Abstract
The geometry of the alternative reconstruction of Eudoxan planetary theory is studied. It is shown that in this framework the hippopede acquires an analytical role, consolidating the theorys geometrical underpinnings. This removes the main point of incompatibility between the alternative reconstruction and Simpliciuss account of Eudoxan planetary astronomy. The analysis also suggests a compass and straight-edge procedure for drawing a point by point outline of the retrograde loop created by any given arrangement of the three inner spheres.
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