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Poncelet was the illegitimate son of a well-off landowner and lawyer. He was sent to live with a family in Saint-Avold, France, who took on the responsibility of educating him. Poncelet returned to his native Metz and attended the lycée (secondary school). In Paris, he entered the Ècole Polytechnique but fell behind in his studies after three years due to poor health.
In 1810 Poncelet joined the Corps of Military Engineers. He eventually received his degree from the Ècole d'Application in Metz and in that same year became lieutenant of engineers in the French Army. The year was 1812 and Poncelet took part in Napoleon Bonaparte's (1769-1821) invasion of Russia. At the battle of Krasnoy he was left for dead, captured by the Russians, and sent to a prison camp in Saratov.
Incarcerated for nearly two years, Poncelet worked on mathematical problems to pass the time. Without textbooks or sources of any kind, save his own memory, he reconstructed the elements of analytical mathematics and geometry, and performed original research on conics. The work he accomplished during his imprisonment later was included in an important book on projective geometry, Traité des propriétés projectives des figures, which he produced a few years later after his return to France. This book, published in 1822, is considered by many to be the foundation of modern projective geometry.
Poncelet's work was not appreciated by contemporary authorities such as Augustin-Louis Cauchy, who opposed his theories. Criticism by his peers and disputes over priority in elaborating the principles of "duality" in geometry, a controversy that raged between Poncelet and Joseph Gergonne (1771-1859), caused Poncelet such bitterness that he abandoned further work in projective geometry.
Poncelet next turned his considerable talents to the field of applied mechanics and the in-depth study of machines. Among his accomplishments in this field was a radical design for a variable counterweight drawbridge and detailed study and analysis of hydraulics and the properties of flowing water. In the final decades of his life, Poncelet devoted himself to studying and upgrading the vast base of industrial machinery in use in France's largest factories. He died in Paris in 1867.