of Bordeaux in 1716, for her essay on fire.Mairan wisely wrote 200-300 letters to go with the prize essays he mailed to the learned of eighteenth-centuryEurope. Thus, when he returned toParis, he won election to theAcademie at the rank of associate in mathematics in 1718 and, with remarkable speed, only seven months later in July of 1719 to the coveted status of pensionnaire. Even so,Mairan's work remained pedestrian. His essay on the aurora borealis, published in 1731, showed his greatest strengths as a natural philosopher. He collected all references to its occurrence stretching back to the fifthcentury. He thenused geometry only descriptively, to indicate, for example, the height of one manifestation, and ascribed the phenomenon to a Cartesian interaction of solar and terrestrialatmospheric particles.15

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Always the careful observer of society,Mairan cultivated his association with Fontenelle and the other leaders of theAcademie such as abbe Bignon and Bignon's surrogate as he grew older, the geometre Rene-Antoine Ferchauld de Reaumur, now most famous as an early entomologist. They acknowledged his loyalty to Cartesian explanations and his expertise in experiment by having him serve for a number of terms as the group's science officer, the member with the very visible responsibility for public demonstrations. In addition, Mairan was an editor of the influential Journal des scavans. His elegant style of writing gained him admission to theAcademie francaise in 1743, a dual honour he shared with Fontenelle and Maupertuis. Mairan also frequented the rarefied, aristocratic world of the court and the salons. Through the duc d'Orleans he had been invited to sit at Cardinal Fleury's table at Versailles, and thus became known to Louis XV's principal minister. He had attended Mme Lambert's salon and after her death was one of the 'Seven Sages' of Mme Tencin's gatherings. She not only designated him her executor but also willed her inheritance 'to the relatives and friends ofM. de Mairan'. He, in turn, left all of his wealth to Tencin's successor, Mme Geoffrin. Du Chatelet and he met at this kind of gathering in Paris. Mme de Graffigny described a dinner they both attended one Thursday in September of 1739. When another guest, a geometre fromBasel, foolishly broached the controversial subject of the shape of the Earth, Mairan's quick response highlighted theman's gauche behavior: 'Ah,monsieur, you make us tremble. It [such a discussion] is equivalent to being inebriated by the time of the soup course.' 16 For all his political acumen and social skills, however, Mairan did not aspire to be Fontenelle's successor as principal administrator of theAcademie; when asked, he initially declined the honour. When the older generation of members and government ministers insisted, he agreed to serve, but for only one term.Mairan's selection as perpetual secretary meant more than just an endorsement of 'le doux [themild-natured one]', as he was called by his society friends.Royal ministers and Fontenelle and Reaumur counted onMairan to carry on the established traditions of theAcademie and to defend the Cartesian, rather than the Newtonian or Leibnizian, universe and the superior authority of themathematical rather than experimental scientific approach to research. In particular, he was to be the institutions's principal defender of the royal astronomer Jacques Cassini, whose calculations seemed to prove the flatteningof theEarth at theEquator, rather than at the poles as advocated by the Newtonians such as Maupertuis. In lateDecember 1740, when Du Chatelet had the copy of her Institutions delivered to his hotel, Mairan was in his sixties, a small, portly man, used to his regulated life at the Academie, thebest salons, and at his country house (figure 5). A pleasant, methodical man, he had never married, and was purported to have organized a scale of temperatures and materials so thathis valet would know exactly what to lay out forhim on any given day.When Mairan discovered that Du Chatelet had reopened a controversy that he believed his 1728 Dissertation sur 1'estimation & la mesure des forces motrices des corps [Dissertation on the estimation & measurement of themotorforce of bodies] had settled, he found her arguments impossible to ignore. As his colleagues had hoped, he saw himself as the one who must take up this challenge to French science to defend not only his honour but also that of the Academie, forwhich he had now become the official spokesman. It was the clarity of her presentation of Leibniz's ideas, as well as the pages specifically arguing with his position on forces vives, thatdecided him. As he explained in his published response, this 'young lady of quality' had overstepped theboundaries of polite disputation, and had brought 'theirdifferent manner of thinking about Forces Vives' before the 'Tribunal' of the public. He showed

