Poncelet's discovery of homology.

Homology was among the concepts introduced in Jean Victor Poncelet's 1822 Traité des Propriétés Projectives des Figures. Homology is a projective transformation which has an axis, a line of fixed points. The Traité develops a straightedge construction of points under homology , essentially that found in work on perspective drawing and by Phillipe de la Hire, 1673. However, Poncelet's very distinct path to homology was through similitude , where the radical axis of a pair of circles became the axis of homology. We end with Poncelet's application of homology involving the focus of a conic section. [ABSTRACT FROM AUTHOR]