Previously Unpublished Works, Fascicle 16

In the Metaphysics, I showed through useful methods that no science can be obtained without this science mathematics. No one can perceive their own ignorance in other sciences unless they have been very clearly instructed in this one otherwise: here. 5 The things of this world cannot be known, nor can a person possess the benefits of the body and of material things, unless they are steeped in the great wonders of this science. The goods of the body, of science, and of fortune are of great value to the goods of the soul if they are managed correctly. Since the wisdom of mathematics is effective for these goods, it follows that the science 10 of mathematics is very necessary for obtaining the goods of the soul. Since human things serve divine things, I suggested in the Metaphysics that mathematics is necessary for divine wisdom beyond what anyone can sufficiently explain.

Second part of the third chapter.

15 I will therefore leave behind the methods of metaphysics so that those things necessary for the useful praises of mathematics may be investigated. In this book, I wish to touch upon some more specific details and fulfill my purpose through the specific principles of this science. At the start, we must consider a threefold path. The first is through authorities. 20 The second is through induction to be performed within the sciences. The third is through the division of mathematics into its parts. The noble properties of these parts show the praises and utilities of this science to be wonderful and pleasing. There is also a fourth path. This involves the application of mathematics to knowing the things of this world 25 and certain sciences, both divine and human. It shows how all sciences require mathematical demonstrations, works, and instruments. They cannot be known otherwise: will not be able to be known or taught in any other way. However, this fourth mode cannot be fully expressed before the end of the study of mathematics. It will be taught 30 clearly and openly when we descend to the other sciences.

Proceeding then with the first path, I begin with Boethius An influential 6th century philosopher whose works on the Quadrivium served as standard medieval textbooks.. In the prologue to the second book of his Arithmetic, he says of the four parts of mathematics These four parts are Arithmetic, Geometry, Music, and Astronomy, which together form the Quadrivium.: "If an inquirer lacks these four parts, truth can hardly be found." f. 73 b 2. And again: "Without this contemplation of truth, no one should be considered truly wise." Further, 35 he says: "Whoever scorns these paths of wisdom, I declare original: "demonstro," though Boethius uses "denuntio" meaning "I announce" to him that he cannot reason original: "probandum," though Boethius uses "philosophandum" meaning "to philosophize" correctly." And again he says: "It is certain..."