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Figure 5. Engraved portrait of Jean-Jacques Dortous de Mairan, by Carmontelle. (Supplied courtesy of the Bibliotheque nationale de France, and reproduced with permission.)

himself ready to accept its judgement.17 Mairan's elite salon companions had tried to dissuade him and encouraged him to ignore the attack, not to draw the e'pe'e [fencing sword] against 'thispoor Emilie!' His hostess feared thathe would be mocked for such an action, an epee against a fan. His response, given in his most courtly style, was widely reported: 'I implore you to observe that itwould not be an e'pe'e: a compass suffices. ... That is quite enough to check the strikes of a fan'. 'The most annoying of all this', he wrote in the cover letter thatwent with his pamphlet to all of his colleagues and friends, 'is the time it cost. My [response] to Mme Du Chatelet is an affair of three or four mornings, but all of the accompaniments to the printing ... tookmonths.' 18 The controversy overforces vives began long before Du Chatelet was born. InDescartes's and Newton's world therewas but one kind of force, our concept of 'momentum', and one way tomeasure it:mv. They agreed that this force was cancelled out or dissipated in the collisions of bodies. Leibniz's 1686 article for theActa Eruditorum ascribed a dynamic quality tomatter, and hypothesized an alternative kind of force described as mv2. This active force (a forerunnerof our kinetic energy) was not lost in collisions and never diminished throughout the Universe. Mairan's 1728 Dissertation had been an answer to Johann Bernoulli's presentation of this Leibnizian concept. The seventeenth-century and early eighteenth-centuryphysiciens could not conceive of both forces operating in theiruniverse. 19

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Du Chatelet had tried to solve the puzzles of this controversy throughout 1738 and 1739. At first she soughtMaupertuis's guidance, but finally arrived at her own resolution of the inherentcontradictions. Her essay on fireappeared with her public disavowal ofMairan' s and Newton's formula and her adherence to the Continental description of force enunciated by Leibniz and JohannBernoulli. In Chapter XXI of her Institutions she gave Leibniz' s rationale for the concept of forces vives: a moving body accumulates force, and thus the formula describing thismovement must include the squaring of the speed, with forces vives working like an 'infinite spring' putting greater and greater pressure on a body. Du Chatelet then moved on to consider the fourmajor arguments posed against Leibniz and Bernoulli. She chose the 1728 Dissertation by Dortous de Mairan to refute because of its authority and because, as she explained in the Institutions, his argument, although wrong, was themost ingenious of the defenses given.20 Du Chatelet, schooled well in the rhetoric of theAcademie and scientific discourse, took up each of the arguments againstf= mv2: experiments, the role of time, the difficultyposed by 'hard bodies', and the dissipation of force in theUniverse. It was in her reasoning on the last point that she came to consider ideas very similar to our modem conservation of energy. As she explained toMaupertuis, 'all things being equal', the immutable quantity of force 'would be more worthy of the eternal geometre'.21 Mairan's plan failed miserably. He, not she, became the object of veiled derision. Just the fact of his response gave Du Chatelet unprecedented status. As she confided to the comte d'Argental, a close friend of hers and Voltaire's: 'I am very honored to have such an adversary'22 Her husbanddelivered her 37-page published answer to Mairan inParis, and she arranged for500 copies to be sent tomembers of theAcademie and to others in theRepublic of Letters and the salons. Du Chatelet changed none of her views, and having felt, as she admitted toMaupertuis, 'all the ridicule of the secretary's letter', she responded with equal sarcasm and feigned respect. She even made Mairan responsible for her biting mockery: 'because it is in spite ofmyself, & only to follow you, that I sometimes distance myself in this Letter, from the strict style that I believe to be the only one suitable in philosophic matters'. 23 When the Journal de Trevoux reviewed her interchange with Mairan, it confirmed what the secretary's attack had initiated, her acceptance as a member of theRepublic of Letters. Although the author did not agree with her position on the formulaf= mv, he complimented her for leaving nothing unanswered, 'opposing reason for reason, witticism forwitticism, courtesy for courtesy', and for her mastery of thatmost French skill, irony.24Du Chatelet appreciated the significance of the secretary's challenge and her successful response. He found himself inwhat she described as 'a cruel situation': silence suggested he had admitted thathe was wrong, towrite so ineffectually again would be worse.25 Even Mairan's friends, such as the Swiss mathematician, Gabriel Cramer, later acknowledged her victory: 'She is right on all the points and she proved it with much force, clarity and elegance'. 26 The favourable two-part review of the Institutions in the Journal des scavans also signalled her new intellectual status. Her majestic synthesis had already prompted compliments from confirmed Cartesians and from those, like Clairaut, who were opposed to Leibniz's metaphysics. Both the Institutions and her response toMairan were translated intoGerman and Italian. Laura Bassi, the lecturer on Newton at theUniversity of Bologna, reputedly used the Institutions as a textbook. Du Chatelet's admission to theBologna Academy of Science brought more accolades from her contemporaries as 'the firstFrench woman to have applied herself to the study of Philosophy, & [to have] written on such abstract matters'. 27 Her subsequent translation of Newton's Principia and her commentary presenting the mathematical confirmations of universal attraction developed by Clairaut and Bernoulli's

