The proof is an easy exercise that reduces to the discussion in Chasles_Steiner.html .

Next figure shows how important is the condition for the points {A,B} to be on the conic. In this figure the points {A,B} do not lie on the conic, and we repeat the same construction: For varying P on the conic consider the coordinate x of the intersection of AP with line L and the corresponding intersection y of BP with L.

Then we plot the points (x,y) for all possible positions of P. The plot shows that the curve cannot be the graph of a function in general.

Find the equation f(x,y)=0 satisfied by these points (x,y) in dependence of the four given data {c, L, A, B}.

File Chasles_Steiner3.html contains an exeptional case of this figure occuring when the conic c degenerates to a line.

Chasles_Steiner_Envelope.html

Chasles_Steiner.html

Chasles_Steiner3.html

ChaslesSteinerExample.html

HomographicRelation.html

HomographicRelationExample.html

Line_Homography.html

ProjectiveBase.html

RectHypeRelation.html

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