...Almagest ¹

The true title of this work is Syntaxis Mathematica, which means something like ``Mathematical Treatise''. The name Almagest is probably an Arabic corruption of the work's later Greek nickname, H Megiste (Syntaxis), meaning ``The Greatest (Treatise)''.

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... days.²

This corresponds to the length of the so-called tropical year, which is slightly shorter than that of the more conventional sidereal year because of the precession of the equinoxes, which we are neglecting in this study.

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... positives.³

See the NASA eclipse homepage http://sunearth.gsfc.nasa.gov/eclipse/eclipse.html for the exact details of these eclipses.

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