Pierre Louis Maupertuis
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Pierre Louis Moreau de Maupertuis (; ; 1698 – 27 July 1759) was a French mathematician, philosopher and
man of letters An intellectual is a person who engages in critical thinking, research, and reflection about the reality of society, and who proposes solutions for the normative problems of society. Coming from the world of culture, either as a creator or a ...
. He became the Director of the
Académie des Sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at the ...
, and the first President of the
Prussian Academy of Science The Royal Prussian Academy of Sciences (german: Königlich-Preußische Akademie der Wissenschaften) was an academy established in Berlin, Germany on 11 July 1700, four years after the Prussian Academy of Arts, or "Arts Academy," to which "Berlin ...
, at the invitation of
Frederick the Great Frederick II (german: Friedrich II.; 24 January 171217 August 1786) was King in Prussia from 1740 until 1772, and King of Prussia from 1772 until his death in 1786. His most significant accomplishments include his military successes in the Sil ...
. Maupertuis made an expedition to Lapland to determine the shape of the Earth. He is often credited with having invented the
principle of least action The stationary-action principle – also known as the principle of least action – is a variational principle that, when applied to the '' action'' of a mechanical system, yields the equations of motion for that system. The principle states tha ...
; a version is known as Maupertuis's principle – an integral equation that determines the path followed by a physical system. His work in natural history is interesting in relation to modern science, since he touched on aspects of
heredity Heredity, also called inheritance or biological inheritance, is the passing on of traits from parents to their offspring; either through asexual reproduction or sexual reproduction, the offspring cells or organisms acquire the genetic inform ...
and the
struggle for life The concept of the struggle for existence concerns the competition or battle for resources needed to live. It can refer to human society, or to organisms in nature. The concept is ancient, and the term ''struggle for existence'' was in use by the ...
.


