Lazare Carnot
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Lazare Nicolas Marguerite, Comte Carnot (; 13 May 1753 – 2 August 1823) was a French
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
,
physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...
, military officer, politician and a leading member of the
Committee of Public Safety The Committee of Public Safety () was a committee of the National Convention which formed the provisional government and war cabinet during the Reign of Terror, a violent phase of the French Revolution. Supplementing the Committee of General D ...
during the French Revolution. His military reforms, which included the introduction of mass conscription ('' levée en masse''), were instrumental in transforming the French Revolutionary Army into an effective fighting force. Carnot was elected to the
National Convention The National Convention () was the constituent assembly of the Kingdom of France for one day and the French First Republic for its first three years during the French Revolution, following the two-year National Constituent Assembly and the ...
in 1792, and a year later he became a member of the Committee of Public Safety, where he directed the French war effort as one of the Ministers of War during the
War of the First Coalition The War of the First Coalition () was a set of wars that several European powers fought between 1792 and 1797, initially against the Constitutional Cabinet of Louis XVI, constitutional Kingdom of France and then the French First Republic, Frenc ...
. He oversaw the reorganization of the army, imposed discipline, and significantly expanded the French force through the imposition of mass conscription. Credited with France's renewed military success from 1793 to 1794, Carnot came to be known as the "Organizer of Victory". Increasingly disillusioned with the radical politics of the Montagnards, Carnot broke with
Maximilien Robespierre Maximilien François Marie Isidore de Robespierre (; ; 6 May 1758 â€“ 28 July 1794) was a French lawyer and statesman, widely recognised as one of the most influential and controversial figures of the French Revolution. Robespierre ferv ...
and played a role in the latter's overthrow on
9 Thermidor Maximilien Robespierre addressed the National Convention on 26 July 1794, was arrested the next day, and executed on 28 July. In his speech on 26 July, Robespierre spoke of the existence of internal enemies, conspirators, and calumniators, with ...
and subsequent execution. He became one of the five initial members of the Directory but was ousted after the Coup of 18 Fructidor in 1797 and went into exile. Following
Napoleon Napoleon Bonaparte (born Napoleone di Buonaparte; 15 August 1769 – 5 May 1821), later known by his regnal name Napoleon I, was a French general and statesman who rose to prominence during the French Revolution and led Military career ...
's rise to power, Carnot returned to France and in 1800 was briefly
Minister of War A ministry of defence or defense (see American and British English spelling differences#-ce.2C -se, spelling differences), also known as a department of defence or defense, is the part of a government responsible for matters of defence and Mi ...
. A fervent Republican, he chose to withdraw from public life after Napoleon's coronation as Emperor. In 1812, he returned to serve under Napoleon and oversaw the defense of Antwerp against the Sixth Coalition, and during the Hundred Days he was Napoleon's Minister of the Interior. Carnot was exiled after the second Bourbon Restoration and died in
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,
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in 1823. In addition to his political career, Carnot was also an eminent mathematician. His 1803 ''Géométrie de position'' is considered a pioneering work in the field of
projective geometry In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting (''p ...
. He is also remembered for developing the Carnot wall, a system of fortification that became widely employed in continental Europe during the 19th century.


