Poncelet (and Pole and Polar)

Abstract

Jean-Victor Poncelet, a former student of Monge, re-invented projective geometry while in prison in Russia in 1812–1813. For him, his patriotic feelings, his wish for simple, general methods in geometry, and his version of projective geometry were inextricably mixed. He described his approach to a non-metrical geometry at length in his Traité des propriétés projectives des figures in 1822. Some of his controversial ideas are introduced, notably the so-called method of continuity according to which non-intersecting lines and conic sections may still be said to meet.

The fundamental technique of pole and polar with respect to a conic is also described in an algebraically simple case.