 Poncelet’s claims for transformations of the plane that map lines to lines were rewritten by Chasles (1837) in a more rigorous way that highlighted the invariance of cross-ratio. Consider \(AB\) to represent the distance between the two points. The cross-ratio of four points \(A\), \(B\), \(C\), \(D\) on a line is defined to be \(AB{\cdot}CD \mathbin{/} AD{\cdot}CB\), and if the points are mapped to \(A'\), \(B'\), \(C'\), \(D'\) respectively by a projective transformation, then