Poncelet a la presó de Saratov

Poncelet was a soldier in the French army who took part in the Battle of Krasnoï
where the Napoleonic troops were defeated in the Russian war. During his stay as a prisoner in Saratov, based on his recollection of the inspiring lectures of
Gaspard Monge at the École Polytechnique, he worked on the foundations of
projective geometry. The influence of the work of Poncelet extends throughout
the 19th century. Among the results proved by Poncelet in this period the
most remarkable is the acclaimed Poncelet's porism which deals with the
existence of polygons with vertices in a given conic and edges that are tangents
to another fixed conic. In this paper we review certain facts of Poncelet's life
and we set out a notion of one of the demonstrations of the porism.