Biography

Maupertuis was born at
Saint-Malo Saint-Malo (, , ; Gallo: ; ) is a historic French port in Ille-et-Vilaine, Brittany, on the English Channel coast. The walled city had a long history of piracy, earning much wealth from local extortion and overseas adventures. In 1944, the Alli ...
, France, to a moderately wealthy family of merchant- corsairs. His father, Renė, had been involved in a number of enterprises that were central to the
monarchy A monarchy is a form of government in which a person, the monarch, is head of state for life or until abdication. The political legitimacy and authority of the monarch may vary from restricted and largely symbolic (constitutional monarchy) ...
so that he thrived socially and politically. The son was educated in mathematics by a private tutor, Nicolas Guisnée, and upon completing his formal education his father secured him a largely honorific
cavalry Historically, cavalry (from the French word ''cavalerie'', itself derived from "cheval" meaning "horse") are soldiers or warriors who fight mounted on horseback. Cavalry were the most mobile of the combat arms, operating as light cavalry ...
commission. After three years in the cavalry, during which time he became acquainted with fashionable social and mathematical circles, he moved to
Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. S ...
and began building his reputation as a mathematician and literary wit. In 1723 he was admitted to the
Académie des Sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at the ...
. His early mathematical work revolved around the
vis viva ''Vis viva'' (from the Latin for "living force") is a historical term used for the first recorded description of what we now call kinetic energy in an early formulation of the principle of conservation of energy. Overview Proposed by Gottfried L ...
controversy, for which Maupertuis developed and extended the work of
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the grea ...
(whose theories were not yet widely accepted outside England) and argued against the waning
Cartesian Cartesian means of or relating to the French philosopher René Descartes—from his Latinized name ''Cartesius''. It may refer to: Mathematics *Cartesian closed category, a closed category in category theory *Cartesian coordinate system, modern ...
mechanics. In the 1730s, the
shape of the Earth Figure of the Earth is a term of art in geodesy that refers to the size and shape used to model Earth. The size and shape it refers to depend on context, including the precision needed for the model. A sphere is a well-known historical approxim ...
became a flashpoint in the battle among rival systems of mechanics. Maupertuis, based on his exposition of Newton (with the help of his mentor Johan Bernoulli) predicted that the Earth should be
oblate In Christianity (especially in the Roman Catholic, Orthodox, Anglican and Methodist traditions), an oblate is a person who is specifically dedicated to God or to God's service. Oblates are individuals, either laypersons or clergy, normally livi ...
, while his rival
Jacques Cassini Jacques Cassini (18 February 1677 – 16 April 1756) was a French astronomer, son of the famous Italian astronomer Giovanni Domenico Cassini. Cassini was born at the Paris Observatory. Admitted at the age of seventeen to membership of the French ...
measured it astronomically to be
prolate A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has circu ...
. In 1736 Maupertuis acted as chief of the
French Geodesic Mission The French Geodesic Mission to the Equator (french: Expédition géodésique française en Équateur, also called the French Geodesic Mission to Peru and the Spanish-French Geodesic Mission) was an 18th-century expedition to what is now Ecuador c ...
sent by King
Louis XV Louis XV (15 February 1710 – 10 May 1774), known as Louis the Beloved (french: le Bien-Aimé), was King of France from 1 September 1715 until his death in 1774. He succeeded his great-grandfather Louis XIV at the age of five. Until he reache ...
to Lapland to measure the length of a degree of
arc of the meridian In geodesy and navigation, a meridian arc is the curve between two points on the Earth's surface having the same longitude. The term may refer either to a segment of the meridian, or to its length. The purpose of measuring meridian arcs is to ...
. His results, which he published in a book detailing his procedures, essentially settled the controversy in his favour. The book included an adventure narrative of the expedition, and an account of the Käymäjärvi Inscriptions in Sweden. On his return home he became a member of almost all the scientific societies of Europe. After the Lapland expedition, Maupertuis set about generalising his earlier mathematical work, proposing the
principle of least action The stationary-action principle – also known as the principle of least action – is a variational principle that, when applied to the '' action'' of a mechanical system, yields the equations of motion for that system. The principle states tha ...
