Martianus Capella (fl. 450), De nuptijs philologie [et] Mercurij (Vicenza, 1499), 1st printed ed. “On the Marriage of Philology and Mercury.”

Capella described the seven liberal arts. The first three are **grammar**, logic or **dialectic**, and **rhetoric.** Then come the mathematical sciences, **geometry** and **arithmetic.** Geometrical circles in motion make **astronomy**. Numbers in motion make **music.**

Capella also argued that Venus and Mercury revolve around the Sun. Capella’s cosmic system was consistent with Galileo’s later discovery of the phases of Venus.

**Mathematics in the Liberal Arts Tradition**

The strange title, *The* *Marriage of Philology and Mercury,* refers to a wedding of the swiftest god and the most learned goddess. Its meaning is the joining of speech and insight, as if our thoughts and language were as agile as a spherule of mercury rolling around on a sheet of glass.

Quadrivium |
Numbers |
Magnitudes |

Entities |
Arithmetic | Geometry |

Entities in motion |
Music | Astronomy |

Capella (5th century C.E.) described the seven *liberal* arts, *i.e.*, the education appropriate to a *free citizen* rather than a slave.

According to the opening page, the first three liberal arts are **grammar**, how to write well; logic or **dialectic**, how to think well; and **rhetoric**, how to speak well. These three became known as the *trivium*.

Next come the last four liberal arts, the *quadrivium*. These are all mathematical sciences, beginning with **geometry**, the study of magnitudes, like lines and circles; and **arithmetic**, the study of numbers. If magnitudes are put in motion, we then have **astronomy**, a branch of geometry. If numbers are put in motion, we then have **music**, a branch of arithmetic. So music and astronomy, for the liberal arts tradition as for the ancient Pythagoreans, are sister sciences.