Mathematics (Mathematica)

The learned body of knowledge that contemplates abstract quantities is called mathematics (mathematica) in Latin. An abstract (abstractus) quantity is something that we investigate (tractare) by reasoning alone, separating it by means of the intellect from matter or from accidental qualities such as even and odd, and other things of this kind. There are four types of mathematics, namely, Arithmetic (arithmetica), Music (musica), Geometry (geometria), and Astronomy (astronomia). Arithmetic is the study of numeric quantity in and of itself. Music is the study that is occupied with the numbers that are found in sounds. Geometry is the study of size and shapes. Astronomy is the study that contemplates the course of the heavenly bodies and all the figures and positions of the stars. We will cover these studies, each in turn, a little more fully, so that their principles can be suitably shown.

i. Words belonging to the study of arithmetic (De vocabulo arithmeticae disciplinae) 1. Arithmetic (arithmetica) is the study of numbers, for the Greeks call numbers (numerus) ἀριϑμός. The writers of secular literature would have this discipline be the first among the mathematical disciplines, as this discipline relies on no other for its existence. 2. However, music, geometry, and astronomy, which follow arithmetic, require its support in order to exist and hold their place.

ii. Originators of mathematics (De auctoribus eius) People say that Pythagoras was the first among the Greeks to commit the study of numbers to writing.