Previously Unpublished Works, Fascicle 16

Many necessary things are omitted, and intolerable difficulty is introduced. Common principles are postponed, and they are mixed with specific topics against the natural order. Even the order of specific topics is perverted, and things that are naturally distinct are shamefully confused with one another. Because of these seven disadvantages original: "dispendia." These are the specific wastes of time or intellectual losses caused by poor methodology. of this science, students despise mathematics. They can hardly learn it in a whole lifetime, even though it could be known in a short time if it were taught correctly.

The third part of the second chapter of the first distinction.

ALTHOUGH we should be grateful to the authors who gave us the roots of science, nothing is perfect in human inventions. They have not yet drawn out all the tall branches, nor have they brought forth the full sweetness of the flowers or the fullness of the fruit. There is no doubt that they concealed many things because of the unworthy, and they neglected many things to challenge diligent students. Therefore, those who come after and enter upon the foundations of the ancients can rectify the study otherwise the building of wisdom in many ways. This applies both to the substance of the sciences and the method of knowing. I will explain this more certainly in the present volume for every well-disposed person who is not corrupted by the four causes mentioned before.

Chapter 3, in which it is suggested that the primary utility and praise of mathematics should be sought, and how these were shown through a universal treatise in metaphysics. Secondly, he moves to particular ways of proving this in this volume, choosing one of those ways through elegant authorities: but in this chapter, authorities of those who purely philosophize are introduced.

folio 73 b, column 1

HAVING REMOVED the four aforementioned causes of error completely from our current habits, I wish to find something concerning the utility and praise of mathematics In the medieval period, mathematics included the four sciences of the Quadrivium: arithmetic, geometry, music, and astronomy. so that we may be more pleasantly encouraged to study it. Every thing is neglected, no matter how excellent it is, as long as its praise and utility are unknown. Since mathematicians do not work toward this goal, or do so only slightly at the beginning of their books or elsewhere, few people are encouraged to study mathematics. I have shown, however, in...