Maupertuis, Pierre Louis Moreau De
MAUPERTUIS, PIERRE LOUIS MOREAU DE
(b. St.-Malo, France, 28 September 1698; d. Basel, Switzerland, 27 July 1759)
mathematics, biology, physics.
It was said of Maupertuis, in the official eulogy by Samuel Formed, that “Madame Moreasu idolized her son rather than loved him. She could not refuse him anything.” It seems highly probable that the spoiled child inevitably developed some of those personality characteristics that later made him not only proud but intransigent and incapable of bearing criticism, traits that ultimately led to great unpleasantness in his life and, quite literally, to his undoing.
After private schooling Maupertuis went to Paris at the age of sixteen to study under Le Blond, but he found ordinary philosophical disciplines quite distasteful. In 1717 he began to study music; but he soon developed a strong interest in mathematics, which he pursued under the tutelage of Guisnée and, later, Nicole. Maupertuis was elected to the Academy of Sciences in 1723, at the age of twenty-five, and presented a dissertation, “Sur la forme des instruments de musique.” This was soon followed by a mathematical memoir on maxima and minima, some biological observations on a species of salamander, and two mathematical works of much promise: “Sur la quadrature et rectification des figures formées par le roulement des polygones reguilers” and “Sur une nouvelle maniére de développer les courbes.”
In 1728 Maupertuis made a trip to London that was to exert a major influence upon his subsequent career. From a conceptual world of Cartesian vortices he was transported into the scientific milieu of Newtonian mechanics, and he was quickly converted to these views. From this time on, Maupertuis was the foremost proponent of the Newtonian movement in France and a convinced defender of Newton’s ideas about the shape of the earth. After returning to France he visited Basel, where he was befriended by the Bernoullis.
While pursuing, in conjunction with Clairaut, further studies in mathematics—resulting in a steady flow of notable memoirs—Maupertuis was readying his first work on Newtonian principles, “Discours sur les différentes figures des astres” (1732). It brought him the attention of the Marquise du Châtelet and of Voltaire, both of whom he instructed in the new doctrines. His position as the leading Continenta lNewtonian was confirmed the following year by his “Sur la figure de la terre et sure lese moynes que l’astronomie et la géographie fournissent pour la déterminer,” which was accompanied by a complementary memoir by Clairaut.
Thus it came about that in 1735 France sent an expedition to Peru under the leadership of La Condamine and another to Lapland under the leadership of Maupertuis. Clairaut, Camus, and other scientists accompanied the latter. The mission of each expedition was to measure as accurately as possible the length of a degree along the meridian of longitude. If, indeed, the earth is flattened toward the poles, as Newton had predicted, the degree of latitude should be shorter in far northern latitudes than near the equator. The voyage began on 2 May 1736 and lasted over a year. The local base for the expedition’s fieldwork was Torneå, in northern Sweden—then, according to Maupertuis, a town of fifty or sixtly houses and wooden cabins. On the return journey the ship was wrecked in the Baltic Sea, but without loss of life, instruments, or records.
Maupertuis reached Paris on 20 August 1737, only to meet with a rather chilly reception. Envy and jealousy were already at work; he had few Newtonian supporters in France except Voltaire; and La Condamine’s expedition had not yet returned from Peru. At this time Maupertuis found respite at Saint-Malo and at Cirey, where Mme du Châtelet and Voltaire made him welcome. He stayed only briefly at Cirey, however, intending to revisit Basel. There he met Samuel Köning, a young student of Johann I Bernoulli. He persuaded König to accompany him back to Cirey, where Köning behaved so arrogantly that he angered Mme du Châtelet, who through this episode became temporarily estranged from Maupertuis.
The laborious analysis of the data on the length of the are of a meridional degree at various latitudes took much time and created much controversy. The measurements made in France had to be corrected. In December 1739 Maupertuis announced to the Academy the value found for the distanced along the merdian between Paris and Amiens. The expedition to Peru having returned after an arduous three years, the degree between Quito and Cuenca was added to the comparisons. Still later (1751) measurements made by Lacaille at the Cape of Good Hope permitted a fourth comparison.