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son Daniel drew similar praise from contemporaries and resulted in her inclusion in the Encyclopedie of Diderot and D'Alembert as one of seven scholars who had made Newton accessible. As yet another indication of her significance and her effectiveness,many passages from the Institutions, especially from the firstmore metaphysical chapters and her explanations of Leibniz, found theirway into entries for theEncyclopedie, sometimes with attribution,sometimes not.28

HISTORICAL MEMORY

Why, then, has so little been known of her until the past decade? Why were Du Chatelet's accomplishments ignored in our narratives of theEnlightenment and the history of science? Why was her story reduced to a series of sexual liaisons and her 15-year relationship with Voltaire? Why could themarquise's contemporaries accept her authorship of the translation of and commentary on Newton's Principia while twentieth-century scholars denied it?29 What subsequent traditions and authorities does her history challenge? Certainly, the marquise' s decision towrite about Newtonian mechanics in a metaphysical context, however appropriate in her own day, would by the end of the eighteenth century set her apart from what became the mainstream of European scientific enquiry. Voltaire's famous pronouncement to Frederick of Prussia expressed the opinion of many in the Republic of Letters and would characterize the physics to come, whether or not practitioners favoured an observational and experimental or mathematical approach to the sciences: 'All of metaphysics, inmy opinion, consists of two things, firstwhat all men of good sense know, 30 second what they will never know'. Du Chatelet maintained her adherence to the more inclusive concept of 'natural philosophy' for two reasons. First, she knew that the principal Continental arguments against Newton's hypothesis that universal attraction governed the workings of the Solar System had been its lack of a clear causal explanation. How was it transmitted, say, from the Sun to theEarth? Although Du Chatelet in the Institutions acknowledged that scientists still had to discover this mechanism, she provided an overall metaphysical context that answered the larger philosophical questions raised by attraction. Second, she herself could not ignore the metaphysical implications inherent in any discussion of Newtonian mechanics. For example, if all matter is subject to the law of attraction, what of the human body? How might one exercise choice, have free will, if all were subject to this mechanical force? Also, Newton had argued that objects on impact caused force to dissipate. Itwas lost to theUniverse and thus necessitated a Deity who would replenish that force periodically. Du Chatelet insisted on a system that allowed freewill and thatwas not subject to arbitrary, divine intervention. Such a situation, she argued, would be a 'nightmare' and make a mockery of all natural laws so far established for theUniverse. There could be no scientific certainty in this cosmos of miracles. The learned taste for such questions and such explanations waned in the excitement and success of more concrete and particular explanations. Observations confirmed new mathematical and experimental models of aspects of Newton's theoryof universal attraction, and ultimately led to its acceptance across Europe. In his writings Newton had suggested three potential confirmations of the working of universal attraction. All proved true: Maupertuis and La Condamine's expeditions confirmed the flattened shape of the Earth's polar regions; Clairaut and Daniel Bernoulli's Memoires for the Academie des sciences described the relationship of the Sun, Earth and Moon and explained the irregularities of the

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AL.~~~~~~~~~~~~~~~~~~~~

Figure 6. Portrait of Bernard le Bovier de Fontenelle. (Copyright ?D The Royal Society.)

tides; Clairaut and Mine Lapaute's mathematics predicted the return of Halley's comet almost to the day and thus validated Newton's suppositions about its orbit.

