Kepler's Road to Damascus

Summary
In Astronomia Nova Kepler established the two laws that govern the motion of an individual planet. I show here that his achievement depended on the Euclidean - geometrical - method he invented to determine a typical point of each of the three curves he successively proposed (corresponding respectively to the three stages of his progress). At the final stage, Kepler's first flash of enlightenment was sparked by his discovery of a general construction-rule for the (medial-grade) curve he required; the second, by his realization that this rule would produce a perfect ellipse, described in accordance with the (Keplerian-style) area law. This exact curve-time correlation is notable for attaining, by modern standards, the status of an orbit.