The Medieval Quadrivium

As Proclus wrote:  The Pythagoreans considered all mathematical science to be divided into four parts: one half they marked off as concerned with quantity, the other half with magnitude; and each of these they posited as twofold. A quantity can be considered in regard to its character by itself or in its relation to another quantity, magnitudes as either stationary or in motion. Arithmetic, then, studies quantities as such, music the relations between quantities, geometry magnitude at rest, spherics [astronomy] magnitude inherently moving.

Thus arithmetic is number in itself, music is number in time, geometry is number in space, and cosmology is number in space and time.

References:

http://en.wikipedia.org/wiki/Quadrivium

http://quadriformisratio.wordpress.com/2013/07/01/the-curriculum-in-ancient-times/

[*6.66, *7.40]

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