as a metaphysical principle that underlies all the laws of mechanics. He also expanded into the biological realm, anonymously publishing a book that was part popular science, part philosophy, and part erotica: ''Vénus physique''. In that work, Maupertuis proposed a theory of generation (i.e., reproduction) in which organic matter possessed a self-organizing “intelligence” that was analogous to the contemporary chemical concept of affinities, which was widely read and commented upon favourably by
Georges-Louis Leclerc, Comte de Buffon Georges-Louis Leclerc, Comte de Buffon (; 7 September 1707 – 16 April 1788) was a French naturalist, mathematician, cosmologist, and encyclopédiste. His works influenced the next two generations of naturalists, including two prominent Fr ...
. He later developed his views on living things further in a more formal pseudonymous work that explored
heredity Heredity, also called inheritance or biological inheritance, is the passing on of traits from parents to their offspring; either through asexual reproduction or sexual reproduction, the offspring cells or organisms acquire the genetic inform ...
, collecting evidence that confirmed the contributions of both sexes and treated variations as statistical phenomena. In 1740 Maupertuis went to
Berlin Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constitue ...
at the invitation of
Frederick II of Prussia Frederick II (german: Friedrich II.; 24 January 171217 August 1786) was King in Prussia from 1740 until 1772, and King of Prussia from 1772 until his death in 1786. His most significant accomplishments include his military successes in the Sil ...
, and took part in the
Battle of Mollwitz The Battle of Mollwitz was fought by Prussia and Austria on 10 April 1741, during the First Silesian War (in the early stages of the War of the Austrian Succession). It was the first battle of the new Prussian King Frederick II, in which both si ...
on a
donkey The domestic donkey is a hoofed mammal in the family Equidae, the same family as the horse. It derives from the African wild ass, ''Equus africanus'', and may be classified either as a subspecies thereof, ''Equus africanus asinus'', or as a ...
, where he was taken prisoner by the Austrians. On his release he returned to Berlin, and thence to
Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. S ...
, where he was elected director of the Academy of Sciences in 1742, and in the following year was admitted into the
Académie française An academy (Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of secondary education, secondary or tertiary education, tertiary higher education, higher learning (and generally also research or honorary membershi ...
. Returning to Berlin in 1744, again at the desire of Frederick II, he was chosen president of the
Royal Prussian Academy of Sciences The Royal Prussian Academy of Sciences (german: Königlich-Preußische Akademie der Wissenschaften) was an academy established in Berlin, Germany on 11 July 1700, four years after the Prussian Academy of Arts, or "Arts Academy," to which "Berlin ...
in 1746, which he controlled with the help of
Leonhard Euler Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ma ...
until his death. His position became extremely awkward with the outbreak of the
Seven Years' War The Seven Years' War (1756–1763) was a global conflict that involved most of the European Great Powers, and was fought primarily in Europe, the Americas, and Asia-Pacific. Other concurrent conflicts include the French and Indian War (1754 ...
between his home country and his patron's, and his reputation suffered in both Paris and Berlin. Finding his health declining, he retired in 1757 to the south of France with a young girl, leaving his wife and children behind and went in 1758 to
Basel , french: link=no, Bâlois(e), it, Basilese , neighboring_municipalities= Allschwil (BL), Hégenheim (FR-68), Binningen (BL), Birsfelden (BL), Bottmingen (BL), Huningue (FR-68), Münchenstein (BL), Muttenz (BL), Reinach (BL), Riehen (BS ...
, where he died a year later. Maupertuis's difficult disposition involved him in constant quarrels, of which his controversies with
Samuel König Samuel ''Šəmūʾēl'', Tiberian Hebrew, Tiberian: ''Šămūʾēl''; ar, شموئيل or صموئيل '; el, Σαμουήλ ''Samouḗl''; la, Samūēl is a figure who, in the narratives of the Hebrew Bible, plays a key role in the transit ...
and
Voltaire François-Marie Arouet (; 21 November 169430 May 1778) was a French Age of Enlightenment, Enlightenment writer, historian, and philosopher. Known by his ''Pen name, nom de plume'' M. de Voltaire (; also ; ), he was famous for his wit, and his ...
during the latter part of his life are examples. :"The brilliance of much of what he did was undermined by his tendency to leave work unfinished, his failure to realise his own potential. It was the insight of genius that led him to least-action principle, but a lack of intellectual energy or rigour that prevented his giving it the mathematical foundation that Lagrange would provide... He reveals remarkable powers of perception in heredity, in understanding the mechanism by which species developed, even in immunology, but no fully elaborated theory. His philosophical work is his most enthralling: bold, exciting, well argued."


