Reconstructing Kepler’s Reasoning in the Astronomia Nova
The argument about the equant in chapter 4
2026-11-10
The model, explicit
- B centre of the eccentric
- A the eye
- C the equant point — about it the planet makes equal angles in equal times
- D, F apogee and perigee
- E the planet
- what varies: the angle DCE, uniform in time
The model is Ptolemy’s, as Kepler presents it.
What the reconstruction shows
DBE < DCE holds in every position, with equality only at the apsides — not only at the right angle Kepler supposes.
The hypothesis BC = BA is stated and needed by no step.
Elements I.32 needs a triangle CBE: at the apsides there is none.
Coda: “Schema loquitur Geometrae”
In chapter 2 Kepler states the equivalence of eccentric and concentric with epicycle and leaves the proof to the figure: “Nec verbis opus est.”