Perhaps more significantly for her future reputation,Du Ch'atelet's unorthodoxy fell prey to the inheritedgender traditions of European culture. Despite her genius, her writings and the contemporary recognition, these ancient images of the female and attitudes about even a marquise presuming to function in a man's world proved too strong to protect thememory of this remarkable woman. Her era had a powerful, seductive countermodel that spoke directly to past prejudices. While ineffectual in the hands of a Dortous de Mairan, this traditional model achieved his purpose in the writings of future generations. 31 Although Bernard le Bovier de Fontenelle (figure 6) did not intend to create a stereotype in his Entretiens, he drew on familiar, hallowed views of the female that could not help but perpetuate assumptions about women's inability to undertake serious learning or tomake significant contributions in mathematical and scientific studies. With each new edition-he corrected the 14th in his

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eighties-another generation could equate Du Chatelet with Fontenelle's eager, flirtatious marquise.32 In the 1730s Francesco Algarotti, a Venetian physicien and visitor to Du Chatelet's informalAcademy at Cirey, borrowed the characters, the scene and the lacing of Newtonian formulas with analogies to love for his In Newtonianismo per le dame [Newtonianism for the ladies]. Algarotti's description of evenings spent in delightful conversation with another lively, young noblewoman easily led to such an association in the salons and cafes of Paris. Ironically, Fontenelle was a friend of Du Chatelet's family and probably attended her father's salon at no. 12 Place Royale (now the prestigious Place des Vosges). His success in theRepublic of Letters of the firsthalf of the eighteenth century was unrivalled. Elected to both theAcademie des sciences and theAcademie franqaise, contemporaries called him 'le roi [theKing]', in recognition of his mastery of every genre.33 He was, in fact, themodel of the self-definedphilosophe, able to navigate the currents of Paris's social and intellectual worlds. From a bourgeois family inNormandy, as a young man, new from the provinces, he made excellent use of his connections: 'le grand Comeille', one of Louis XIV's most successful playwrights, was an uncle. Fontenelle wrote for the new periodical, theMercure galant, developed an elegant prose style and a reputation forpresenting thenew natural philosophy in ways thatcould be understood by the interested reader. Plays and histories, and theEntretiens published in 1686, demonstrated his adherence to the 'moderns', thegroup inParis arguing for the new sciences of reason and the senses, with observation, experiment and mathematics as the cornerstones of knowledge that now surpassed that of the 'ancients'. Monies from his publications, his royal pensions and his astute loans and investments enabled him to live well. According to a French visitor fromBerlin, he paid a princely rentof 3000 livres a year forhis hotel on the rue Saint-Honore in themost fashionable section of Paris, and, according to rumour, could still afford to give a quarter of his income to his parish each year.34 Fontenelle never married. Such a ridiculous act, he explained, would have shown 'a lack of taste' in a philosophe. A regularmember of the salons, including, as a young man, the famous gatherings of Mme de Scudery's precieuses [precious ones], he learned the French 'art of pleasing'. He would subsequently be a favoured member of the salons of theRegency and Louis XV' s reign.Tuesday evenings he reserved forMme Lambert; on her death he honoured her successor, Mme Tencin, with his presence, and after she died, at the age of 92 years he graced the evenings ofMme Geoffrin. A contemporary memoir mentions his height, 5 feet 8 inches, tall for the era, his nice figure and his ability to respond with calm, measured sensitivity to the repartee that constituted the principal entertainment in these privileged gatherings.When one of his hostesses commented thathe never laughed, he indicated thathe thought it a noisy, intrusive act. Instead he offered the hint of a smile, and his refined conversation, his subtle wit and sarcasm. It was his quiet, pure, reasoned control that all commented on, even in his nineties. To an Englishman who rushed up to the elderly gentleman, exclaiming how eager he was tomeet and talkwith him, Fontenelle replied: 'I have waited for you long enough, monsieur; ithas not been my fault thatyou have not seen me; I have lived to ninety-six years in order to give you thepleasure, ifpleasure it is. See what I have done for you; a sort of miracle.' Fontenelle's most obvious legacy, his years as the perpetual secretary of the royal Academy of Sciences, have been well chronicled. Historians are now beginning to speculate on other aspects of his career and the significance of his writings. His images in theEntretiens of the intelligent woman and her male mentor were not original and would proliferate throughout the eighteenth century. It was, however, Fontenelle's rendition in his elegant,

