Émilie Du Châtelet addresses her Institutions physiques to her thirteen-year-old son, emphasizing the importance of geometry as the key to all discoveries. Her aim is to make the current state of research known in France, as one can find it in Latin, Italian, and English journals.
Du Châtelet clearly distinguishes her work from Jacques Rohault’s Traité de physique (Paris, 1671). Rohault’s Traité was the standard Cartesian textbook for half a century in France. It went through no fewer than twelve editions in France alone and was translated into both Latin and English. Du Châtelet considers the book to be out of date. However, she proposes neither a new, modern textbook nor the whole history of physical revolutions. She focuses on what must be known (InstPhy, V):
Je ne vous ferai point ici l’histoire des révolutions que la Physique a éprouvées, il faudroit pour les rapporter toutes, faire un gros Livre; je me propose de vous faire connaître, moins ce qu’on a pensé que ce qu’il faut savoir. (Amsterdam 1742)
I will not write the history of the revolutions experienced by physics here. A thick book would be needed to report them all. I propose to make you acquainted less with what has been thought than with what must be known. (Copyright © 2009 BZ)
The last sentence of the above quotation (which is underpinned in the manuscript) appears verbatim in a letter that Voltaire has written to Nicolas Claude Thieriot (28 November 1738): “Moins ce qu’on a pensé que ce qu’il faut savoir.” Mme Du Châtelet, however, puts it into another context, using Voltaire’s remark as a bridge to the following passages. She refers to the merits of Descartes, Galileo, and Kepler, paraphrasing a famous and often-quoted statement by Isaac Newton from his 1676 letter to Robert Hooke (InstPhy, V) :
We rise to the knowledge of truth, like those giants who climbed up to the sky by standing on the shoulders of one another. (Copyright © 2009 BZ)
These words express the optimistic conviction that the approximation to scientific truth is possible. For Du Châtelet, scientific progress consists of learning from our errors. In this sense, “the Huygenses, and the Leibnizens learned from Descartes and Galilieo,” not to mention Newton, who discovered his universal law of gravitation by studying Kepler and Huygens.
Du Châtelet continues: The Élémens de la philosophie de Neuton offer an introduction to this topic, i.e. “how the phenomena are explained by the hypothesis of attraction” (« comment les Phénomènes s’expliquent par l’hypothèsè de l’Attraction »). Mme Du Châtelet does not mention the author, but it is clear who is meant: Voltaire. Disagreements with Voltaire had forced her to publish her own book about Newton’s natural philosophy. What follows is an appeal to search for truth, free of prejudice and impartial (InstPhy, VII):
About a book of physics one must ask if it is good, not if the author is English, German, or French. (Copyright © 2009 BZ)
As an example, Mme Du Châtelet refers to the question regarding the nature of attraction: On the one hand the Cartesians do not even accept attraction as a hypothesis. On the other hand, Newtonians declare attraction as an inherent property of matter. At this point, Mme Du Châtelet draws an analogy to the stage play “Bellerophon,” in order to show why both claims are problematic. On stage, Bellerophon floats in the air because he hangs on ropes. This is the reason, why Bellerophon is able to fly. In terms of attraction, it is not that simple. We are still very far from knowing the cause of attraction. This does not, however, seem to be a sufficient reason to ban attraction as a hypothesis.
