Lazare Carnot

Lazare Nicolas Marguerite, Comte
Comte is a title of Catalan, Occitan and French nobility. In the English language, the title is equivalent to count, a rank in several European nobilities. The corresponding rank in England is earl...

(13 May 1753 – 2 August 1823), the Organizer of Victory in the French Revolutionary Wars
French Revolutionary Wars
The French Revolutionary Wars were a series of major conflicts, from 1792 until 1802, fought between the French Revolutionary government and several European states...

, was a French politician, engineer, and mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....


Education and early life

Born in Nolay
Nolay, Côte-d'Or
Nolay is a commune in the Côte-d'Or department in eastern France.- Geography :Nolay is located in the heart of the Cozanne Valley. The town marks the transition between the forests and plains to the north and west and the hillside vineyards of the wealthy Burgundian wine regions surrounding Beaune...

, Côte-d'Or, Carnot was educated in Burgundy at the Collège d’Autun
Collège d’Autun
Collège d’Autun is college of University of Paris. It was founded by Pierre Bertrand in 1337.-Famous alumni:* Louis Renault - Nobel Peace Prize 1907...

, an artillery and engineering prep school. He graduated from Mezieres School of Engineering, where he had met and studied with Benjamin Franklin
Benjamin Franklin
Dr. Benjamin Franklin was one of the Founding Fathers of the United States. A noted polymath, Franklin was a leading author, printer, political theorist, politician, postmaster, scientist, musician, inventor, satirist, civic activist, statesman, and diplomat...

, at the age of twenty and obtained commission as a lieutenant in the Prince of Condé
Prince of Condé
The Most Serene House of Condé is a historical French house, a noble lineage of descent from a single ancestor...

’s engineer corps. It was here that he early made a name for himself both in the line of physics and in his work in the field of fortifications. Although in the army, he continued his study of mathematics. 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 of the fact that kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...

 is lost in the collision of imperfectly elastic bodies
Solid mechanics
Solid mechanics is the branch of mechanics, physics, and mathematics that concerns the behavior of solid matter under external actions . It is part of a broader study known as continuum mechanics. One of the most common practical applications of solid mechanics is the Euler-Bernoulli beam equation...

. This publication earned him the honour of admittance to a literary society. In that same year, he also received a promotion to the rank of captain.

Political career

At the outbreak of the French Revolution
French Revolution
The French Revolution , sometimes distinguished as the 'Great French Revolution' , was a period of radical social and political upheaval in France and Europe. The absolute monarchy that had ruled France for centuries collapsed in three years...

 in 1789, Carnot entered political life. He became a delegate to the Legislation
Legislative Assembly (France)
During the French Revolution, the Legislative Assembly was the legislature of France from 1 October 1791 to September 1792. It provided the focus of political debate and revolutionary law-making between the periods of the National Constituent Assembly and of the National Convention.The Legislative...

 in 1791. While a member of the Legislative Assembly, Carnot was elected to the Committee for Public Instruction. Carnot believed all citizens should be educated and 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.

When the Legislative Assembly dissolved, Carnot was then elected to the National Convention
National Convention
During the French Revolution, the National Convention or Convention, in France, comprised the constitutional and legislative assembly which sat from 20 September 1792 to 26 October 1795 . It held executive power in France during the first years of the French First Republic...

 in 1792. He spent the last few months of 1792 on a mission to Bayonne, organizing the military defense effort in an attempt to ward off any possible attacks from Spain. Upon returning to Paris, Carnot voted for the death of King Louis XVI
Louis XVI of France
Louis XVI was a Bourbon monarch who ruled as King of France and Navarre until 1791, and then as King of the French from 1791 to 1792, before being executed in 1793....

, although he had been absent for the debates surrounding the king’s trial.