Education and early life

Carnot was born on 13 May 1753 in the village of Nolay, in
Burgundy Burgundy ( ; ; Burgundian: ''Bregogne'') is a historical territory and former administrative region and province of east-central France. The province was once home to the Dukes of Burgundy from the early 11th until the late 15th century. ...
, as the son of a local judge and royal notary, Claude Carnot and his wife, Marguerite Pothier. He was the second oldest of seven children. At the age of fourteen, Lazare and his brother were enrolled at the ''Collège d'
Autun Autun () is a Subprefectures in France, subprefecture of the Saône-et-Loire Departments of France, department in the Bourgogne-Franche-Comté Regions of France, region of central-eastern France. It was founded during the Principate era of the e ...
'', where he focused on the study of philosophy and the classics. He held a strong belief in stoic philosophy and was deeply influenced by Roman civilization. When he turned fifteen, he left school in Autun to strengthen his philosophical knowledge and study under the Society of the Priests of Saint Sulpice. During his short time with them, he studied logic, mathematics and theology under the Abbé Bison. Impressed with Lazare's work as a scholar, the (Marquis de Nolay) recommended a military career for the youngster. Carnot was soon sent by his father to the Aumont residence to further his education. Here, he was enrolled in M. de Longpré's pension school in 1770 until he was ready to enter one of two prestigious engineering and artillery schools in Paris. A year later, in February 1771, he was ranked the third highest among twelve who were chosen out of his class of more than one hundred who took the entrance exams. It was at this point when he entered the École royale du génie de Mézières, appointed as a second lieutenant. Studies at the Mézières included geometry, mechanics, geometrical designing, geography, hydraulics and material preparation. On 1 January 1773 he graduated the school, ranked as a
first lieutenant First lieutenant is a commissioned officer military rank in many armed forces; in some forces, it is an appointment. The rank of lieutenant has different meanings in different military formations, but in most forces it is sub-divided into a se ...
. He was eighteen years old. Carnot obtained a commission as a
lieutenant A lieutenant ( , ; abbreviated Lt., Lt, LT, Lieut and similar) is a Junior officer, junior commissioned officer rank in the armed forces of many nations, as well as fire services, emergency medical services, Security agency, security services ...
in Louis Joseph, Prince of Condé's engineer corps. At this moment, he made a name for himself both in the line of (physics) theoretical engineering and in his work in the field of
fortification A fortification (also called a fort, fortress, fastness, or stronghold) is a military construction designed for the defense of territories in warfare, and is used to establish rule in a region during peacetime. The term is derived from Lati ...
s. While in the army, stationed in Calais, Cherbourg and
Béthune Béthune ( ; archaic and ''Bethwyn'' historically in English) is a town in northern France, Subprefectures in France, sub-prefecture of the Pas-de-Calais Departments of France, department. Geography Béthune is located in the Provinces of Fran ...
, he continued his study of mathematics. In December 1783, he received a promotion to the rank of captain. In 1784 he published his first work ''Essay on Machines,'' which contained a statement that foreshadowed the principle of energy as applied to a falling weight, and the earliest proof that
kinetic energy In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion. In classical mechanics, the kinetic energy of a non-rotating object of mass ''m'' traveling at a speed ''v'' is \fracmv^2.Resnick, Rober ...
is lost in the collision of imperfectly elastic bodies. This publication earned him the honor of the Académie des Sciences, Arts et Belles-Lettres de Dijon. Another turning point was his essay on Vauban in which he praised the engineer on his works while at the same time developing his own career as a writer/engineer. Vauban's work had a profound effect on his work as a general and engineer. In 1786 he became acquainted with Robespierre, a lawyer in
Arras Arras ( , ; ; historical ) is the prefecture of the Pas-de-Calais department, which forms part of the region of Hauts-de-France; before the reorganization of 2014 it was in Nord-Pas-de-Calais. The historic centre of the Artois region, with a ...
, in the local literary club. In 1788 he returned to Béthune, where he was imprisoned with a lettre de cachet, because of a broken promise to marry a woman from Dijon. After his release he was stationed in Aire-sur-la-Lys and married Sophie Dupont from
Saint-Omer Saint-Omer (; ; Picard: ''Saint-Onmé'') is a commune and sub-prefecture of the Pas-de-Calais department in France. It is west-northwest of Lille on the railway to Calais, and is located in the Artois province. The town is named after Sa ...
in May 1791. For two months he served as president of the local literary society.


