It can be easily shown that the requirement, to have a point A such that all lines through it remain invariant is a redundant one. It is implied by the property of the axis to include

In fact, consider two points {D,E} and their images {D'=F(D), E'=F(E)} under the elation. Lines {DD',EE'} are invariant under F and must intersect at a point A

[2] The product F' = F

[3] The map Z --> Z* is the

Take Y=F

[2] Every elation F

[3] The product of three harmonic perspectivities sharing the same axis (a) and having their centers {A,B,C} aligned is a harmonic perspectivity.

Line CE is invariant under the composition G = F

Harmonic_Perspectivity.html

Perspectivity.html

Projectivity.html

ProjectivityResolutionPerspectivities.html

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