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Poncelet, Jean-Victor

projective geometry french mathematics

[põslay] (1788–1867) French mathematician: substantially advanced projective geometry.

In November 1812 the bedraggled rearguard of the French Grande Armée under Marshal Ney was overwhelmed at Krasnoi on the frozen plains of Russia; Poncelet, a young engineer, was left for dead on the battlefield. A search party who found him took him for questioning, as he was an officer, and so he survived to be marched through a Russian winter for 5 months before entering a prison at Saratov in March 1813.

He passed what turned out to be 2 years of captivity recalling all the mathematics he could from his 3 years at the École Polytechnique (1807–10); and he went on to contribute new mathematics to projective geometry. After he was released his sense of duty led him to put his creative urge on one side and to do routine military engineering tasks, and later to work on water-power. However, in the notes that he produced under such difficult conditions are the principle of duality (the equivalence of various geometric theorems) and the first use of imaginary points in projective geometry.

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