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conversational style that created themodel for subsequent authors. Although his intended audience was female, Fontenelle had few expectations about women's minds, and in any case he did not believe thatwomen should be obvious in their display of any intelligence they might possess. As he explained in the preface to theEntretiens, 'I only ask of the ladies, for thiswhole system of Philosophy, the same amount of concentration thatmust be given to The Princess of Cleves in order to follow the plot closely and understand all its beauty'. Fontenelle intended the comparison with this popular tragic love story, his references to Ovid's Art of Love and toAriosto, the Italian erotic poet, and his 'mixing foolish lovetalk with our serious conversation', as the devices needed to '[draw] Madame theMarquise into the philosophicalfold'.3 Le roi never allowed his readers to forget that the speculations about life on other planets and in other universes, like his comparisons of 'the logic ofmathematics' to 'talk of love', had more to do with gallantry than pedantry. This fictionalmentor worried in fact thathis honour might be tarnished should others ever learn that 'I talked of philosophy to themost beautiful woman I know'. Even theyoung noblewoman's eagerness to learn about Descartes's universe became part of the flirtation:"'I've never seen you so transported"', he told her; "'It's a shame all this should be wasted on mere vortices"'. Opportunities fordouble meanings abound. Her mention of 'intense pleasures' prompts his wish for her promise 'that if anyone offered you these intense pleasures you'd remember thevortices and me, and not shut yourself away from us?' His equal in this flirtatious interchange, themarquis replied, 'Yes, ... but you must make sure that [natural] Philosophy always furnishesme with new pleasures'.36 Fontenelle didmake itclear from theopening preface of theEntretiens that itwas not only the marquise's lovely eyes but also her 'vivacity of intelligence' that led to these playful evenings of tutelage. This mentor, having rejected the reading of endless tomes as themeasure of learning, explained thathe considered his hostess and companion, despite her lack of formal education, 'a scholar because of the extreme ease with which she could become one'. Indeed, Fontenelle portrayed her as quick to understand, with a 'lively and prompt discernment'. She posed appropriate questions as theuniverse was revealed toher, marvelled that 'all this ismagnificently arranged', was astonished to discover 'that there should be so littlemystery to eclipses'. 37 Itwas he, not she,who refused to give both theirdays and evenings to thediscussions. Itwas she who occasionally expressed annoyance and insisted on a returnto serious topics: 'I'll not be bought off with words ... let's get to facts'. Such positive images, however, were always countered by the lightness of her tone, and in the last evening by her increasing confusion. To the complexity of successive revelations she responded: "'Have mercy, ... I give up! You overwhelm me with systems and vortices"'. The plenitude of stars, and the fact that they too are suns, prompted: 'here's a universe so large I'm lost'. Learning that suns can die was 'too grim' to contemplate, 'Couldn't you have sparedme this?'38 Du Chatelet's contemporaries would have smiled at themarquise's exclamation at the end of theEntretiens "'Well!" she cried. "I have thewhole system of the universe inmy head! I'm a scholar!"' The mentor's response sounds withering to a twenty-first-centuryear: "'Yes," I answered, "you are,well enough, and you've theadvantage of being able tobelieve nothing at all of what I've told you, whenever you choose".'39 In the end, as Fontenelle knew, theEntretiens was not about learningbut about entertainment.The ever-gallant narrator concluded: 'I only ask you as payment formy trouble, thatyou never look at the Sun, the sky, or the stars,without thinkingof me'. I admit thatI have a similar purpose. After readingLa Dame d'Esprit, I hope that you will never be able to thinkof Leibniz orNewton without remembering theirbrilliant French interpreter,Gabrielle Emilie le Tonnelier de Breteuil, marquise Du Chatelet (figure 7).