On 14 August 1793 he was elected to the Committee of Public Safety
Committee of Public Safety
The Committee of Public Safety , created in April 1793 by the National Convention and then restructured in July 1793, formed the de facto executive government in France during the Reign of Terror , a stage of the French Revolution...

 where he took charge of the military situation as one of the Ministers of War.
The creation of the French Revolutionary Army
French Revolutionary Army
The French Revolutionary Army is the term used to refer to the military of France during the period between the fall of the ancien regime under Louis XVI in 1792 and the formation of the First French Empire under Napoleon Bonaparte in 1804. These armies were characterised by their revolutionary...

 was largely due to his powers of organization and enforcing discipline. In order to raise more troops for the war Carnot introduced conscription
Conscription is the compulsory enlistment of people in some sort of national service, most often military service. Conscription dates back to antiquity and continues in some countries to the present day under various names...

: the levée en masse
Levée en masse
Levée en masse is a French term for mass conscription during the French Revolutionary Wars, particularly for the one from 16 August 1793.- Terminology :...

approved by the National Convention was able to raise France’s army from a meager 645,000 troops in mid-1793 to 1,500,000 in September 1794. 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
House of Bourbon
The House of Bourbon is a European royal house, a branch of the Capetian dynasty . Bourbon kings first ruled Navarre and France in the 16th century. By the 18th century, members of the Bourbon dynasty also held thrones in Spain, Naples, Sicily, and Parma...

 areas – such as the Vendée
The Vendée is a department in the Pays-de-la-Loire region in west central France, on the Atlantic Ocean. The name Vendée is taken from the Vendée river which runs through the south-eastern part of the department.-History:...

, which had broken out in open revolt
Revolt in the Vendée
The War in the Vendée was a Royalist rebellion and counterrevolution in the Vendée region of France during the French Revolution. The Vendée is a coastal region, located immediately south of the Loire River in western France. The uprising was closely tied to the Chouannerie, which took place in...

 5 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
French Revolutionary Wars: Campaigns of 1793
The French Revolutionary Wars continued from 1792, with new powers entering the First Coalition after the execution of King Louis XVI. Spain and Portugal entered the coalition in January 1793, and on 1 February France declared war on Great Britain and the Netherlands.At the opening of the year,...

, and contributed to Jean-Baptiste Jourdan
Jean-Baptiste Jourdan
Jean-Baptiste Jourdan, 1st Comte Jourdan , enlisted as a private in the French royal army and rose to command armies during the French Revolutionary Wars. Emperor Napoleon I of France named him a Marshal of France in 1804 and he also fought in the Napoleonic Wars. After 1815, he became reconciled...

's victory in the Battle of Wattignies
Battle of Wattignies (1793)
The Battle of Wattignies was fought at the village of Wattignies-la-Victoire, France, on 15 and 16 October 1793 during the French Revolutionary Wars. The French army commanded by Jean-Baptiste Jourdan and Lazare Carnot defeated the army of Habsburg Austria led by Prince Josias of Coburg...


He had taken no steps to oppose the Reign of Terror
Reign of Terror
The Reign of Terror , also known simply as The Terror , was a period of violence that occurred after the onset of the French Revolution, incited by conflict between rival political factions, the Girondins and the Jacobins, and marked by mass executions of "enemies of...

, but he, along with other technocrats
Technocracy (bureaucratic)
Technocracy is a form of government where technical experts are in control of decision making in their respective fields. Economists, engineers, scientists, health professionals, and those who have knowledge, expertise or skills would compose the governing body...

 on the committee like Robert Lindet and Louis-Bernard Guyton de Morveau
Louis-Bernard Guyton de Morveau
Louis-Bernard Guyton de Morveau was a French chemist and politician...

, turned on Maximilien Robespierre
Maximilien Robespierre
Maximilien François Marie Isidore de Robespierre is one of the best-known and most influential figures of the French Revolution. He largely dominated the Committee of Public Safety and was instrumental in the period of the Revolution commonly known as the Reign of Terror, which ended with his...

 and his allies during the Thermidorian Reaction
Thermidorian Reaction
The Thermidorian Reaction was a revolt in the French Revolution against the excesses of the Reign of Terror. It was triggered by a vote of the Committee of Public Safety to execute Maximilien Robespierre, Antoine Louis Léon de Saint-Just de Richebourg and several other leading members of the Terror...


