PONCELET, Jean Victor (1788-1867), mathematician, was born at Metz, July 1, 1788. From 1808 to 1810 he attended the Polytechnic School, and afterwards, till 1812, the Practical School at Metz. He then became lieutenant of engineers, and took part in the Russian campaign, during which he was taken prisoner and was confined at Saratoff on the Volga. It was during his imprisonment here that, “privé de toute espèce de livres et de secours, surtout distrait par les malheurs de ma patrie et les miens propres,” as he himself puts it, he began his researches on projective geometry which led to his great treatise on that subject. This work, the Traité des Propriétés Projectives des Figures, which was published in 1822 (2d ed., 1865), is occupied with the investigation of the projective properties of figures, that is, such properties as are not altered by projection. In his investigation he employs the ideas of continuity, of homologous figures, and of reciprocal polars; and by means of these, without any analysis, he was able to establish all the known properties of lines and surfaces of the second degree, and to discover others unknown before. This work entitles Poncelet to rank as one of the greatest of those who took part in the development of the modern geometry of which Monge was the founder. From 1815 to 1825 he was occupied with military engineering at Metz; and from 1825 to 1835 he was professor of mechanics at the Practical School there. In 1826, in his Mémoire sur les Rôties Hydrauliques à Aubes Courbes, he brought forward improvements in the construction of water-wheels, which more than doubled their efficiency. In 1834 he became a member of the Academy; from 1838 to 1848 he was professor to the faculty of sciences at Paris, and from 1848 to 1850 ...