Evolution

Some historians of science point to his work in biology as a significant precursor to the development of evolutionary theory, specifically the theory of
natural selection Natural selection is the differential survival and reproduction of individuals due to differences in phenotype. It is a key mechanism of evolution, the change in the heritable traits characteristic of a population over generations. Charle ...
. Other writers contend that his remarks are cursory, vague, or incidental to that particular argument. Mayr's verdict was "He was neither an
evolutionist Evolutionism is a term used (often derogatorily) to denote the theory of evolution. Its exact meaning has changed over time as the study of evolution has progressed. In the 19th century, it was used to describe the belief that organisms deliberate ...
, nor one of the founders of the theory of
natural selection Natural selection is the differential survival and reproduction of individuals due to differences in phenotype. It is a key mechanism of evolution, the change in the heritable traits characteristic of a population over generations. Charle ...
uthe was one of the pioneers of
genetics Genetics is the study of genes, genetic variation, and heredity in organisms.Hartl D, Jones E (2005) It is an important branch in biology because heredity is vital to organisms' evolution. Gregor Mendel, a Moravian Augustinian friar wor ...
". Maupertuis espoused a theory of
pangenesis Pangenesis was Charles Darwin's hypothetical mechanism for heredity, in which he proposed that each part of the body continually emitted its own type of small organic particles called gemmules that aggregated in the gonads, contributing herita ...
, postulating particles from both mother and father as responsible for the characters of the child. Bowler credits him with studies on heredity, with the natural origin of human races, and with the idea that forms of life may have changed with time. Maupertuis was a strong critic of the natural theologians, pointing to phenomena incompatible with a concept of a good and wise Creator. He was also one of the first to consider animals in terms of variable populations, in opposition to the natural history tradition that emphasised description of individual specimens. The difficulty of interpreting Maupertuis can be gauged by reading the original works. Below is a translation from the ''Essai de cosmologie'', followed by the original French passage:
''Mais ne pourroit-on pas dire, que dans la combinaison fortuite des productions de la Nature, comme il n'y avoit que celles où se trouvoient certains rapports de convenance, qui pussent subsister, il n'est pas merveilleux que cette convenance se trouve dans toutes les especes qui actuellement existent? Le hasard, diroit-on, avoit produit une multitude innombrable d'Individus; un petit nombre se trouvoit construit de maniere que les parties de l'Animal pouvoient satisfaire à ses besoins; dans un autre infiniment plus grand, il n'y avoit ni convenance, ni ordre: tous ces derniers ont péri; des Animaux sans bouche ne pouvoient pas vivre, d'autres qui manquoient d'organes pour la génération ne pouvoient pas se perpétuer; les feuls qui soient restés, sont ceux où se trouvoient l'ordre & la convenance: & ces especes que nous voyons aujourd'hui, ne sont que la plus petite partie de ce qu'un destin aveugle avoit produit.''
The same text was published earlier (1748) as " Les loix du mouvement et du repos déduites d'un principe metaphysique" (translation: " Derivation of the laws of motion and equilibrium from a metaphysical principle"). King-Hele (1963) points to similar, though not identical, ideas of thirty years later by
David Hume David Hume (; born David Home; 7 May 1711 NS (26 April 1711 OS) – 25 August 1776) Cranston, Maurice, and Thomas Edmund Jessop. 2020 999br>David Hume" ''Encyclopædia Britannica''. Retrieved 18 May 2020. was a Scottish Enlightenment philo ...
in his ''
Dialogues Concerning Natural Religion ''Dialogues Concerning Natural Religion'' is a philosophical work by the Scottish philosopher David Hume, first published in 1779. Through dialogue, three philosophers named Demea, Philo, and Cleanthes debate the nature of God's existence. Whet ...
'' (1777). The chief debate that Maupertuis was engaged in was one that treated the competing theories of generation (i.e.
preformationism In the history of biology, preformationism (or preformism) is a formerly popular theory that organisms develop from miniature versions of themselves. Instead of assembly from parts, preformationists believed that the form of living things exist, ...
and epigenesis). His account of life involved
spontaneous generation Spontaneous generation is a superseded scientific theory that held that living creatures could arise from nonliving matter and that such processes were commonplace and regular. It was hypothesized that certain forms, such as fleas, could arise fr ...
of new kinds of animals and plants, together with massive elimination of deficient forms. These ideas avoid the need for a Creator, but are not part of modern thinking on evolution. The date of these speculations, 1745, is concurrent with
Carl Linnaeus Carl Linnaeus (; 23 May 1707 – 10 January 1778), also known after his ennoblement in 1761 as Carl von Linné Blunt (2004), p. 171. (), was a Swedish botanist, zoologist, taxonomist, and physician who formalised binomial nomenclature, the ...
's own work, and so predates any firm notion of
species In biology, a species is the basic unit of classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is often defined as the largest group of organisms in which any two individuals of the appropriate s ...
. Also, the work on
genealogy Genealogy () is the study of families, family history, and the tracing of their lineages. Genealogists use oral interviews, historical records, genetic analysis, and other records to obtain information about a family and to demonstrate kins ...
, coupled with the tracing of
phenotypic In genetics, the phenotype () is the set of observable characteristics or traits of an organism. The term covers the organism's morphology or physical form and structure, its developmental processes, its biochemical and physiological proper ...
characters through lineages, foreshadows later work done in genetics.