With the establishment of the Directory
French Directory
The Directory was a body of five Directors that held executive power in France following the Convention and preceding the Consulate...

 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 Letourneur
Étienne-François-Louis-Honoré Letourneur, Le Tourneur, or Le Tourneur de la Manche was a French lawyer, soldier, and politician of the French Revolution.-Early career:...

, followed by François de Barthélemy
François-Marie, marquis de Barthélemy
François, marquis de Barthélemy was a French politician and diplomat, active at the time of the French Revolution.-Diplomat and member of the Directory:...

, on the one side, and the triumvirate of Paul François Jean Nicolas, vicomte de Barras
Paul François Jean Nicolas, vicomte de Barras
Paul François Jean Nicolas, vicomte de Barras was a French politician of the French Revolution, and the main executive leader of the Directory regime of 1795–1799.-Early life:...

, Jean-François Rewbell
Jean-François Rewbell
Jean-François Rewbell was a French lawyer, diplomat, and politician of the Revolution.-The revolutionary:...

, and Louis Marie de La Révellière-Lépeaux
Louis Marie de La Révellière-Lépeaux
Louis Marie de La Révellière-Lépeaux was a French politician, member of the French DirectoryHe was born at Montaigu , the son of J. B. de la Révellière. He adopted the name Lépeaux from a small property belonging to his family, and he was known locally as M. de Lépeaux. He studied law at Angers...

 on the other side. Carnot and Barthélemy both supported concessions to end the war, and hoped to oust the triumvirate and replace them with more conservative men. His and Étienne-François Letourneur's moderation was viewed as weakness, and it probably contributed to France's failure to capitalize on the Treaty of Campo Formio
Treaty of Campo Formio
The Treaty of Campo Formio was signed on 18 October 1797 by Napoleon Bonaparte and Count Philipp von Cobenzl as representatives of revolutionary France and the Austrian monarchy...

. 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
Council of Five Hundred
The Council of Five Hundred , or simply the Five Hundred was the lower house of the legislature of France during the period commonly known as the Directory , from 22 August 1795 until 9 November 1799, roughly the second half of the period generally referred to as the...

, were ousted in the Fructidor
Fructidor is the twelfth month in the French Republican Calendar. The month was named after the Latin word fructus, which means "fruit".Fructidor is the third month of the summer quarter . By the Gregorian calendar, Fructidor starts on either August 18 or August 19 and ends exactly thirty days...

 coup d'état of (4 September 1797), engineered by Generals Napoleon Bonaparte
Napoleon I of France
Napoleon Bonaparte was a French military and political leader during the latter stages of the French Revolution.As Napoleon I, he was Emperor of the French from 1804 to 1815...

 (originally, Carnot's protégé
Mentorship refers to a personal developmental relationship in which a more experienced or more knowledgeable person helps a less experienced or less knowledgeable person....

) and Pierre François Charles Augereau
Pierre François Charles Augereau, duc de Castiglione
Charles Pierre François Augereau, 1st Duc de Castiglione was a soldier and general and Marshal of France. After serving in the French Revolutionary Wars he earned rapid promotion while fighting against Spain and soon found himself a division commander under Napoleon Bonaparte in Italy...

. He took refuge in Geneva
Geneva In the national languages of Switzerland the city is known as Genf , Ginevra and Genevra is the second-most-populous city in Switzerland and is the most populous city of Romandie, the French-speaking part of Switzerland...

, and there in 1797 issued his La métaphysique du calcul infinitésimal.

In 1800 he was appointed Minister of War by Bonaparte, and served in that office at the time of the Battle of Marengo
Battle of Marengo (1800)
The Battle of Marengo was fought on 14 June 1800 between French forces under Napoleon Bonaparte and Austrian forces near the city of Alessandria, in Piedmont, Italy...

. In 1802, he voted against the establishment of Napoleon's Consular powers for life
French Consulate
The Consulate was the government of France between the fall of the Directory in the coup of 18 Brumaire in 1799 until the start of the Napoleonic Empire in 1804...

