| Philosophy | - | Practical | - | Ethics. | ||
| Economics. | ||||||
| Politics. | ||||||
| Theoretical | - | Theology. | ||||
| Mathematics. | - | Arithmetic | - | = Quadrivium. | ||
| Music | ||||||
| Geometry | ||||||
| Astronomy | ||||||
| Physics. | ||||||
The author expressly says that "Mathematica quadrivium continet"; but he plainly does not include the Trivium under Philosophy. This, however, was done the following century. In the Itinerarium Mentis in Deum of St. Bonaventura (1221-74) we find the following arrangements:—
| Philosophy | - | Natural | - | Metaphysics--essence: leads to First Principle = Father. | ||
| Mathematics--numbers, figures: leads to Image = Son. | ||||||
| Physics--natures, powers, diffusions: leads to Gift of Holy Spirit. | ||||||
| Rational | - | Grammar--power of expression = Father. | ||||
| Logic--perspicuity in argument = Son. | ||||||
| Rhetoric--skill in persuading = Holy Spirit. | ||||||
| Moral | - | Monastics--innascibility of Father. | ||||
| Œconomics--familiarity of Son. | ||||||
| Politics--liberality of Holy Spirit. | ||||||
Here we have the Trivium, under the division "Rational," while the Quadrivium must still be included under "Mathematics." In both cases we get nine sciences or disciplines, and the number was apparently chosen, because it is the square of three, the number of the Holy Trinity. In the latter case this was certainly true. Speaking of the primary divisions of Philosophy, the Saint says: "The first treats of the cause of being, and therefore leads to the Power of the Father; the second of the ground of understanding, and therefore leads to the Wisdom of the Word; the third of the order of living, and therefore leads to the goodness of the Holy Spirit."
Dante, in his Convivio (II, 14, 15), gives the following scheme, based upon the "ten heavens," nine of which are moved by angels or intelligences, while the last rests in God.
| Liberal Arts | - | Trivium | - | Grammar | Moon | Angels. | ||
| Dialectic | Mercury | Archangels. | ||||||
| Rhetoric | Venus | Thrones. | ||||||
| Quadrivium | - | Arithmetic | Sun | Dominions. | ||||
| Music | Mars | Virtues. | ||||||
| Geometry | Jupiter | Principalities. | ||||||
| Astrology | Saturn | Powers. | ||||||
| Philosophy | - | Physics and Metaphysics | Starry Heaven | Cherubim. | |
| Moral Science | Crystalline Heaven | Seraphim.[15] | |||
| Theology | Empyrean | God. |
In Dante are summed up the ancient and mediæval systems of education.