Least action principle

The
principle of least action The stationary-action principle – also known as the principle of least action – is a variational principle that, when applied to the '' action'' of a mechanical system, yields the equations of motion for that system. The principle states tha ...
states that in all natural phenomena a quantity called 'action' tends to be minimised. Maupertuis developed such a principle over two decades. For him, action could be expressed mathematically as the product of the mass of the body involved, the distance it had travelled and the velocity at which it was travelling. In 1741, he gave a paper to the Paris Academy of Sciences, ''Loi du repos des corps'', (''Law of bodies at rest''). In it he showed that a system of bodies at rest tends to reach a position in which any change would create the smallest possible change in a quantity that he argued could be assimilated to action. In 1744, in another paper to the Paris Academy, he gave his ''Accord de plusieurs lois naturelles qui avaient paru jusqu'ici incompatibles'' (''Agreement of several natural laws that had hitherto seemed to be incompatible'') to show that the behaviour of light during refraction – when it bends on entering a new medium – was such that the total path it followed, from a point in the first medium to a point in the second, minimised a quantity which he again assimilated to action. Finally, in 1746 he gave a further paper, the ''Loix du mouvement et du repos'' (''Laws of movement and rest''), this time to the Berlin Academy of Sciences, which showed that point masses also minimise action. Point masses are bodies that can be treated for the purposes of analysis as being a certain amount of matter (a mass) concentrated at a single point. A major debate in the early part of the eighteenth century concerned the behaviour of such bodies in collisions. Cartesian and Newtonian physicists argued that in their collisions, point masses conserved both momentum and relative velocity. Leibnizians, on the other hand, argued that they also conserved what was called ''live force'' or ''vis viva''. This was unacceptable for their opponents for two reasons: the first that live force conservation did not apply to so-called ‘hard’ bodies, bodies that were totally incompressible, whereas the other two conservation principles did; the second was that live force was defined by the product of mass and square of velocity. Why did the velocity appear twice in this quantity, as squaring it suggests? The Leibnizians argued this was simple enough: there was a natural tendency in all matter towards motion, so even at rest, there is an inherent velocity in bodies; when they begin to move, there is a second velocity term corresponding to their actual motion. This was anathema to Cartesians and Newtonians. An inherent tendency towards motion was an ‘occult quality’ of the kind of favoured by mediaeval scholastics and to be resisted at all costs. Today the concept of a ‘hard’ body is rejected; and mass times the square of velocity is just twice kinetic energy so modern mechanics reserves a major role for the inheritor quantity of ‘live force’. For Maupertuis, however, it was important to retain the concept of the hard body. And the beauty of his principle of least action was that it applied just as well to hard and elastic bodies. Since he had shown that the principle also applied to systems of bodies at rest and to light, it seemed that it was truly universal. The final stage of his argument came when Maupertuis set out to interpret his principle in cosmological terms. ‘Least action’ sounds like an economy principle, roughly equivalent to the idea of economy of effort in daily life. A universal principle of economy of effort would seem to display the working of wisdom in the very construction of the universe. This seems, in Maupertuis's view, a more powerful argument for the existence of an infinitely wise creator than any other that can be advanced. He published his thinking on these matters in his ''Essai de cosmologie'' (''Essay on cosmology'') of 1750. He shows that the major arguments advanced to prove God, from the wonders of nature or the apparent regularity of the universe, are all open to objection (what wonder is there in the existence of certain particularly repulsive insects, what regularity is there in the observation that all the planets turn in nearly the same plane – exactly the same plane might have been striking but 'nearly the same plane' is far less convincing). But a universal principle of wisdom provides an undeniable proof of the shaping of the universe by a wise creator. Hence the principle of least action is not just the culmination of Maupertuis's work in several areas of physics, he sees it as his most important achievement in philosophy too, giving an incontrovertible proof of God. The flaws in his reasoning are principally that there is no obvious reason why the product of mass, velocity and distance should be particularly viewed as corresponding to action, and even less reason why its minimisation should be an 'economy' principle like a minimisation of effort. Indeed, the product of mass, velocity and distance is mathematically the equivalent of the product of the live force and time; thus the integral over distance of the product of mass and velocity is equivalent of the integral over time of the live force. Leibniz had already shown that this quantity is likely to be either minimised ''or maximised'' in natural phenomena. Minimising this quantity could conceivably demonstrate economy, but how could maximising it? (See also the corresponding principles of ''stationary'' actions by Lagrange and
Hamilton Hamilton may refer to: People * Hamilton (name), a common British surname and occasional given name, usually of Scottish origin, including a list of persons with the surname ** The Duke of Hamilton, the premier peer of Scotland ** Lord Hamilt ...
).


