Abstract
Summary Kepler's investigation of Mars in Astronomia Nova progressed through three distinct stages, each associated with an ‘ovoid’ curve of a particular grade (the egg-metaphor was originated by Kepler himself). The geometrical separation of the first two proposed ovoids is greatest for their quadrant-positions, so that is where Kepler assessed them. Via a previously-unnoticed diagram, I exhibit the simple Euclidean construction he used to determine the optimum position of the Earth acting as a mobile observing-platform. Then I extend Kepler's method to verify that, for at least half its orbit, the Earth will provide a viewing-angle amply large enough to justify his conclusion that the observed quadrant-position lay ‘in the middle’. Hence - regardless of shape - the planetary orbit is identified as an ovoid of medial grade.
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