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P RN CI PE S

MATHEMATIQUES

D E L A

PHILOSOPHIE NATURELLE,

Par feueMadame laMarquife D U C HAS T E L L E T'^

TOME PREMIER..

A PAR IS,

SDESAINT & SAILLANT, rue S. Jeani de Beauvais. LE T Chez LAMBERT, rue & ctc6te de la Comedie Franpoite ) au Parnaffe.

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Figure7. Frontispieceof Du Chatelet'stranslation ofNewton's Prinicipia. (Copyright C) The Royal Society.)

Notes

1 On Maupertuis, see E. Badinter, Les Passions intellectuelles (Fayard, Paris, 1999), vol. 1,pp. 50-53, 62-63; M. Terral 1, The man who flattened the earth: Maupertuis and the sciences in the

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on see Enlightenment (University of Chicago Press, 2002), chs 1 and 3 passim, and his rise particularly pp. 27-33, 43-45; J. B. Shank, Before Voltaire: Newtonianism and the origins of the Enlightenment inFrance, 1687-1734 (PhD thesis, Stanford University, 2000), pp. 516-526,550-558. 2 See D. J. Sturdy, Science and social status: the members of the Acad?mie des Sciences, 1666 1750 (Boydell Press,Woodbridge, Suffolk, 1995), pp. 346, 365, 377; R. Hahn, The anatomy of a scientific institution: the Paris Academy of Sciences, 1666-1803 (University of California Press, Berkeley, 1971), pp. 28-30, 97. See also C. B. Paul, Science and immortality: the ?loges of the Paris Academy of Sciences (1699-1971) (University of California Press, Berkeley, 1980), pp. 68-77, 76, table 3. 3 On Maupertuis's difficulties, see Terrall, op. cit. (note 1), pp. 10-11, 13, 15, 64-78. In contrast, D. Beeson inMaupertuis: an intellectual biography (The Voltaire Foundation, Oxford, 1992) presents Maupertuis as an able mathematician: see ch. 3, pp. 88-110. 4 Bernoulli as quoted in Badinter, op. cit. (note 1), vol. I, p. 54, note 3 on p. 54. sur 5 P.-L. Moreau de Maupertuis, Discours les diff?rentes figures des astres avec une exposition des syst?mes de MM. Descartes et Newton (Paris, 1732), pp. 11, 34-37. On his goal and this line of reasoning see ibid., pp. iv, v, 10-11, 26-27, 29-33, 37-39, 45, 81, 132, 133. Note that accepting attraction did not mean a complete rejection of Descartes's explanations. Proponents of attraction such as Bernoulli and the g?om?tre Leonhard Euler continued to believe in a on mechanical universe based particles in motion. On the larger context of Maupertuis and Clairaut's work, see Beeson, op. cit. (note 3), pp. 79-87. 6 Du Ch?telet toMaupertuis, no. 16, 7 June 1734, in Lettres de la marquise Du Ch?telet, vol. I (ed. Theodore Besterman), p. 44 (Institut et Mus?e Voltaire, Geneva, 1958). 7 Emilie Du Ch?telet, Institutions de physique (Prault, Paris, 1740), ch. XVI, p. 327. 8 On Clairaut's background see Badinter, op. cit. (note 1), vol. I, pp. 57-59. Graffigny as quoted in O. Courcelle, 'Probl?me physico-math?matique', Quadrature, no. 36, p. 33 (1999); for the problem quoted, see p. 30.1 am grateful to Olivier Courcelle for this article and for his expertise on Clairaut. 'Bout de banc' referred to a child's game similar to 'Musical Chairs', when there