In a final revision of the reports on the “Opérations pour déterminer a figure de la terre” (Oeuvres, IV, 335) Maupertuis summarized the corrected measurements for a degree of longitude as follows:
|Cape of Good Hope||33°18’||56,994|
In 1738 Voltaire recommended Maupertuis to Frederick the Great, who was eager to rehabilitate the academy of sciences at Berlin. Frederick commenced overtures to Mauperuis, who visited Berlin after publication of his new, anonymously printed Éléments de géographie and his reconciliation with Mme du Châtelet. In Berlin he met Francesco Algarotti and the family of M. de Borck, whose daughter he was later to marry. After the outbreak of the War of the Austrian Succession, Maupertuis joined Frederick in Silesia, only to be captured when his horse bolted into the enemy lines. For a time he was feared dead by his friends, but Maupertuis soon emerged safely in Vienna; ominously, he took offense at the jests of Voltaire regarding his military exploit.
Maupertuis was elected to the Académie Française in 1743. In 1744 he presented the memoir “Accord de différentes lois de la nature” and published “Dissertation sur le négre blanc.” The latter was the precursor of the Vénus physique of 1745, which was an enlarged and more fully analyzed argument against the then dominant biological theory of the preformation of the embryo. Maupertuis argued convincingly that the embryo could not be preformed, either in the egg or in the animalcule (spermatozoon), since hereditary characteristics could be passed down equally through the male or the female parent. He rejected the vitalistic notion that some “essence” from one of the parents could affected the preformed fetus in the other parent, or that maternal impressions could mold the characteristics of the offspring. A strict mechanist, although a believer in the epigenetic view of the origin of the embryo, he looked for some corporeal contribution from each parent as a basis of heredity.
In the middle of 1745 Maupertuis finally accepted Frederick’s invitation and took up residence in Berlin. In the same year he married Mlle de Borck; and on 3 March 1746 he was installed as president of the Academy. His first contribution was the brief paper “Les lois du mouvement et du repos,” in which he set forth the famous principle of least action, which he regarded as his own most significant scientific contribution. It states simply that “in all the changes that take place in the universe, the sum of the products of each body multiplied by the distance it moves and by the speed with which it moves is the least possible” (Oeuvres, II, 328). That is, this quantity tends to a minimum, This principle was later clarified and expounded by Euler, developed by Hamilton and Lagrange, and incorporated in modern times into quantum mechanics and the biological principle of homeostasis. As Maupertuis himself said:
The laws of movement thus deduced [from this principle], being found to be precisely the same as those observed in nature, we can admire the application of it to all phenomena, in the movement of animals, in the vegetation of plants, in the revolution of the heavenly bodies: and the spectacle of the universe becomes so much the grander, so much the more beautiful, so much worthier of its Author.…
These laws, so beautiful and so simple, are perhaps the only ones which the Creator and Organizer of things has established in matter in order to effect all the phenomena of the visible world [Oeuvres, I, 44–45].
Maupertuis clearly was successful in attracting to Berlin scientific luminaries who greatly enhanced the luster of the new Academy. Euler, one of the greatest mathematicians of the day, was already there. La mettrie came in 1748; Mérian and Meckel in 1750; and, in the same year, after the death of Mme du Châtelet, Voltaire arrived in Berlin. With others the brusque impatience of Maupertuis rendered his efforts less successful. On the whole, however, matters were going well when the celebrated “affaire König” erupted. Samuel König, a protégé of Maupertuis, after having been elected a member of the Academy, visited Berlin, was warmly received by Maupertuis, and shortly thereafter submitted a dissertation attacking the validity of the principle of least action and then—most strangely for a devoted adherent of Leibniz—ascribed the discredited law to the latter, citing a letter from Leibniz to Hermann. Maupertuis was incensed. He demanded that the letter be produced. König produced a copy but stated that the original was in the bands of a certain Swiss named Henzi, who had been decapitated at Bern following involvement in a conspiracy. After exhaustive search no trace of the letter was found in Henzi’s belongings. Maupertuis then demanded that the Academy take action against König.
At the same time Maupertuis was embroiled in a controversy between Haller and La Mettrie. The latter had dedicated to Haller, much to Haller’s dismay, his L’homme machine (1748). La Mettrie had, in response to Haller’s rejection, responded with a diatribe. Haller demanded an apology; but inasmuch as La Mettrie died at just that time, Maupertuis tried —without success—to assuage Haller with a politeletter. The episode certainly contributed to the extraordinary bitterness and tension that Maupertuis experienced in 1751.
