almagest

If they were familiar with Ptoloemy's almagest, they would be able to predict eclipses using geometric methods.

Al-Mamun also famously accepted a peace treaty from Roman Byzantine Empire in the form of original copy of Ptolemy's Almagest [4].

This makes Al-Ma'mun the patron of the Almagest mentioned the OP article [5].

And writing ptolemaic is probably too charitable because the Almagest at least predicted movements quite well at the time (apparently it now deviates too much).

And as has been the tradition at least from the times of Ptolemy's Almagest in the 2nd century, we started with spherical trigonometry.

>He cannot possibly have been the patron of the Almagest as Ptolemy lived centuries before he did.

The Almagest version of the Galileo notes in the OP article is the Latin translation of the Arabic translation by Gerard of Cremona in Toledo around 1175.

Toomer, a historian of astronomy, has suggested that Ptolemy's knowledge of eclipse records and other Babylonian observations in the Almagest came from a list made by Hipparchus.

This makes Al-Ma'mun the patron of Almagest [1].

Another fun facts, the Almagest version of the Galileo notes in the OP article is the Latin translation of Almagest by Gerard of Cremona in Toledo around 1175, from the Arabic translation of Almagest performed in the House of Wisdom (or Baitul Hikmah).

It's also reported that at one time, Abbasid Caliph Al-Ma'mun was demanding an original copy of the Ptolemy's Almagest book as the condition of a truce between Byzantine Empire and the Abbasid Empire.

I've also mentioned that according to history he accepted the offer of the original copy of Almagest (Almajisti) in Greek from the Roman (Byzantine) emperor the time for a truce.

Not perfect but surprisingly accurate according to Jayant Shah in the paper "Accuracy of Ptolemy’s Almagest in predicting solar eclipses" More accurate methods using Newton's theories were yet to come.

The Almagest was hand written about 1400 years before Galileo lived, so it's not so much looking at different printings as at different editions that are based on different set of copies of the copies of the copies etc, further many editors would try to "fix" the ancient work, removing material they didn't like and adding their own stuff or material from other works...

> In 1900, Franz Xaver Kugler demonstrated that Ptolemy had stated in his Almagest IV.2 that Hipparchus improved the values for the Moon's periods known to him from "even more ancient astronomers" by comparing eclipse observations made earlier by "the Chaldeans", and by himself.

In 1561, the statutes of the University of Salamanca specified that in the second year of the astronomy course the professor must teach either “the Almagest of Ptolemy, or its Epitome by Regiomontanus, or Geber, or Copernicus,” and that the students could vote on which text they wanted (Navarro-Brotóns 1995, 55).

He painstakingly discusses the proof that the earth is a sphere in Almagest.

If you haven't read Ptolomy (and in particular all of Tetrabiblos, the Almagest, and his Geographia), you really should.

He does mention the inclination of the earth relative to the equator though, iirc, in Almagest.