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In
the above diagram AEP is an ellipse with foci S and F, D is the apparent
position of a planet; equal angles are swept out about F in equal times.
AP is the line of apsides, C the center and M some point about C on the
major axis. FM = 1/3FS, which Mercator called the 'divine section'; MD
= CA = 1/2AP. MD describes a circle about M, and the problem is to
find angle ASD from angle AFD. An brilliant and otherwise successful
mathematician, Nicolas Mercator had few advocates for his elliptical hypothesis,
which was rivaled only by the modified hypotheses of Boulliau and, eventually,
Thomas Streete.
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