Political career

In September 1791 he became a delegate for
Pas-de-Calais The Pas-de-Calais (, ' strait of Calais'; ; ) is a department in northern France named after the French designation of the Strait of Dover, which it borders. It has the most communes of all the departments of France, with 890, and is the ...
to the
Legislature A legislature (, ) is a deliberative assembly with the legal authority to make laws for a political entity such as a country, nation or city on behalf of the people therein. They are often contrasted with the executive and judicial power ...
. While a member of the Legislative Assembly, Carnot was elected to the Committee of Public Instruction. He believed that all citizens should be educated. As a member of that committee, he wrote a series of reforms for the teaching and educational systems, but they were not implemented due to the violent social and economic climate of the Revolution. After the Legislative Assembly was dissolved, Carnot was elected to the
National Convention The National Convention () was the constituent assembly of the Kingdom of France for one day and the French First Republic for its first three years during the French Revolution, following the two-year National Constituent Assembly and the ...
in September 1792. He spent the last few months of 1792 on a mission to
Bayonne Bayonne () is a city in southwestern France near the France–Spain border, Spanish border. It is a communes of France, commune and one of two subprefectures in France, subprefectures in the Pyrénées-Atlantiques departments of France, departm ...
, organizing the military defense effort in an attempt to ward off any possible attacks from
Spain Spain, or the Kingdom of Spain, is a country in Southern Europe, Southern and Western Europe with territories in North Africa. Featuring the Punta de Tarifa, southernmost point of continental Europe, it is the largest country in Southern Eur ...
. Upon returning to Paris, Carnot voted for the death of
Louis XVI Louis XVI (Louis-Auguste; ; 23 August 1754 – 21 January 1793) was the last king of France before the fall of the monarchy during the French Revolution. The son of Louis, Dauphin of France (1729–1765), Louis, Dauphin of France (son and heir- ...
, although he had been absent for the debates surrounding his trial. By mid-February Carnot proposed that annexation be undertaken on behalf of French interests whether or not the people to be annexed so wished. Following the king's veto of the Assembly's efforts to suppress nonjuring priests on 27 May, on a proposal of Carnot and Servan in the Assembly to raise a permanent militia of volunteers on 8 June, and the reinstatement of Brissotin ministers dismissed on 18 June, the monarchy faced an abortive demonstration of 20 June. On 14 August 1793 Carnot was elected to the
Committee of Public Safety The Committee of Public Safety () was a committee of the National Convention which formed the provisional government and war cabinet during the Reign of Terror, a violent phase of the French Revolution. Supplementing the Committee of General D ...
, where he took charge of the military situation as one of the Ministers of War. He was friendly with Johan Valckenaer who tried to hasten the invasion of the
Dutch Republic The United Provinces of the Netherlands, commonly referred to in historiography as the Dutch Republic, was a confederation that existed from 1579 until the Batavian Revolution in 1795. It was a predecessor state of the present-day Netherlands ...
. With the establishment of the Directory in 1795, Carnot became one of the five initial directors. For the first year, the Directors did well working harmoniously together as well as with the Councils. However, difference of political views led to a schism between Carnot and
Étienne-François Letourneur Étienne-François-Louis-Honoré Letourneur, also known as, Le Tourneur, or Le Tourneur de la Manche (15 March 1751 – 4 October 1817) was a French lawyer, soldier, and politician of the French Revolution. Early life and career Born in Granv ...
, followed by François de Barthélemy, on the one side, and the triumvirate of
Paul François Jean Nicolas, vicomte de Barras Paul François Jean Nicolas, Viscount, Vicomte de Barras (; 30 June 1755 – 29 January 1829), commonly known as Paul Barras, was a French people, French politician of the French Revolution, and the main executive leader of the French Directory ...
, Jean-François Rewbell and Louis Marie de La Révellière-Lépeaux on the other side. Carnot and Barthélemy supported concessions to end the war, and hoped to oust the triumvirate and replace them with more conservative men. After Letourneur had been replaced by another close collaborator of Carnot, François de Barthélemy, both of them, alongside many deputies in the Council of Five Hundred, were ousted in the Coup of 18 Fructidor (4 September 1797), engineered by Generals
Napoleon Bonaparte Napoleon Bonaparte (born Napoleone di Buonaparte; 15 August 1769 – 5 May 1821), later known by his regnal name Napoleon I, was a French general and statesman who rose to prominence during the French Revolution and led Military career ...
(originally, Carnot's '' protégé'') and Pierre François Charles Augereau. Carnot took refuge in
Geneva Geneva ( , ; ) ; ; . is the List of cities in Switzerland, second-most populous city in Switzerland and the most populous in French-speaking Romandy. Situated in the southwest of the country, where the Rhône exits Lake Geneva, it is the ca ...
, and there in 1797 issued his ''La métaphysique du calcul infinitésimal''.