Nevertheless, at this very time Maupertuis was able to publish one of his most significant works, later called Système de la nature. A sequel to the Vénus physique, it was a theoretical speculation on the nature of biparental heredity that included, as evidence, an account of a study of polydactyly in the family of a Berlin barber-surgeon, Jacob Ruhe, and the first careful and explicit analysis of the transmission of a dominant hereditary trait in man. Not only did Maupertuis demonstrate that polydactyly is transmitted through either the male or the female parent, but he also made a complete record of all normal as well as abnormal members of the family. He furthermore calculated the mathematical probability that the trait would occur coincidentally in the three successive generations of the Ruhe family had it not been inherited.
On the basis of this study, Maupertuis founded a theory of the formation of the fetus and the nature of heredity that was at least a century ahead of its time. He postulated the existence of hereditary particles present in the semen of the male and female parents and corresponding to the parts of the fetus to be produced. They would come together by chemical attraction, each particle from the male parent joining a corresponding particle from the female parent. chemical affinity would also account for the property formation of adjacent parts, since particles representing adjacent parts would be more alike than those of remote parts. At certain times the maternal character would dominate; at others the paternal character. The theory was applied to explain the nature of hybrids between species and their well-known sterility; and it was extended to account for aberrations with extra structures as well as to those characterized by a missing part. The origin of new sorts of particles, as well as the presence of those representing ancestral types, was envisaged. Finally, Maupertuis thought it possible that new species might originate through the geographical isolation of such variations.
During 1752 the König affair reached a climax and a hearing was held, from which Maupertuis absented himself. The letter cited by König was held to be unauthentic and undeserving of credence, and König resigned from the Academy—only to issue a public appeal and defense. Voltaire had already run afoul of Maupertuis, and jealousy existed between them regarding their influence with the king. Maupertuis had shown scant enthusiasm for a proposed monumental dictionary of metaphysics, to be developed by the Academy as a counterpoise to the Encyclopédie, for Maupertuis considered the talents of the Berlin Academy insufficient to keep such a work from being superficial. In September 1752 Voltaire attacked Maupertuis, charging him not only with plagiarism and error but also with persecution of honest opponents and with tyranny over the Academy. In the Diatribe du Cocteur Akakia, Voltaire poured invective on the ideas that Maupertuis had expressed in his Lettre sur le progrés des sciences (1752) and Lettres (1752)—in which, among other daring speculations regarding the future course of science, Maupertuis had included his most substantial account of the investigation of polydactyly in the Ruhe family and of his own breeding experiments with Iceland dogs. In Micromégas Voltaire made fun of the voyage to Lapland undertaken to measure the are of the meridian and lampooned Maupertuis’s amorous adventures in the North. His mockery made a great contrast with the grandiloquent words that he had once inscribed beneath a portrait of Maupertuis. In vain Frederick supported Maupertuis and tried to restore good feeling. Maupertuis was crushed, his health gave way, and he requested a leave to recuperate at Saint-Malo. Pursued by an unceasing volley of Voltaire’s most savage satires, Maupertuis withdrew. He remained at Saint-Malo until the spring of 1754, when he returned to Berlin at Frederick’s insistence. Here he delivered the eulogy of his friend Montesquieu, who died at Paris early in 1755. He departed again for France, a very sick man, in May 1756. Greatly distressed by the outbreak of the Seven Years’ War, he decided to return home by way of Switzerland. He went to Toulouse, whence he set out again in May 1758. At Basel, too ill to proceed, he was received warmly by his old friend Johan Bernoulli. On 27 July 1759, before his wife could reach him, he died and was buried in Dornach.
Maupertuis was a man of singular aspect. He was very short. His body was always in motion; he had numerous tics. He was careless of his apparel. Perhaps he was always endeavoring to attract attention. Perhaps he shared the Napoleonic complex of little men. Certainly he was both highly original and possessed of qualities that attracted friends, especially among the ladies; the Marquise du Châctelet and many other French women corresponded regularly with him. He could be gay as well as fiery and violent. Above all he was proud, both of his intelligence and of his accomplishments, and to attack either was to wound him deeply. Above all, he could not understand the character of Köning, whom he had sponsored and who the gratuitously attacked him, or of Voltaire, whose adulation and friendship so quickly turned to malice and vituperation.