In physics, Du Châtelet says, we are like the man blind from birth whose sight Cheselden restored (VII). It took some time till he was able to see well. In physics, this time has not quite come for us, and perhaps will never come. Presumably, there are many truths that are not made to be perceived by the eyes of our intellect (“yeux de notre esprit”), just as there are objects which our embodied eye (“ceux de notre corps “) will never perceive. Nevertheless, we must be careful not to draw the conclusion it would be better not to learn, because we may never know some truths and may never perceive some objects (InstPhy, VII):
mais celui qui refuseroit de s’instruire par cette considération, reflembleroit à un boiteux qui ayant la fièvre, ne voudroit pas prendre les remèdesqui peuvent l’en guérir, parce que ces remèdes ne pourroient l’empêcher de boiter. (Amsterdam 1742)
But one who refused to learn because of this limitation would resemble a lame person who, having a fever, would not take the remedies which can cure it, because these remedies would not cure her limp. (Copyright © 2009 BZ)
Learning is the pursuit of knowledge. For that reason, it would be misleading to ban hypotheses from physics. They are as necessary as the scaffoldings of a house that one builds. Without hypotheses, almost no progress would have been made in science (InstPhy, VIII):
Un des torts de quelques Philosophes de ce tems, c’est de vouloir bannir les Hypotheses de la Physique; elles y sont aussi neecessaires que les Echafauts dans une maison que l’on bâtit; il est vrai que lorsque le Bâtiment est acheve, les Echafauts deviennent inutiles, mais on n’auroit pû l’elever sans leur secours. Toute l’Astronomie, par Exemple, n’est fondee que sur des Hypotheses, & si on les avoit toujours évitées en Physique, il y a apparence qu’on n’auroit pas fait tant de decouvertes; aussi rien n’est-il plus capable de retarder les progres des Sciences que de vouloir les en bannir, & de se persuader que l’on a trouve le grand ressort qui fait mouvoir toute la nature. (Amsterdam 1742)
One of the mistakes some philosophers of our time make is to want to banish hypotheses from physics; they are necessary as the scaffolding of a house being built; it is true, when the house is completely built, the scaffolding becomes useless, but it could not have been erected without it. All of astronomy, for example, is founded only on hypotheses; and if they had always been avoided in physics, it seems that fewer discoveries would have been made. So nothing is more likely to delay the progress of sciences than to want to banish hypotheses, and to persuade oneself that one has found the great mainspring that moves all nature. (Copyright © 2009 BZ)
Scientific research as a collective endeavor relies on hypotheses. This is, of course, a clear plea for hypotheses. However, Du Châtelet also warns of their misuse and risk of confusing them with proven facts, or fictions. Contrary to fictions, fables, or dreams, hypotheses aim to explain empirical phenomena. They are supposed to agree with facts of experience.
Experience is the cane that nature gave to us blind ones, to guide us in our research: “l’Expérience est le bâton que la Nature a donné à nous autres aveugles, pour nous conduire dans nos recherches.” The same sentence can be found in Voltaires’s Traite de metaphysique and in his Correspondance with Frederick II (17 April 1737). Du Châtelet herself strikes a balance between reason and experience insofar as it is for our reason to use our experience. Again, she pleads against partiality and for modesty (InstPhy, X):
chaque Philophe a vu quelque choie, & aucun n’a tout vu j il n’y a point de si mauvais livre où il n’y ait quelque chose à apprendre, & il n’y en a gueres d’assez bon pour qu’on ne puisse y rien reprendre. (Amsterdam 1742)
Each philosopher has seen something, and none has seen all; no book is so bad that nothing can be learned from it, and no book is so good that one might not improve it. (Copyright © 2009 BZ)
One should not just adopt the opinions and theories of famous philosophers without further consideration. Every assertion should be examined critically (InstPhy, XI):
La Physique est un Bâtiment immense, qui surpasse les forces d’un seul homme; les uns y mettent une pierre, tandis que d’autres bâtissent des aîles entieres, mais tous doivent travailler sur les fondemens solides qu’on a donnés à cet Edifice dans le dernier siecle, par le moyen de la Géometrie, & des Observations; il y en a d’autres qui levent le Plan du Bâtiment, & je suis du nombre de ces derniers. (Amsterdam 1742)