Military accomplishments

The creation of the French Revolutionary Army was largely due to his powers of organization and enforcing discipline. In order to raise more troops for the war, Carnot introduced
conscription Conscription, also known as the draft in the United States and Israel, is the practice in which the compulsory enlistment in a national service, mainly a military service, is enforced by law. Conscription dates back to antiquity and it conti ...
: the '' levée en masse'' approved by the National Convention was able to raise France's army from 645,000 troops in mid-1793 to 1.5 million in September 1794. He was the first to execute the modern waging of war with mass armies and strategic planning realized by the Revolution. As a military engineer, Carnot favored fortresses and defensive strategies.R.R. Palmer, The Twelve Who Ruled. Princeton: Princeton University Press (1941) He developed innovative defensive designs for forts, including the Carnot wall, named after him. However, with the constant invasions he decided to take his strategic planning to an offensive strike. From his intellect sprang the maneuvers and organization that turned the tides of war from 1793 to 1794. The basic idea was to have a massive army separated into several units that could move more quickly than the enemy and attack from the flanks rather than head on, which had led to resounding defeats before Carnot was elected to the Committee of Public Safety. This tactic was extremely successful against the more traditional tactics of existing European armies. It was his initiative to train the conscripts in the art of war and to place new recruits with experienced soldiers rather than having a massive volunteer army without any real idea of how to wage battle. Once the problem of troop numbers had been solved, Carnot turned his administrative skills to the supplies that this massive army would need. Many of the munitions and supplies were in short supply: copper was lacking for guns so he ordered church bells seized in order to melt them down; saltpeter was lacking and he called chemistry to his aid; leather for boots was scarce so he demanded and secured new methods for tanning. He quickly organized the army and helped to turn the tide of the war. It added significantly to discontent with the course of the Revolution in still Bourbon-loyalist areas—such as the
Vendée Vendée () is a department in the Pays de la Loire region in Western France, on the Atlantic coast. In 2019, it had a population of 685,442.open revolt five months earlier—but the government of the time considered it a success, and Carnot became known as the ''Organizer of Victory''. In autumn 1793, he took charge of French columns on the Northern Front, and contributed to Jean-Baptiste Jourdan's victory in the Battle of Wattignies.


Relationship with Maximilien Robespierre and the Jacobin Club

Carnot met Robespierre for the first time in Arras where he was assigned for military duty and shortly after Robespierre finished his legal studies. Both of them were members of the literary club, and they sang ''Societe des Rosati'' together. The group was founded in 1778 and was inspired by the works of
Chapelle Chapelle or La Chapelle may refer to: Communes in France * La Chapelle, Allier * La Chapelle, Ardennes * La Chapelle, Charente * La Chapelle, Savoie * Les Chapelles, Savoie department * La Chapelle (Seine), a former commune of Paris Other place ...
, La Fontaine and Chaulieu. It was here where they became acquaintances and eventually friends. Robespierre preceded Carnot into the Academy of Arras entering in April 1784 while he entered in 1786. While they were active members of the Committee of Public Safety in 1794, tensions between Carnot and Robespierre began to rise massively. During his time on the committee, which was heavily radical, Carnot signed a total of 43 decrees and drafted 18 of them. Most of them dealt with military tactics and education. Despite leaning on Jacobin beliefs, Carnot was considered the "conservative" of his half. He was not an official member of the radical group and therefore took on his own independent beliefs in regards to many issues. One of these issues included Robespierre's proposal on an egalitarian social system with which he feverishly disagreed. Although he had taken no steps to oppose the
Reign of Terror The Reign of Terror (French: ''La Terreur'', literally "The Terror") was a period of the French Revolution when, following the creation of the French First Republic, First Republic, a series of massacres and Capital punishment in France, nu ...
, he and some other technocrats on the committee, including Robert Lindet and Louis-Bernard Guyton de Morveau, turned on
Maximilien Robespierre Maximilien François Marie Isidore de Robespierre (; ; 6 May 1758 â€“ 28 July 1794) was a French lawyer and statesman, widely recognised as one of the most influential and controversial figures of the French Revolution. Robespierre ferv ...
and his allies during the Thermidorian Reaction by having him arrested. Robespierre was later killed along with 21 of his followers. Shortly after Robespierre's fall, Carnot was charged for his role during the time but the charges were quickly dismissed when he became a member of the Directory.