A Philosopher as well as a scientist, Maupertuis proved himself a powerful and original thinker in Essai de cosmologie(1750). According to A.O. Lovejoy, he anticipated Beccaria and Bentham and, along with helvétius, represents “the headwaters of the important stream of utilitarian influence which became so broad and sweeping a current through the work of the Benthamites” (Popular Science Monthly, 65 , 340). He rejected the favorite eighteenth-century argument in favor of God— the argument from design— and instead, like Hume, he formulated a view of adaptation based on the elimination of the unfit. He recognized that Newton’s kaws are ubsufficient to explain chemistry, and even more so life, and turned to Leibniz for ideas about the properties of consciousness. In the Systèeme de la Nature we may, with Ernst Cassirer (Philosophy of the Enlightenment,p. 86), see an attempt to “reconcile the two great opponents of the philosophy of nature of the seventeenth century,” Newton and Leibniz. Yet in it must also be recognized a highly original work based on his own investigations of heredity. In his effort to introduce a calculus of pleasure and pain, in order to evaluate the good life and to measure happiness, Maupertuis proposed that the amount of pleasure or pain is a product of intensity ad duration. This formulation is strictly analogous to his principle of least action in the physical world and shows how he extended his philosophy of nature into a philosophy of life.
The works of Maupertuis are collected in Oeuvers, 4 vols. (Lyons, 1756). For his life see Grandjean de Fouchy, “Éloge be Maupertuies,” in L. Angliviel de la Beaumella, Vie de Maupertuies (Paris, 1856); Damiron, Mémoires sur Maupertuis(Paris, 1858); and P. Brunet, Maupertuis, I. Étude Biographique (Paris, 1929).
See also B. Glass, “Maupertuis, pioneer of Genetics and Evolution,” in B. Glass, O. Temkin, and W. Straus, Jr., eds., Forerunners of Darwin,1745–1859(Baltimore, 1959); and Ernst Cassirer, The Philosophy of the Enlightenment (Princeton, 1951).
Maupertuis, Pierre Louis Moreau De
MAUPERTUIS, PIERRE LOUIS MOREAU DE
(b. St. Malo, France, 28 September 1698; d. Basel, Switzerland, 27 July, 1759),
mathematics, mechanics, natural philosophy, life sciences. For the original article on Maupertuis see DSB, vol. 9.
Maupertuis was an original and eclectic thinker whose contributions to the science of the eighteenth century ranged widely across fields and genres. He was at the center of scientific activity from the 1730s through most of the 1750s, first in Paris and then in Berlin. His career was fraught with controversies and contradictions, bitterness and triumph. Expending considerable effort in forging a public reputation, initially as a mathematician, then more broadly as a man of letters and a philosopher, he ventured into the speculative areas of life science and metaphysics as well as mathematics and mechanics. He was a favorite of princes and duchesses, and a friend of some of the best mathematicians and philosophers of his day. His major scientific work falls into the following categories: geodesy (the shape of Earth), rational mechanics (principle of least action), and life science (reproduction and heredity). In addition, he wrote on mathematics, cosmology, metaphysics and the philosophy of language. When the original DSB article was written, very little research on Maupertuis had made use of unpublished sources (especially letters), or sources held in archives outside of Paris, and as a result, Maupertuis’s published works had not been linked to their historical and cultural context. This update offers a revised perspective on the scientific work of this Enlightenment figure. For a full account of Maupertuis’s career, institutional position, scientific correspondence, and works, see Terrall (2002), which has full references to unpublished archival material.
Maupertuis has been remembered, in the history of science and in physics and biology textbooks (Glass, 1959; Guéroult, 1934; and Brunet, 1938) for certain of his ideas that gained significance through some relation, genealogical or not, to more modern concepts such as evolution or the dynamical principle of least action. Though his reputation as a brilliant innovator was largely eclipsed by the end of the eighteenth century, in part because of Voltaire’s witty attacks, in his day Maupertuis was a major player in the European scientific and literary worlds. The social location of science and philosophy in these worlds, where hierarchical power relations coexisted with the cosmopolitan and egalitarian ideals of the republic of letters, informed the articulation of Maupertuis’s ideas, the self-conscious presentation of these ideas to his contemporaries, and the reactions they provoked.
Defense of Newtonian Theory . Although Newton’s mathematics was well known in France around the turn of the eighteenth century, Maupertuis was one of the first French mathematicians to defend the Newtonian theory of gravitation. He traveled to London in 1728, where he made social contact with Newtonian mathematicians and physicists, and other members of the Royal Society. This trip, however, was not in any substantive way the source of his Newtonianism. His own work on attraction, especially the mathematical application of gravitation theory to the vexed problem of the shape of the Earth, dates from somewhat later, after his mathematical studies with Johann Bernoulli in Basel. Bernoulli was anything but a Newtonian. He objected strenuously to empty space and action-at-a-distance, and he considered Continental mathematics, in the Leibnizian tradition, far superior to that of the English. His importance for Maupertuis’s mathematical career, documented in their extensive correspondence, cannot be overestimated.
