I stumbled on this image from here: enter image description here

It's mentioned w.r.t. to the elliptical orbits of planets and how the focus-directrix property comes into play. It's an interesting POV but when was such a thing known about an ellipse's directrix? Does it predate Kepler or was it a modern discovery? Or a side effect of Dandelin's spheres which are relatively modern? Or something discovered as a result of studying projective geometry?

  • $\begingroup$ For someone who knew the theory of perspective this would have been a relatively trivial consequence of Apollonius's Conics. In Book 1 he defines them as sections of oblique cones (i.e. central projections of circles), and in Book 3 establishes focal properties of ellipses. Once Kepler introduced points at infinity orthogonal projection becomes a particular case of central projection, so this would not have been a "discovery". I doubt that Kepler would have stated it this way though, you may look at La Hire's Conics (1729), it was the first projective "translation" of Apollonius. $\endgroup$ – Conifold Mar 17 '18 at 5:40

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