Relationship with Napoleon Bonaparte

In 1795, Carnot appointed Napoleon Bonaparte as general in chief of the Army of Italy. He is known to be the only member of the Directory to have supported Napoleon during this time. In 1800 Bonaparte appointed Carnot as
Minister of War A ministry of defence or defense (see American and British English spelling differences#-ce.2C -se, spelling differences), also known as a department of defence or defense, is the part of a government responsible for matters of defence and Mi ...
, and he served in that office at the time of the Battle of Marengo. In 1802 he voted against the establishment of Napoleon's Consular powers for life and the passing of the title to his children, for as Carnot said when speaking of the power necessary to govern a state "If this power is the appendage of a hereditary family it becomes despotic." After
Napoleon Napoleon Bonaparte (born Napoleone di Buonaparte; 15 August 1769 – 5 May 1821), later known by his regnal name Napoleon I, was a French general and statesman who rose to prominence during the French Revolution and led Military career ...
crowned himself emperor on 2 December 1804, Carnot's republican convictions precluded his acceptance of high office under the
First French Empire The First French Empire or French Empire (; ), also known as Napoleonic France, was the empire ruled by Napoleon Bonaparte, who established French hegemony over much of continental Europe at the beginning of the 19th century. It lasted from ...
, and he resigned from public life. Probably in response to the fall of the fortress of
Vlissingen Vlissingen (; ) is a Municipalities of the Netherlands, municipality and a city in the southwestern Netherlands on the island of Walcheren. With its strategic location between the Scheldt river and the North Sea, Vlissingen has been an importan ...
to the British during the
Walcheren Campaign The Walcheren Campaign () was an unsuccessful United Kingdom of Great Britain and Ireland, British expedition to the Kingdom of Holland in 1809 intended to open another front in the Austrian Empire's struggle with First French Empire, France ...
in 1809, Napoleon employed Carnot to write a treatise describing how fortifications could be improved, for the use of the . Building on the theories of the controversial engineer Montalembert, Carnot advanced ideas on how the long-established bastioned system of fortification could be modified for close defense and to allow for counter attack by the besieged garrison. In 1812, Carnot returned to office in defense of Napoleon during the disastrous invasion of Russia and was assigned the
defense Defense or defence may refer to: Tactical, martial, and political acts or groups * Defense (military), forces primarily intended for warfare * Civil defense, the organizing of civilians to deal with emergencies or enemy attacks * Defense industr ...
of
Antwerp Antwerp (; ; ) is a City status in Belgium, city and a Municipalities of Belgium, municipality in the Flemish Region of Belgium. It is the capital and largest city of Antwerp Province, and the third-largest city in Belgium by area at , after ...
against the Sixth Coalition. He surrendered only at the demand of the Count of Artois, the younger brother of
Louis XVIII Louis XVIII (Louis Stanislas Xavier; 17 November 1755 â€“ 16 September 1824), known as the Desired (), was King of France from 1814 to 1824, except for a brief interruption during the Hundred Days in 1815. Before his reign, he spent 23 y ...
who later reigned as
Charles X Charles X may refer to: * Charles X of France (1757–1836) * Charles X Gustav (1622–1660), King of Sweden * Charles, Cardinal de Bourbon (1523–1590), recognized as Charles X of France but renounced the royal title See also * * King Charle ...
. He was later made a Count of the Empire by Napoleon as Lazare Nicolas Marguerite, Comte Carnot. During the Hundred Days, Carnot served as Minister of the Interior for Napoleon, and was exiled as a regicide during the White Terror after the Second Restoration during the reign of Louis XVIII.


