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Jean-Victor Poncelet (July 1, 1788 – December 22, 1867) was a mathematician and engineer who did much to revive projective geometry.

Jean-Victor Poncelet was born in Metz, France on July 1, 1788. His father Claude Poncelet, a lawyer at the Metz Parlement, had to send him, very young, to Saint-Avold, where he was set in the excellent family Olier. Poncelet won a scholarship to the lycée and then the École Polytechnique where he studied under Gaspard Monge. In 1810 entered the military engineering college at Metz. He was commissioned a lieutenant of engineers and served in Napoleon's invasion of Russia in 1812. He fought at the Battle of Smolensk (1812) and was captured at the Battle of Krasnoi, he was imprisoned by the Russians at Saratov before being repatriated to France in 1814.

During Poncelet's imprisonment, he studied projective geometry and started to investigate those properties that figures share with their shadows, drafting the book Applications d'analyse et de géométrie that was to be published in two volumes in 1862–1864. He studied conic sections and developed the principle of duality independently of Joseph Gergonne.

On Poncelet's repatriation to France, he resumed military engineering duties at Metz, being appointed professor of mechanics at the école d'application in 1825. There, in his lectures, he coined the term fatigue to describe the failure of materials under repeated stress. He took a particular interest in the design of turbines and waterwheels, proposing the inward-flow turbine in 1826, though the first model was not built until 1838. In his book Industrial Mechanics (1829) he proved the work-kinetic energy theorem and demonstrated its wide applicability. Gaspard de Coriolis was simultaneously developing the same ideas, but this work makes Poncelet the most influential engineer in history. Poncelet has been attributed to have introduced the concept of work as the product of force and translation.

Poncelet left Metz in 1835 and became professor of mechanics at the Sorbonne in 1838. From 1848, he held the rank of general, commanding the École Polytechnique. Poncelet retired from his administrative duties in 1850 to devote himself to mathematical research. He died in Paris. In 1868 Adhémar Jean Claude Barré de Saint-Venant was elected to succeed Jean-Victor Poncelet in the mechanics section of the Académie des Sciences.

A French unit of power, the poncelet, was named after him.

• Poncelet-Steiner theorem
• Poncelet's porism
• Poncelet point

• (1822) Traité des des figures
• (1826) Cours de mécanique appliqué aux machines
• (1829) Introduction a la mécanique industrielle
• (1862/64) Applications d'analyse et de géométrie

• Bertrand, J, (1879) Mémoires de l'Académie des Sciences vol. 41
• Notice sur la vie et les ouvrages du général J. V. Poncelet, par M. le général Didion. in Mémoires de l'Académie nationale de Metz 1870 (50e année / 1868-1869; 2e série) pp. 101-159. [1]

• O'Connor, John J; Edmund F. Robertson "Jean-Victor Poncelet". MacTutor History of Mathematics archive.