would be no more room at the 'end of the bench' for the salon participant who had failed to provide a worthy contribution to an evening's entertainment. 9 See J. P. Zinsser and O. Courcelle, 'A remarkable collaboration: the marquise Du Ch?telet and Alexis Clairaut', SVEC 12, 107-120 (2003). 10 A.-C. Clairaut, El?mens de g?om?trie (David fils, Paris, 1741), preface, p. iv. 11 A.-C. Clairaut, El?mens d'alg?bre (Fr?res Guerin, David, Durand, Paris, 1746), part I, pp. 30, 60; part II, p. 100. 12 On Clairaut's role in her translation and commentary, see Zinsser and Courcelle, op. cit. (note 9). 13 For biographical information, see Badinter op. cit. (note 1), vol. I, pp. AI-A9, 143-144; H. Guerlac, 'The Newtonianism of Dortous de Mairan', in Essays on the Age of Enlightenment in honor of Ira O. Wade (ed. JeanMcCary) (Geneva, Librairie Droz, 1977); Ellen McNiven Hine, 'Dortous de Mairan, the "Cartonian"', SVEC 266, 163-179 (1989). 14 Mairan took first prize in 1715 and 1716, and third prize in 1717, all in physics. See Geurlac, op. cit. (note 13), p. 136. In his first presentation to the Academy, Mairan spoke on Newton's optics. a However, he offered Cartesian explanation of impulsion for refraction. This mixing of apparently contradictory systems and hypotheses, combining the Englishman's experimental results with the Frenchman's material, mechanical cause for phenomena, was a common practice both in France and elsewhere on the Continent. 'Natural philosophy' in Mairan's and Du Ch?telet's day did not mean complete adherence to one physicien or another. For example, Du Ch?telet in her Institutions de physique created an original synthesis that took from Leibniz as well as from Descartes and Newton. For background on the scientific controversies of the day, see Beeson, op. cit. (note 3), pp. 15-61. 15 See Shank, op. cit. (note 1), pp. 352-353, note 101 on p. 353.

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16 Badinter, op. cit. (note 1), vol. I, pp. 29-31. Marquise de Cr?qui, Souvenirs de la marquise de Cr?qui (Michel Levy Fr?res, Paris, 1867), vol. III, pp. 66, 67. The guest was Samuel K?nig, brought to the dinner at the duchesse de Richelieu's by Du Ch?telet. Graffignyto Devaux, 4 September 1739, no. 179, Correspondance de Madame de Graffigny, vol. II (ed. J. A. Dainard et al), p. 139 (Voltaire Foundation, Oxford, 1985- ). 17 Mairan to Du Ch?telet, no. D2449, [c20] March 1741, in Complete works of Voltaire, vol. 91 (ed. Theodore Besterman et al), p. 450 (Voltaire Foundation, Geneva and Oxford, 1968- ). See J.-J. Dortous de Mairan, Lettre ? Madxxx sur la Question des Forces vives [en response] (Acad?mie royale des sciences, Paris, 1741), pp. 3-5. 18 Cr?qui, op. cit. (note 16), vol. III, pp. 66-61. Mairan to Cramer, 4 April 1741, as quoted in Badinter, op. cit. (note 1), vol. I, p. 178.

19 Today, two formulae are used: mv for momentum and l/2mv2 for kinetic energy. For a clear description of the relation between these concepts and contemporary physics, see G. E. Smith, 'The vis viva dispute: a controversy at the dawn of dynamics', Physics Today (October), 31-36 (2006). I am grateful to R. K. Smeltzer for bringing this article to my attention. 20 On the history of the controversy, see M. Terrall, 'Vis viva', Hist. Sei. 42, 196-197 (2004); Terrall, op. cit. (note 1), p. 40. Du Ch?telet, op. cit. (note 7), ch. XXI, 429.

21 Du Ch?telet toMaupertuis, no. 127, 22 May 1738, op. cit. (note 6), vol. I, p. 233. The concept of 'hard bodies' had particular significance if '?tres simples' (the basic constituents of all matter) were to be impenetrable and indivisible. See Du Ch?telet, op. cit. (note 7), ch. I, p. 34, in which? like Bernoulli?she accepted that 'there are not any perfectly hard bodies in nature', the position of modern science but for different reasons. On the dissipation of force and its relevance for the evolution of the 'law of conservation of energy', see Carolyn Merchant [Iltis], 'Mme Du Ch?telet's metaphysics and mechanics', Stud. Hist. Phil. Sei. 8, 28-48 (1977), especially at pp. 47-48. See Du Ch?telet, op. cit. (note 7), ch. XXI, pp. 446-448.

