Projection of Conic Section is Conic Section

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Theorem

Let $K$ be a conic section.

Let $K'$ be a projection of $K$.


Then $K'$ is also a conic section.



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In particular: Background work to be completed to properly define projection, which at the moment supports the plane version only. This is a $3$ dimensional version of the projection, projecting the plane in which $K$ lies onto another arbitrary plane.
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Proof


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In particular: needs background work completed
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Historical Note

Girard Desargues developed the concept of the conic section in the context of projective geometry.

Hence he was able to demonstrate Projection of Conic Section is Conic Section.

This was widely disregarded at the time, caused in part by the obscure terminology he used, but also because the influence of projective geometry was overshadowed by the contemporary development of analytic geometry.


Sources

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