Little did Bernoulli suspect, while he painstakingly reviewed Maupertuis’s mathematical problem solutions, that his protégé would subsequently become famous as a pioneering French Newtonian. In fact, Maupertuis
solidified his position in the Paris Academy of Sciences in the early 1730s with a series of papers applying Leibnizian analysis to problems from Newton’s Principia. He made a conscious choice to work on controversial material, but he did not initially present it as a defense of Newton. His work in geodesy came directly out of this Leibnizian-Newtonian mathematics, because the shape of Earth was a problem Newton had discussed in some detail. Having established his credibility in the academy on the basis of mathematics, Maupertuis published a comparison of Cartesian and Newtonian cosmologies for a non-specialist audience. This book, Discours sur les figures des astres (1732), brought the theory of universal attraction to the attention of a literary audience in France well before Voltaire wrote his Letters on the English (1738). Indeed, Voltaire admired Maupertuis’s book and turned to the mathematician for clarification of Newtonian physics.
Geodetic Expedition . In 1736 Maupertuis led a high-profile expedition mounted by the academy to make astronomical and geodetical measurements in the Arctic. This expedition, the product of a dispute about measuring and calculating techniques with implications for the Newtonian theory of gravitation, gave Maupertuis the opportunity to expand his reputation outward from the specialist environment of the academy and the mathematics community to the genteel literary public. On his return from Lapland, he was hailed as a hero by the social elite, who appreciated the exotic combination of Arctic travel and mathematical acumen. He was also lionized by Voltaire and his allies, because the Lapland results supported Newton’s mathematical deduction that Earth must be slightly flattened at the poles. The Paris Observatory astronomers, headed by Jacques Cassini, were less enthusiastic about the new measurements, which called into question their own measurements of the Paris meridian. Cassini objected to Maupertuis’s astronomical practices and to his use of mathematics; although the Paris meridian measurements seemed to imply an elongated Earth, this was strictly an empirical matter and had nothing to do with Cartesian mechanics. (There was no Cartesian explanation for an elongated Earth.) Although the conflict was complicated by Cassini’s hostility toward universal gravitation, this was not essentially a dispute about cosmology. Nevertheless, because of the unmistakable Newtonian overtones of the flattened Earth, the Lapland expedition brought related cosmological and philosophical issues into the public eye.
Berlin Academy and Principle of Least Action . By 1740, Maupertuis’s expedition account had made him famous throughout Europe. Frederick II, the new king of Prussia, attempted to woo him to Berlin to revitalize the Prussian Academy of Sciences. Disillusioned about the prospects for a viable academy in Berlin after an initial visit in 1740 to 1741, when Frederick was at war in Silesia, Maupertuis ultimately succumbed to the Prussian monarch’s flattering attentions. He moved to Berlin in 1745 as president of the Academy of Sciences and as a key player in the lively intellectual life of the court at Potsdam, where several French philosophers and writers had taken refuge from censorship at home. Maupertuis governed the Berlin Academy autocratically, modeling his administrative style on that of the Prussian king. He was genuinely interested in enhancing the reputation of Berlin as a home for serious scientific and philosophical endeavors, and he worked hard to attract foreign scholars to Berlin—a project that met with only mixed success.
Shortly before moving to Berlin, Maupertuis introduced the principle of least action to the Paris Academy, in a paper about the refraction and reflection of light. He framed it as a mathematical version of the metaphysical economy principle that nature acts as simply as possible: “Whenever there is any change in nature, the quantity of action necessary for this change is the smallest possible” (1756, Vol. 4, p. 36). In Berlin, unlike Paris, the academy devoted official attention to speculative philosophy, or metaphysics (one of the academy’s classes was devoted to this subject, explicitly excluded from the Paris Academy). Maupertuis’s first paper in Berlin derived the principle of least action for mechanics (including static equilibrium) from a metaphysical economy principle. Because it was both a unifying principle and a mathematical expression of final causes, he not only brought together different problem areas in physics (optics, mechanics, and statics), but also made his principle the cornerstone of a proof for the existence of God. Maupertuis used the Berlin Academy to promote his rational mechanics, based on this extremum principle. He found an exceptionally able and willing ally in Leonhard Euler, who applied the variational calculus to problems outlined by Maupertuis in less rigorous form. Maupertuis revisited his metaphysical-mechanical principle in several publications, most extensively in Essai de cosmologie (1750), where he made mathematical physics the cornerstone of a rationalist theology that found evidence for God in the most universal principles and offered an alternative to natural theology based on admiration of the details of divine design.