Retirement and legacy

In 1803 Carnot produced his ''Géométrie de position''. This work deals with projective rather than
descriptive geometry Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions by using a specific set of procedures. The resulting techniques are important for engineering, architecture, design an ...
. Carnot is responsible for initiating the use of cross-ratios: "He was the first to introduce the cross (anharmonic) ratio of four points of a line taking account of its sign, thereby sharpening Pappus's concept. He then proved that this ratio is invariant for the four points obtained by cutting four lines of a
pencil A pencil () is a writing or drawing implement with a solid pigment core in a protective casing that reduces the risk of core breakage and keeps it from marking the user's hand. Pencils create marks by physical abrasion, leaving a trail of ...
of lines with different secants. In this way, he established the harmonic properties of the complete quadrilateral." This approach to geometry was used by Karl von Staudt four decades later to set a new foundation to mathematics. The Borda–Carnot equation in
fluid dynamics In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion ...
and several theorems in
geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
are named after him: one that describes a property of the incircle and the circumcircle of triangle, one that describes a relation between triangles and conic sections and one that describes a property of certain perpendiculars on triangle sides. Published in 1810 under the title ''"Traité de la Défense des Places Fortes"'', his ideas on fortification were further developed in the third edition which was published in 1812. An English translation, "A Treatise on the Defence of Fortified Places" was published in 1814. Although few of his proposals were accepted by mainstream engineers, the Carnot wall, a detached wall at the foot of the escarp, became a common feature in fortifications built in the mid-19th century.Lloyd, E. M. (1887)
''Vauban, Montalembert, Carnot: Engineer Studies''
Chapman and Hall, London (pp. 183–195)
He lived in
Warsaw Warsaw, officially the Capital City of Warsaw, is the capital and List of cities and towns in Poland, largest city of Poland. The metropolis stands on the Vistula, River Vistula in east-central Poland. Its population is officially estimated at ...
,
Congress Poland Congress Poland or Congress Kingdom of Poland, formally known as the Kingdom of Poland, was a polity created in 1815 by the Congress of Vienna as a semi-autonomous Polish state, a successor to Napoleon's Duchy of Warsaw. It was established w ...
, and then moved to the
Kingdom of Prussia The Kingdom of Prussia (, ) was a German state that existed from 1701 to 1918.Marriott, J. A. R., and Charles Grant Robertson. ''The Evolution of Prussia, the Making of an Empire''. Rev. ed. Oxford: Clarendon Press, 1946. It played a signif ...
, where he died in the city of
Magdeburg Magdeburg (; ) is the Capital city, capital of the Germany, German States of Germany, state Saxony-Anhalt. The city is on the Elbe river. Otto I, Holy Roman Emperor, Otto I, the first Holy Roman Emperor and founder of the Archbishopric of Mag ...
. Carnot's remains were interred at the Panthéon in 1889, at the same time as those of Théophile Corret de la Tour d'Auvergne, Jean-Baptiste Baudin and François Séverin Marceau-Desgraviers. Carnot survived all the phases of the French Revolution, from its beginnings in 1789 until the fall of
Napoleon Napoleon Bonaparte (born Napoleone di Buonaparte; 15 August 1769 – 5 May 1821), later known by his regnal name Napoleon I, was a French general and statesman who rose to prominence during the French Revolution and led Military career ...
in 1815. On the social and political front, Carnot was the author of many reforms sought to improve the country. One of these was the proposal for compulsory public education for all citizens. He also penned a proposal for the new Constitution which included the "Declaration of the Duties of the Citizens" that held that there should be not only education but military service for all citizens of France between the ages of twenty and twenty-five.


Work in mathematics and theoretical engineering

* 1801
''De la Corrélation des Figures de Géométrie''
containing several theorems in geometry now known as Carnot's theorem * * 1832
''Reflexions on the Metaphysical Principles of the Infinitesimal Analysis''
He also published essays about engineering theory. ''Essai sur les machines en général'' won honorable mention from the Academie sur Science of Paris in 1780. It was revised and published in 1783. In this he outlined a mathematical theory of power transmission in mechanical systems. His essay ''Principes fondamentaux de l'équilibre et du mouvement'' 1803 was a further revision and expansion of the earlier work. Carnot's son, Nicolas, was influenced by his father's work when he undertook his research into the
thermal efficiency In thermodynamics, the thermal efficiency (\eta_) is a dimensionless performance measure of a device that uses thermal energy, such as an internal combustion engine, steam turbine, steam engine, boiler, furnace, refrigerator, ACs etc. For ...
of steam engines. Carnot's name is one of the 72 names inscribed on the Eiffel Tower.


Famous offspring

* His son Sadi Carnot was a founder of the field of
thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...
and the theory of
heat engine A heat engine is a system that transfers thermal energy to do mechanical or electrical work. While originally conceived in the context of mechanical energy, the concept of the heat engine has been applied to various other kinds of energy, pa ...
s (see '' Carnot cycle''). * His second son Lazare Hippolyte Carnot was a French statesman. * His grandson Marie François Sadi Carnot (son of Hippolyte) was President of the French Republic from 1887 until his assassination in 1894.


