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90 intellectual effort. Rather he was moved by an ardent wish to place before his Latin contemporaries what was best in the classic education and philosophy. He is first of all a translator from Greek to Latin, and, secondly, a helpful commentator on the works which he translates.

He was little over twenty years of age when he wrote his first work, the De arithmetica. It was a free translation of the Arithmetic of Nichomachus, a Neo-Pythagorean who flourished about the year 100. Boëthius's work opens with a dedicatory Praefatio to his father-in-law Symmachus. In that and in the first chapter he evinces a broad conception of education, and shows that lovers of wisdom should not despise arithmetic, music, geometry and astronomy, the fourfold path or quadrivium, a word which he may have been the first to use in this sense. With him arithmetic treats of quantity in and by itself; music, of quantity related to measure; geometry, of moveless, and astronomy, of moving, quantity. He was a better Greek scholar than mathematician; and his free translation ignores some of the finer points of Nichomachus's work, which would have impressed one better versed in mathematics.

The young scholar followed up his maiden work with a treatise on Music, showing a knowledge of Greek harmonics. Then came a De geometria, in which the writer draws from Euclid as well as from the practical knowledge of Roman surveyors. He composed or translated other works on elementary branches of education, as appears from a royal letter written by Cassiodorus in the name of Theodoric: "In your translations Pythagoras the musician, Ptolemy the astronomer, Nichomachus the arithmetician, Euclid the geometer are read by Italians, while Plato the theologian and Aristotle the logician dispute in Roman voice; and you have given back the mechanician Archimedes in Latin to the Sicilians." Making