Abstract
It is a formidable challenge to include foci in a projective treatment of the conic sections. They are, of course, not preserved under projection. Poncelet wrote in his 1822 Traité, Art. 446: “Although the properties of foci (foyers) …seem to not be among those we have called projectives, …they follow nevertheless in a very simple manner from foundational principles ….”
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References
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Baltus, C. (2020). Foci. In: Collineations and Conic Sections. Springer, Cham. https://doi.org/10.1007/978-3-030-46287-1_9
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DOI: https://doi.org/10.1007/978-3-030-46287-1_9
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