I am looking for a proof for duality principle in projective geometry. There is an axiomatic and then a homogeneous coordinates development of projective geometry where dual of lines to points and vise versa are defined and dual curves as well. Is there a proof of this duality within that context or does it have to be based on axiomatic development?
Edit : the axiomatic treatment even if proved as theorems does not include “curves”. How do we prove after defining dual curves that the duality principle extends to statements which include curves ? The comment leaves this unanswered.
Edit : The duality principle is about proof of theorems containing points and lines whereby a new theorem can be proven by interchanging points and lines and dualizing the statements but typically not containing curves. But by showing the duality for the curves namely that the dual of dual is the original one, we can extend it to that case.proof of extension ?
