PONCELET, JEAN-VICTOR

born July 1, 1788, Metz, Fr. died Dec. 22, 1867, Paris French mathematician and engineer who was one of the founders of modern projective geometry. As a lieutenant of engineers in 1812, he took part in Napoleon's Russian campaign, in which he was abandoned as dead at Krasnoy and imprisoned at Saratov. He returned to France in 1814. During his imprisonment Poncelet studied projective geometry and wrote Applications d'analyse et de gomtrie, 2 vol. (1862-64; "Applications of Analysis and Geometry"). This work was originally planned as an introduction to his celebrated Trait des proprits projectives des figures (1822; "Treatise on the Projective Properties of Figures"), for which Poncelet is regarded as one of the greatest projective geometers. His development of the pole and polar lines associated with conics led to the principle of duality and a dispute over priority for its discovery. His principle of continuity, a concept designed to add generality to synthetic geometry, led to the introduction of imaginary points. From 1815 to 1825 Poncelet was occupied with military engineering at Metz, and from 1825 to 1835 he was professor of mechanics at the cole d'application there. He applied mathematics to the improvement of turbines and waterwheels. Although the first inward-flow turbine was not built until 1838, he proposed such a turbine in 1826. From 1838 to 1848 he was professor to the faculty of sciences at Paris, and from 1848 to 1850 he was commandant of the cole Polytechnique, with the rank of general.