Bibliography

* 1796 â€
''Exploits des Fran, cais depuis le 22 Fructidor an 1, jusqu'au 15 Pluviose an III, 8 sept. 1793 - 3 febr. 1795''
* 1798 â€
''Réponse de L.N.M. Carnot ... au rapport fait sur la conjuration du 18 fructidor, au conseil des cinq-cents''
* 1799 â€
''Second memoire de Carnot''
* 1810 â€
''De la défense des places fortes, ouvrage composé par ordre de Sa Majesté impériale et royale pour l'instruction des élèves du corps du Génie''
* 1814 â€
''Mémoire adressé au roi, en juillet 1814''
* 1814 – (translated by Baron de Montalembert
''A Treatise on the Defence of Fortified Places''
* 1823 â€
''Mémoire sur la fortification primitive : pour servir de suite au Traité de la défense des places fortes''
* 1888 â€
''Carnot : d'après les archives nationales, le dépot de la guerre et les séances de la convention''
* 1892–1897 â€
''Correspondance générale de Carnot. Publiee avec des notes historiques et biographiques''. Tome I. Aout 1792 - Mars 1793Tome II. Mars - Aout 1793Tome III. Aout - Octobre 1793


Notes


References

* James R. Arnold, ''The Aftermath of the French Revolution''. Minneapolis, MN: Twenty-First Century Books (2009) * W. W. Rouse Ball, ''A Short Account of the History of Mathematics'' (4th Edition, 1908) * Brett-James, Anthony. ''The Hundred Days; Napoleon's Last Campaign from Eye-Witness Accounts''. London: McMillan (1964) * * Gagnon, Paul A. ''France Since 1789''. New York: Harper & Row (1964) * Furet, François and Mona Ozouf, eds. ''A Critical Dictionary of the French Revolution'' (1989), pp. 197–203 *
Charles Coulston Gillispie Charles Coulston Gillispie (; August 6, 1918 – October 6, 2015) was an American historian of science. He was the Dayton-Stockton Professor of History of Science at Princeton University, and was credited with building Princeton's history of scie ...
, ''Lazare Carnot, Savant'', Princeton University Press, (1971) * David Hamilton-Williams. ''Waterloo: New Perspectives. The Great Battle Reappraised''. New York: John Wiley & Sons (1994) * Daniel P. Resnick. ''The White Terror and the Political Reaction After Waterloo''. Cambridge: Harvard University Press (1966) * Carnot, Lazare Nicolas Marguerite. (2011). In L. Rodger, & J. Bakewell, Chambers Biographical Dictionary (9th ed.). London, UK: Chambers Harrap. * Dupre, Huntley (1892). ''Lazare Carnot, Republic Patriot''. Oxford, O: The Mississippi Valley Press. pp. 5–20. * Guillot, F.M. ''Le Jacobinisme Réfuté : Ou, Observations Critiques Sur Le Mémoire De M. Carnot, Adressé Au Roi En 1814''. Paris: C.FF Paris, 1815. 85. Web * Soboul, Albert (28 March 2011)
"Lazare Carnot"
''Britannica''. * Carnot, Lazare Nicolas Marguerite. (2016). In P. Lagasse, & Columbia University, ''The Columbia encyclopedia'' (6th ed.). New York, NY: Columbia University Press. * Carnot, Lazare Nicolas Marguerite. (2011). In L. Rodger, & J. Bakewell, ''Chambers Biographical Dictionary'' (9th ed.). London, UK: Chambers Harrap. * Great Engineers and Pioneers in Technology Vol1 Ed Roland Turner and Steven Goulden St Martins Press Inc NY 1981


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Lazare Carnot – Œuvres complètes
Gallica-Math {{DEFAULTSORT:Carnot, Lazare 1753 births 1823 deaths 18th-century French engineers 19th-century French engineers 18th-century French military personnel 18th-century French writers 19th-century French writers 18th-century French mathematicians 19th-century French mathematicians People from Côte-d'Or Deputies to the French National Convention Regicides of Louis XVI Directeurs of the First French Republic French commanders of the Napoleonic Wars Counts of the First French Empire Thermodynamicists Military leaders of the French Revolutionary Wars French military engineers Burials at the Panthéon, Paris French non-fiction writers History of calculus French interior ministers People on the Committee of Public Safety Members of the Chamber of Representatives (France) Presidents of the National Convention Ministers of war of France Members of the French Academy of Sciences Expatriates in the Kingdom of Prussia French expatriates in the Russian Empire French expatriates in Switzerland Carnot family Names inscribed under the Arc de Triomphe People of the War of the First Coalition