Fundamentals of Arithmetic; Fundamentals of Music

XXII. On the species of greater and lesser quantity.
XXIII. On the multiple and its species and their generations.
XXIIII. On the superparticular ratio and its species and their generations.
5 XXV. On a certain useful point regarding the knowledge of superparticulars.
XXVI. Description by which it is taught that multiplicity is more ancient than the other species of inequality.
10 XXVII. Reason and exposition of the arranged formula.
XXVIII. On the third species of inequality, which is called superpartient, and concerning its species and their generations.
XXVIIII. On the multiple superparticular.
XXX. On the examples of these to be found in the previous formula.
15 XXXI. On the multiple superpartient.
XXXII. Demonstration of how every inequality has proceeded from equality.

20

I. Among all men of ancient authority, who flourished under the guidance of Pythagoras with a purer reasoning of the mind, it is manifest that no one arrives at the peak of perfection in the disciplines of philosophy unless such nobility of prudence is tracked by a certain fourfold path quadrivium the four liberal arts: arithmetic, music, geometry, astronomy, which will not escape the skill of one who rightly looks upon it. For wisdom is the comprehension of the truth of those things which are, and which possess an immutable substance.