Previously Unpublished Works, Fascicle 16

"whoever overlooks these things has lost the teaching of all wisdom." The judgment of all the ancients also confirms this, saying: "Among all those men of ancient authority who flourished under the leadership of Pythagoras with a purer reasoning of the mind, it is clearly established that no one reaches the height of perfection in the disciplines of philosophy that is, attains it unless the nobility of such wisdom is tracked that is, investigated through the Quadrivium." The Quadrivium refers to the four mathematical arts: arithmetic, geometry, music, and astronomy. Furthermore, since there are three essential modes of philosophy, as Aristotle says in the third book of the Metaphysics, namely mathematics, natural philosophy, and the divine referring to metaphysics or theology, mathematics is of great value for the understanding of the other two branches of science. This is taught by Ptolemy in the first chapter of the Almagest. And since the divine science is twofold, as is clear in the first book of the Metaphysics, it includes "first philosophy," which declares that God exists and investigates His noble properties, and "moral or civil science," which establishes divine worship and explains many things worthy of God according to the capacity of human reason. Ptolemy asserts clearly that mathematics is of great value to both of these. For this reason, Boethius teaches at the end of the Arithmetic that mathematical considerations are found in civil affairs. His opinion will be explained below in its proper place. Moreover, Aristotle himself and his commentators explain in many ways in the Civil Science The Politics or Ethics what Boethius teaches. The accidental parts of philosophy are logic and grammar, as I showed in the Metaphysics. That mathematics is of great value to these is clear from what Al-Farabi teaches in the Book of the Sciences and Aristotle in his book On Poetic Arguments. All authors of medicine who treat the subject completely also teach this | f. 74 a 1. clearly. But when we come to the second method of declaring the praises of mathematics, these things will shine forth more clearly.

Chapter four, in which authorities relating more closely to divine matters are introduced. First, he gives the reason for this, and second, he presents them.

JUST as in the case of Boethius, a Christian philosopher and great theologian, as is clear in his books On the Trinity and On the Two Bacon likely refers here to On the Two Natures and One Person of Christ.