Collineation and Correlation

A related type of transformation, which transforms points into lines and lines into points is called a correlation. It transforms collinear points into pencils, quadrangles into guadrilateraJs, and so on. 

A set of collinear points Ai on b correlates with a pencil of concurrent lines Oi on B, such that the cross product of the pencil, measured on an arbitrary line /, 

The projectivity X A re n a transforms any non-self-conjugate point B into another point a Db = C, whose polar is AB. The same projectivity transforms C into B. It therefore interchanges B and C and hence is an involution. 

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