 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 crowned himself emperor on 2 December 1804, Carnot's republican convictions precluded his acceptance of high office under the First French Empire
First French Empire
The First French Empire , also known as the Greater French Empire or Napoleonic Empire, was the empire of Napoleon I of France...

, and he resigned from public life – although he was later made a Count of the Empire
French nobility
The French nobility was the privileged order of France in the Middle Ages and the Early Modern periods.In the political system of the Estates General, the nobility made up the Second Estate...

 by Napoleon as Lazare Nicolas Marguerite, comte Carnot.

In 1803 he produced his Géométrie de position. This work deals with projective
Projective geometry
In mathematics, projective geometry is the study of geometric properties that are invariant under projective transformations. This means that, compared to elementary geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts...

 rather than descriptive geometry
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 and in art...

According to Laptev & Rozenfel'd (1996), Carnot is responsible for initiating the use of cross-ratio
In geometry, the cross-ratio, also called double ratio and anharmonic ratio, is a special number associated with an ordered quadruple of collinear points, particularly points on a projective line...

He was the first to introduce the cross (anharmonic) ratio of four points of a line taking account of its sign, thereby sharpening Pappus' concept
Pappus's hexagon theorem
In mathematics, Pappus's hexagon theorem states that given one set of collinear points A, B, C, and another set of collinear points a, b, c, then the intersection points X, Y, Z of line pairs Ab and aB, Ac and aC, Bc and bC are collinear...

. He then proved that this ratio is invariant for the four points obtained by cutting four lines of a pencil
Pencil (mathematics)
A pencil in projective geometry is a family of geometric objects with a common property, for example the set of lines that pass through a given point in a projective plane....

 of lines with different secants. In this way he established the harmonic properties of the complete quadrilateral.

Carnot returned to office in defense of Napoleon during the disastrous invasion of Russia; he was assigned the defense of Antwerp against the Sixth Coalition – he only surrendered on the demand of the Count of Artois
Charles X of France
Charles X was known for most of his life as the Comte d'Artois before he reigned as King of France and of Navarre from 16 September 1824 until 2 August 1830. A younger brother to Kings Louis XVI and Louis XVIII, he supported the latter in exile and eventually succeeded him...

, who was the younger brother of Louis XVIII and later Charles X.

During the Hundred Days
Hundred Days
The Hundred Days, sometimes known as the Hundred Days of Napoleon or Napoleon's Hundred Days for specificity, marked the period between Emperor Napoleon I of France's return from exile on Elba to Paris on 20 March 1815 and the second restoration of King Louis XVIII on 8 July 1815...

, he served as Minister of the Interior for Napoleon, and was exiled as a regicide
The broad definition of regicide is the deliberate killing of a monarch, or the person responsible for the killing of a monarch. In a narrower sense, in the British tradition, it refers to the judicial execution of a king after a trial...

during the White Terror
White Terror
White Terror is the violence carried out by reactionary groups as part of a counter-revolution. In particular, during the 20th century, in several countries the term White Terror was applied to acts of violence against real or suspected socialists and communists.-Historical origin: the French...

 after the Second Restoration
Bourbon Restoration
The Bourbon Restoration is the name given to the period following the successive events of the French Revolution , the end of the First Republic , and then the forcible end of the First French Empire under Napoleon  – when a coalition of European powers restored by arms the monarchy to the...

 during the reign of Louis XVIII. He lived in Warsaw
Warsaw is the capital and largest city of Poland. It is located on the Vistula River, roughly from the Baltic Sea and from the Carpathian Mountains. Its population in 2010 was estimated at 1,716,855 residents with a greater metropolitan area of 2,631,902 residents, making Warsaw the 10th most...

, and moved to Prussia
Prussia was a German kingdom and historic state originating out of the Duchy of Prussia and the Margraviate of Brandenburg. For centuries, the House of Hohenzollern ruled Prussia, successfully expanding its size by way of an unusually well-organized and effective army. Prussia shaped the history...

