A selfdual generalization of the Theorems of Pascal and Brianchon

We introduce the technique of polarization in the context of projective
incidence geometry. It is discussed how to obtain new incidence results by polarizing known theorems.
The approach leads to a selfdual theorem which contains as special cases both
Pascal’s and Brianchon’s theorem. As corollaries, we find generalizations of
both theorems. A similar technique, regularization, is used to find a generalization of
de La Hire’s fundamental theorem of polarity.