Why was Theodosius's Sphaerics significant?

Answer 1

As Europe fell into the dark ages, much of Classical knowledge was lost, including most of its literature. Fortunately, the Islamic world was entering what is called the Islamic Golden Age, where much of the philosophy and technology of the Western world was translated into Arabic and preserved.

In Europe, Euclidean geometry was one of many things lost, but fortunately Theodosius had written three volumes about spherical geometry called Sphaerics, that had been translated into Arabic. During the crusades, this and the rest of the foundation of the Renaissance was recovered, and during the 12th and subsequent centuries, translated back into Latin.

Therefore, Sphaerics served as a key text in the recovery of Euclidean geometry, helping seed math and physics in the Renaissance.

See the articles "Islamic Golden Age", "Latin Translations of the 12th Century" and Sphaerics, on Wikipedia, for more information.