The quadrivium comprises not only mathematics but many branches of science. The theory of number includes not merely arithmetic but also algebra, calculus, the theory of equations, and other branches of higher mathematics. The applications of the theory of number include not only music (here understood as musical principles, like those of harmony, which constitute t he liberal art of music and must be distinguished from applied instrumental music, which is a fine art) but also physics, much of chemistry, and other forms of scientific measurement of discrete quantities. The theory of space includes analytic geometry and trigonometry. Applications of the theory of space include principles of architecture, geography, surveying, and engineering.
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