, where he died in the city of Magdeburg
Magdeburg , is the largest city and the capital city of the Bundesland of Saxony-Anhalt, Germany. Magdeburg is situated on the Elbe River and was one of the most important medieval cities of Europe....

. Carnot's remains were interred at the Panthéon
Panthéon, Paris
The Panthéon is a building in the Latin Quarter in Paris. It was originally built as a church dedicated to St. Genevieve and to house the reliquary châsse containing her relics but, after many changes, now functions as a secular mausoleum containing the remains of distinguished French citizens...

 in 1889, at the same time as those of Marie Victor de La Tour-Maubourg
Marie Victor de Fay, marquis de Latour-Maubourg
Marie Victor Nicolas de Fay, marquis de Latour-Maubourg was a French cavalry commander starting under the Ancien Régime of France, and rising to prominence during the First French Empire...

, Jean-Baptiste Baudin, and François Séverin Marceau-Desgraviers
François Séverin Marceau-Desgraviers
François Séverin Marceau-Desgraviers was a French general of the Revolutionary Wars.-Early life:Desgraviers was born at Chartres, Eure-et-Loir. His father served as a legal officer, and Marceau received an education for a legal career, but at the age of sixteen he enlisted in the regiment of...



Carnot was able to survive and maintain a place of power during all the phases of the French Revolution
French Revolution
The French Revolution , sometimes distinguished as the 'Great French Revolution' , was a period of radical social and political upheaval in France and Europe. The absolute monarchy that had ruled France for centuries collapsed in three years...

, from its beginnings in 1789 until the fall of Napoleon in 1815. On the social and political front, Carnot was the author of many reforms that he thought to be for the good of the Republic. 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. These proposals were in accordance with the Revolutionaries' thinking at the time, which held that men and women should be honored through ability and intelligence rather than through birthright, even though Carnot himself was nobly born. This style of thinking may well have been instrumental in Napoleon Bonaparte's rise to power as it was Carnot who promoted him from Captain to General.

But perhaps his greatest achievements, in deference to the French Revolution itself, were those of a military nature. If not for Carnot, the modern waging of war with mass armies and strategic planning would not exist. As a military engineer, Carnot favored fortresses and defensive strategies, but with the constant invasions 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. He also created a new political strategy based on disrupting communication between enemy nations of England and Austria while concentrating attack effort on England. Carnot’s military influence and authority were eventually used to bring about the downfall of Robespierre.

Work in mathematics and science

Famous offspring

  • His son Sadi Carnot
    Nicolas Léonard Sadi Carnot
    Nicolas Léonard Sadi Carnot was a French military engineer who, in his 1824 Reflections on the Motive Power of Fire, gave the first successful theoretical account of heat engines, now known as the Carnot cycle, thereby laying the foundations of the second law of thermodynamics...

     was a founder of the field of thermodynamics
    Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

     and the theory of heat engines (see Carnot cycle
    Carnot cycle
    The Carnot cycle is a theoretical thermodynamic cycle proposed by Nicolas Léonard Sadi Carnot in 1824 and expanded by Benoit Paul Émile Clapeyron in the 1830s and 40s. It can be shown that it is the most efficient cycle for converting a given amount of thermal energy into work, or conversely,...

  • His second son Lazare Hippolyte Carnot
    Hippolyte Carnot
    Lazare Hippolyte Carnot was a French statesman.- Early life :Lazare was the younger brother of the founder of thermodynamics Sadi Carnot and second son of the revolutionary politician Lazare Nicolas Marguerite Carnot, who also served in the government of Napoleon. He was born at Saint-Omer,...

     was a French statesman.
  • His grandson Marie François Sadi Carnot
    Marie François Sadi Carnot
    Marie François Sadi Carnot was a French statesman and the fourth president of the Third French Republic. He served as the President of France from 1887 until his assassination in 1894.-Early life:...

     (son of Hippolyte) was President of the French Republic
    President of the French Republic
    The President of the French Republic colloquially referred to in English as the President of France, is France's elected Head of State....

     from 1887 until his assassination in 1894 .

External links

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