Lazare Carnot - Retirement

Retirement

After Napoleon crowned himself emperor on 2 December 1804, Carnot's republican convictions precluded his acceptance of high office under the First French Empire, and he resigned from public life – although he was later made a Count of the Empire by Napoleon as Lazare Nicolas Marguerite, comte Carnot.

In 1803 he produced his Géométrie de position. This work deals with projective rather than descriptive geometry. 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' concept. He then proved that this ratio is invariant for the four points obtained by cutting four lines of a pencil 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 of fluid dynamics and Carnot's theorem in plane geometry are named after him.

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

During the Hundred Days, he 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. He lived in Warsaw, and moved to Prussia, where he died in the city of Magdeburg. Carnot's remains were interred at the Panthéon in 1889, at the same time as those of Marie Victor de La Tour-Maubourg, Jean-Baptiste Baudin, and François Séverin Marceau-Desgraviers.