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which states:
:Given a projective transformation f, between the pencil of lines passing through a point X and the pencil of lines passing through a point Y, the set C of intersection points between a line x and its image forms a conic.
::Note that X and Y are on this conic by considering the preimage and image of the line XY (which is respectively a line through X and a line through Y).This can be shown by taking the points X and Y to the standard points and by a projective transformation, in which case the pencils of lines correspond

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