He was also the author of rhetorical exercises on hackneyed sophistical themes; of a Quadrivium (Arithmetic, Music, Geometry, Astronomy), valuable for the history of music and astronomy in the middle ages; a general sketch of Aristotelian philosophy; a paraphrase of the speeches and letters of Dionysius Areopagita; poems, including an autobiography; and a description of the Augusteum, the column erected by Justinian in the church of St Sophia to commemorate his victories over the Persians.
More remarkable still were his methods of teaching the quadrivium.
The influence of Varro's last work on the nine disciplinae, or branches of study, long survived in the seven " liberal arts " recognized by St Augustine and Martianus Capella, and in the trivium and quadrivium of the middle ages.
The subjects in which the medieval universities examined were (i.) those of the trivium and quadrivium in the faculty of arts; (ii.) theology; (iii.) medicine; and (iv.) civil and canon law.
In medieval times obtained after studying the quadrivium; now obtainable by any Cambridge Bachelor of Arts six clear years after matriculation.
We see from a statement of Cassiodorus that he furnished manuals for the quadrivium of the schools of the middle ages (the " quattuor matheseos disciplinae," as Boetius calls them) on arithmetic, music, geometry and astronomy.
When brought before the emperor, Gerbert admitted his skill in all branches of the quadrivium, but lamented his comparative ignorance of logic. Eager to supply this deficiency he followed Lothair's ambassador Germanus, archdeacon of Reims, to that city, for the sake of studying under so famous a dialectician in the episcopal schools which were rising into reputation under Archbishop Adalbero (969-989).
In medieval times obtained after studying the Quadrivium; now obtainable by any Cambridge Bachelor of Arts six clear years after matriculation.
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