Relation to Kant

In ''
Universal Natural History and Theory of the Heavens ''Universal Natural History and Theory of the Heavens'' (german: Allgemeine Naturgeschichte und Theorie des Himmels), subtitled ''or an Attempt to Account for the Constitutional and Mechanical Origin of the Universe upon Newtonian Principles'', ...
'',
Immanuel Kant Immanuel Kant (, , ; 22 April 1724 – 12 February 1804) was a German philosopher and one of the central Enlightenment thinkers. Born in Königsberg, Kant's comprehensive and systematic works in epistemology, metaphysics, ethics, and ...
quotes Maupertuis' 1745 discussion of
nebula A nebula ('cloud' or 'fog' in Latin; pl. nebulae, nebulæ or nebulas) is a distinct luminescent part of interstellar medium, which can consist of ionized, neutral or molecular hydrogen and also cosmic dust. Nebulae are often star-forming regio ...
-like objects, which Maupertuis notes are actually collections of stars, including Andromeda.
Arthur Schopenhauer Arthur Schopenhauer ( , ; 22 February 1788 – 21 September 1860) was a German philosopher. He is best known for his 1818 work ''The World as Will and Representation'' (expanded in 1844), which characterizes the phenomenal world as the prod ...
suggested that
Immanuel Kant Immanuel Kant (, , ; 22 April 1724 – 12 February 1804) was a German philosopher and one of the central Enlightenment thinkers. Born in Königsberg, Kant's comprehensive and systematic works in epistemology, metaphysics, ethics, and ...
's "most important and brilliant doctrine"—contained in the '' Critique of Pure Reason'' (1781)—was asserted by Maupertuis:


Main works

*''La Figure de la Terre, déterminée par les Observations de Messieurs Maupertuis, Clairaut, Camus, Le Monnier & de M. l’Abbé Outhier, accompagnés de M. Celsius.'' (1738
link
from Gallica *''Réflexions philosophiques sur l'origine des langues et la signification des mots'', (1740), read online. *''Discours sur la parallaxe de la lune'' (1741) *''Discours sur la figure des astres'' (1742) *''Eléments de la géographie'' (1742) *''Lettre sur la comète de 1742'' (1742) *''Astronomie nautique : ou Elémens d'astronomie , tant pour un observatoire fixe, que pour un observatoire mobile, (1743)
link to Gallicia
' * Accord de différentes loix de la nature qui avoient jusqu'ici paru incompatibles (1744, English translation) *''Vénus physique'' (1745) * Les loix du mouvement et du repos déduites d'un principe metaphysique (1746, English translation) *''Essai de philosophie morale'' (1749
link
from Gallica. *''Essai de Cosmologie'' (1750). *


Publications

* *


Honours

* The crater
Maupertuis Pierre Louis Moreau de Maupertuis (; ; 1698 – 27 July 1759) was a French mathematician, philosopher and man of letters. He became the Director of the Académie des Sciences, and the first President of the Prussian Academy of Science, at the ...
on the
Moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
is named after him, as is the asteroid
3281 Maupertuis 3281 Maupertuis ( ''prov. designation'': ) is a bright Vesta asteroid from the inner regions of the asteroid belt. It was discovered on 24 February 1938, by Finnish astronomer Yrjö Väisälä at the Turku Observatory in southwest Finland. The l ...
.


References


Works cited

* *


Further reading

* * * * Pekonen, O. and A. Vasak (2014) ''Maupertuis en Laponie.'' Paris : Hermann.


External links

*
Nineteenth century account of Maupertuis and the Principle of Least Action

Read online
the ''Réflexions philosophiques sur l'origine des langues et la signification des mots'', (1740). {{DEFAULTSORT:Maupertuis, Pierre Louis 1698 births 1759 deaths 18th-century French mathematicians People from Saint-Malo French physicists 18th-century French astronomers French biologists Proto-evolutionary biologists French philosophers French geodesists Members of the Académie Française Members of the French Academy of Sciences Members of the Prussian Academy of Sciences Fellows of the Royal Society Recipients of the Pour le Mérite (civil class) French male non-fiction writers 18th-century French male writers