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CHAP. XII syllogisms—the logical writings expounded by Gerbert at Rheims. The school had likewise Gerbert's own Libellus de ratione uti and Boëthius's De consolatione, that chief ethical compend for the early Middle Ages; also the writings of Eriugena, and Dionysius the Areopagite in Eriugena's translation. Whether or not it possessed the current Latin version of Plato's Timaeus, Fulbert and Berengar at all events refer to Plato in terms of eulogy.

Passing to the Quadrivium, we find that Fulbert had studied its four branches under Gerbert. In Arithmetic the students used the treatise of Boëthius, and also the Abacus, a table of vertical columns, with Roman numerals at the top to indicate the order of units, tens, and hundreds according to the decimal system. In Geometry the students likewise fell back upon Boëthius. Astronomy, the third branch of the Quadrivium, had for its practical object the computation of the Church's calendar. The pupils learned the signs of the Zodiac and were instructed in the method of finding the stars by the Astrolabius, a sphere (such as Gerbert had constructed) representing the constellations, and turning upon a tube as an axis, which served to fix the polar star. Music, the fourth branch of the Quadrivium, was zealously cultivated. For its theory, the treatise of Boëthius was studied; and Fulbert and his scholars did much to advance the music of the liturgy, composing texts and airs for organ chanting.

In addition to the Quadrivium, medicine was taught. The students learned receipts and processes handed down by tradition and commonly ascribed to Hippocrates. For more convenient memorizing, Fulbert cast them into verse. Such "medicine" was not founded on observation; and a mediaeval scholar-copyist would as naturally transcribe a medical receipt-book as any other work coming within the range of his stylus. One may remember that in the early Middle Ages the relic was the common means of cure.

The seven Artes of the Trivium and Quadrivium were the handmaids of Theology; and Fulbert gave elaborate instruction in this Christian queen of the sciences, expounding the Scriptures, explaining the Liturgy, and taking up the controversies of the time. As a part of this sacred