22 Du Ch?telet to d'Argental, no. 264, 22 March [1741], Du Ch?telet, op. cit. (note 6), vol. II, p. 45. 23 Du Ch?telet toMaupertuis, no. 272, 29 May 1741, Du Ch?telet, op. cit. (note 6), vol. II, p. 57. ... Emilie Du Ch?telet, R?ponse de madame la marquise Du Ch?telet ? la lettre que m. de Mairan (chez Foppens, Bruxelles, 1741), p. 26. 24 See 'ArticleLXVIF, M?moires de Tr?voux, pp. 1390-1391 (August 1740). 25 Du Ch?telet to d'Argental, no. 269, 2 May [1741], Du Ch?telet, op. cit. (note 6), vol. II, p. 51. 26 Cramer to Clairaut, as quoted in Badinter, Intellectuelles, op. cit. (note 1), vol. I, note 4 on p. 176. 27 Le Journal universel, vol. X, p. 421 (August 1746). 28 See for example, Sonia Carboncini, 'L'Encyclop?die et Christian Wolff: ? propos de quelques articles anonymes', m Autour de la philosophie Woljfienne (ed. Jean Ecole), pp. 210-216 (Georg Olms Verlag, New York, 2001). 29 For example, I. B. Cohen, the Newtonian scholar, in his 'Guide' to his English translation of Newton's Principia ascribed the commentary to Clairaux. See J. P. Zinsser, 'Madame Du Ch?telet et les historiens', inMadame Du Ch?telet: la femme des lumi?res (ed. Elisabeth Bainter and Danielle Muzerelle), pp. 118-121 (Biblioth?que nationale de France, Paris, 2006). 30 Voltaire to Frederick of Prussia, no. Dl 320, c. 25 April 1737, in The Complete Works of Voltaire, op. cit. (note 17), vol. 88, p. 295.

31 Voltaire' s role in the subsequent distortion of the marquise' s life and the subtle denigration of her a intellectual accomplishments appears in the epilogue of J. P. Zinsser, La Dame d'Esprit, biographyof themarquise Du Ch?telet (Viking,New York, 2006). nor 32 For a positive interpretation of the Entretiens, see J. B. Shank, 'Neither natural philosophy, sur science, nor literature?gender, writing, and the pursuit of nature in Fontenelle's Entretien la pluralit? des mondes habit?s', in Men, women and the birthing of modern science (ed. J. P. Zinsser), pp. 86-110 (NorthernIllinois University Press, 2005). 33 C. J. F. H?nault, M?moires du Pr?sident H?nault (ed. F. Rousseau), p. 89 (Hachette, Paris, 1911).

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34 For the information on Fontenelle in this and the subsequent paragraph, see B. le B. de Fontenelle, Conversations on the plurality of worlds (intro. Nina Gelbart; transi. H. A. Hargreaves), p. xix (University of California Press, Berkeley, 1990); Cr?qui, op. cit. (note 16), vol. I, p. 76; Sturdy, op. cit. (note 2), pp. 358-360; C. Coll?, Journal [historique] et m?moires de Charles Coll?... (Didot Fr?res, Paris, 1868), p. 281. C.-E. Jordan, Histoire d'un voyage litt?raire fait enMDCCXXXIII (AdorrenHoetiers, The Hague, 1735), p. 52. 35 Fontenelle, op. cit. (note 34), preface, pp. 4-5, 64, 7. 36 Fontenelle, op. cit. (note 34), pp. 11, 53, 64. 37 Fontenelle, op. cit. (note 34), pp. 7, 22, 27, 58, 28. 38 Fontenelle, op. cit. (note 34), pp. 37, 66, 63, 70. 39 The historian of science, Patricia Fara, pointed out the anti-Cartesian quality of this comment, no that by implication there could be certain knowledge. Fontenelle, op. cit. (note 34), p. 73.

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