The Liberal Studies after St. Augustine did not include Philosophy, which rested upon the Seven Arts, as upon "seven pillars," and was usually divided into (1) Physical, (2) Logical, (3) Ethical.[14] After a time Philosophy came to be an all-embracing term. In a commentary on the _Timæus_ of Plato, assigned by Cousin to the twelfth century, we find the following scheme:--
{ Ethics. { Practical { Economics. { { Politics. { { { Theology. PHILOSOPHY { { { Arithmetic } { { Mathematics. { Music } { Theoretical { { Geometry } = Quadrivium. { { { 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:--
{ { Metaphysics--essence: leads to First { { Principle = Father. { Natural { Mathematics--numbers, figures: leads { { to Image = Son. { { Physics--natures, powers, diffusions: { { leads to Gift of Holy Spirit. { PHILOSOPHY { { Grammar--power of expression = Father. { Rational { Logic--perspicuity in argument = Son. { { Rhetoric--skill in persuading = Holy { { Spirit. { { { Monastics--innascibility of Father. { Moral { 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.
{ { Grammar Moon Angels. { Trivium { Dialectic Mercury Archangels. { { Rhetoric Venus Thrones. LIBERAL ARTS { { { Arithmetic Sun Dominions. { Quadrivium { Music Mars Virtues. { { Geometry Jupiter Principalities. { { Astrology Saturn Powers.