All the propositions in Projective Geometry occur in dual pairs which have the property that, starting from either proposition of a pair, the other can be immediately inferred by interchanging the parts played by the words ``point'' and ``line.'' A similar duality exists for Reciprocation (Casey 1893).

**References**

Casey, J. ``Theory of Duality and Reciprocal Polars.'' Ch. 13 in
*A Treatise on the Analytical Geometry of the Point, Line, Circle, and Conic Sections, Containing
an Account of Its Most Recent Extensions, with Numerous Examples, 2nd ed., rev. enl.* Dublin: Hodges, Figgis,
& Co., pp. 382-392, 1893.

Ogilvy, C. S. *Excursions in Geometry.* New York: Dover, pp. 107-110, 1990.

© 1996-9

1999-05-24