Bos, H. J. M.; Kers, C.; Oort, F.; Raven, D. W. Poncelet's closure theorem. Exposition. Math. 5 (1987), no. 4, 289–364.
Joseph Harris wrote for MathSciNet: "the authors trace very carefully the history of the problem, describing various approaches culminating in a modern proof. The paper is fascinating from both a historical and a mathematical point of view, and should serve as the definitive source of information about Poncelet's problem in the future" here
Bos, Henk J. M. Redefining geometrical exactness. Descartes' transformation of the early modern concept of construction. Sources and Studies in the History of Mathematics and Physical Sciences. Springer-Verlag, New York, 2001.