Quadrivium Project

The Quadrivium Project

Introduction

In the sixth century A.D., the Roman Senator and philosopher Marcus Boethius wrote a series of handbooks designed to be an introduction to the seven liberal arts, the arts which a libera (free man) might pursue without loss of status. The seven were viewed as seven roads, or via, to learning, and were divided into two groups. The trivium (three roads) were grammar, rhetoric, and logic. As these three roads were considered easier, these were the trivial arts. The four roads to learning were the quadrivium. These were arithmetic, geometry, music, and astronomy. One of my longterm projects is to do as Boethius did: to construct a series of handbooks introducing the seven liberal arts that would have been studied by a medieval university student.

Except for geometry and logic, none of these were used in quite the same way they are used today. A brief overview of the seven liberal arts:

• • Grammar was specifically Latin grammar.

  • Rhetoric, like grammar, was specifically the ability to write in Latin.

  • Logic consisted primarily of what was found in Aristotle.

  • Arithmetic was the study of number and its properties; it is more closely related to number theory than to computational mathematics.

  • Geometry was Euclidean geometry, though in some circles, it also included geography (see Martianus Capella's The Marriage of Philology and Mercury, where the seven liberal arts are personified and their wedding gift to the couple is a didactic poem on their particular art: geometry gives some familiar geometrical ideas, but also categorizes the geography of the Mediterranean world). If arithmetic was the study of number, geometry was the study of magnitude.

  • Music was actually music theory; it was considered "arithmetic in motion" (as the most characteristic component was the discussion of euphonic ratios).

  • Astronomy was Ptolemaic astronomy; it was considered "geometry in motion".

Very roughly speaking, we might consider the trivium as the subjects you would get from a good, high school education, while the quadrivium were the subjects that were part of a typical four year degree. After that, you would go to a professional school in which you would study theology, medicine or law.

It is reasonable to ask what the study of mathematics has to do with theology, medicine, or law. It is easiest to answer this question with respect to medicine and (to some degree) with law, and there is a simple answer: astrology. There was something called judicial astrology (which I don't yet have much information on).

For physicians, they believed that the health of the patient was influenced by the positions of the planets: hence our word influenza (and ultimately, flu). A patient might, depending on the positions of the planets, have a mercurial or jovial or saturnine temperament, or be subject to fits of lunacy.

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