Theory of Generation . Maupertuis was also well known for his theory of generation. In Vénus physique (1745, an expanded version of a short anonymous work published the previous year), he gathered evidence from microscopy, anatomy, animal breeding, and everyday experience to argue for an epigenetic theory of fetal development. In this model, male and female seminal fluids, made up of heterogeneous corpuscles derived from the different parts of the parents’ bodies, combine to form germs, the particles are driven by their own teleological instincts or affinities for each other. These active properties allow for many possible outcomes within certain parameters, and they locate the capability to produce order in organic matter itself. Maupertuis used chemical affinities, forces of a different order than mechanical forces of impact, to describe organic forces. Strong affinities between those elements “appropriate for forming traits similar to those of the individual parent” account for resemblances between parents and offspring (1980, p. 139).
Maupertuis refined his notion of the forces responsible for organization in Système de la nature (1751). The focus here shifted from arguments about preexistence and epigenesis to a fuller justification of a dynamic conception of matter. Chemistry retained its analogical role as the counterpoint to mechanical reductionism, but in spite of their selectivity and flexibility, affinities could not fully explain organic form and function. “We must have recourse to some principle of intelligence, to something similar to what we call desire, aversion, memory” (Maupertuis, 1756, Vol. 2, p. 147). Desire and aversion operate as forces analogous to the affinities that propel, unite, and separate chemical substances; memory links each organic element to its corresponding part in the parent organism. Every element “retains a kind of memory (souvenir) of its previous situation and will resume it whenever it can, in order to form the same part in the fetus” (Vol. 2, p. 158).
Though his position in Berlin did give him a high profile, Maupertuis was frustrated in his efforts to transform the Prussian academy to his own specifications. He became increasingly combative and embittered about the situation in Berlin. In the 1750s his health deteriorated as he suffered recurrent bouts of debilitating fever and lung disease. He engaged in a bitter and rather pointless controversy with a former friend, Samuel König, about the authorship of the principle of least action. (For a full account of the institutional and intellectual ramifications of this dispute, see Terrall, 2002, Chap. 9.) Voltaire also turned against him in this period, due not so much to philosophical differences as to personal resentment and competition for favor with the Prussian king. It was often said, in the 1750s and subsequently, that Maupertuis’s poor health was due to his contretemps with Voltaire. This was certainly not the case. He continued in this period to produce new work, especially on generation and inheritance, and to re-edit older texts for new editions. His final contribution to the Berlin Academy journal in 1756 reprised his metaphysical mechanics in the context of a discussion of epistemology and the necessity of the laws of motion. He left Berlin for France for the final time in 1756, on the eve of the Seven Years’ War, and spent the last three years of his life (1756–1759) caught between allegiance to France, his native land, and to Frederick, his most illustrious patron. He died at the home of Johann Bernoulli in Basel on his way back to Berlin in 1759.
WORKS BY MAUPERTUIS
Vénus physique: suivi de La lettre sur le progres des sciences. Edited by Patrick Tort. Paris: Aubier-Montagne, 1980.
Oeuvres de Mr. de Maupertuis. 4 Vols. Lyon, France : J.M. Bruyset, 1756.
Beeson, David. Maupertuis: An Intellectual Biography. Oxford: Voltaire Foundation, 1992.
Brunet, Pierre. Étude historique sur la principe de la moindre action. Paris: Hermann, 1938.
Glass, Bentley, William Straus, and Owsei Temkin, eds. Forerunners of Darwin, 1745–1859. Baltimore, MD: Johns Hopkins University Press, 1959.
Greenberg, John. The Problem of the Earth’s Shape from Newton to Clairaut. Cambridge, U.K.: Cambridge University Press, 1995.
Guéroult, Michel. Dynamique et métaphysique leibniziennes. Paris: Les belles lettres, 1934.
Hoffheimer, Michael. “Maupertuis and the Eighteenth-Century Critique of Preexistence.” Journal of the History of Biology 15 (1982): 119–144.
Terrall, Mary. The Man Who Flattened the Earth: Maupertuis and the Sciences in the Enlightenment. Chicago: University of Chicago Press, 2002.