Gerbert had a deep interest in its more advanced elements, the so-called quadrivium. For arithmetic, he revived that lost ancient calculator the abacus. For the study of music, he invented a stringed instrument, the monochord, for demonstrating to students the Pythagorean precision of musical intervals. For geometry, Gerbert wrote a commentary on Euclid and helped to revive an interest in astronomy in the West by telling friends about a marvelous Arab device he had discovered on his travels to Spain, the astrolabe.17 However, Gerbert’s first loves were the subjects of the trivium, especially
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