Physics is an immense building that surpasses the powers of a single person. Some lay a stone there, while others build whole wings, but all must work on the solid foundations that have been laid for this edifice in the last century, by means of geometry and observations; still others survey the plan of the building, and I, among them. (Copyright © 2009 BZ)
Du Châtelet’s “plan” of the immense building, called «la Physique», is twofold. In the first chapters, she aims to summarize Leibniz’s ideas on metaphysics which were still little known in France at the time. She had taken these principal opinions on metaphysics from Christian Wolff by the assistance of “his disciple.” (The name of this disciple, i.e. Johann Samuel König, is not mentioned). Du Châtelet borrows a Leibnizian analogy and calls the principle of sufficient reason a compass capable of leading us in the moving sand of this science, namely metaphysics. In this context, she refers to Leibniz’s idea of a «calcul pour la Métaphysique» and comments on it with optimistic caution. Leibnizs’ calculus of metaphysics might be a possible instrument to prove metaphysical propositions in the same manner as geometrical truths (InstPhy, XII):
cependant il est certain qu’il y a des points de Métaphysique susceptibles de démonstrations aussi rigoureuses que les demonstrations aussi rigoureuses que les démonstrations géométriques, quoiqu’elles soient d’un autre genre: il nous manque un calcul pour la Métaphysique pareil à celui que l’on a trouvé pour la Géométrie, par le moyen duquel avec l’aide de quelques données, on parvient à connaitre des inconnues; peut-être quelque génie trouvera-t’il un jour ce calcul. Monsieur de Leibnits y q beaucoup pensé, il avoit sur cela des idées, qu’il n’a jamais par malheur communiquées à personne, mais quand même on le trouveroit, il y a apparence qu’il y a des inconnues dont on ne trouveroit jamais l’équation. La Métaphysique contient deux espèces de choses; la premiere, ce que tous les gens qui font un bon usage de leur esprit, peuvent savoir; & la seconde, qui est la plus etendue, ce qu’ils ne sauront jamais. (Amsterdam 1742)
We lack a system of calculation for metaphysics similar to that which has been found for mathematics, by means of which, with the aid of certain givens, one arrives at knowledge of unknowns. Perhaps some genius will one day find this system. M. Leibniz gave this much thought, he had ideas in this, which he unfortunately never communicated to anyone, but even if it could be invented, it seems that there are some unknowns for which no equation can ever be found. Metaphysics contains two types of things: the first that which all people who make good use of their intellect, can know; and the second, which is the most extensive, that which they will never know. (Copyright © 2009 BZ)
[missing in the Manuscript Bibliotheque nationale de France (Paris), Fonds français 12265]
Once again, the last quoted passage is allusion to Voltaire who wrote to Frederick II (April 17, 1737): «Toute la métaphysique, à mon gré, contient deux choses: la première, tout ce que les hommes de bon sens savent; la seconde, ce qu’ils ne sauront jamais.» According to Voltaire metaphysics “contains two things: The first all that men of good sense know; the second what they will never know.” Du Châtelet does not go so far as to adopt Voltaire’s radical anti-metaphysical stance and sensualist positivism. On the contrary, she uses Voltaire’s maxim in order to justify the importance of metaphysics. However, it should be noted that the last cited passage alluding to Voltaire is missing from the manuscript.
 Du Châtelet was well familiar with Samuel Clarke’s Latin translation of Jacobi Rohaulti Physica (1697), and of the English version Rohault’s System of Natural Philosophy, illustrated with Dr. Samuel Clarke’s notes taken mostly out of Sir Isaac Newton’s Philosophy (1723). In both, editions Clarke added notes giving a Newtonian perspective to Rohault’s Cartesian text book.
 Frederick II – in reliance on Voltaire’s recommendation – had appointed Claude Nicolas Thieriot as his official literary agent in Paris, and later in Cirey.
 See Newton’s letter to Robert Hooke (5 February 1676): “What Des-Cartes [sic] did was a good step. You have added much several ways, & especially in taking the colours of thin plates into philosophical consideration. If I have seen further it is by standing on the sholders [sic] of Giants” [Turnbull 1959-77, vol. 1, p. 416].