Didascalicon, Book VI: how Scripture is to be read
Chapter XIV. Definition of the three remedies concerning philosophy against as many evils, and on another division of philosophy
There are three: wisdom, virtue, necessity. Wisdom is the comprehension of things as they are. Virtue is a habit of the mind, in the manner of nature, consonant with reason. Necessity is that without which we could not live, but with which we should live more happily. These three remedies are against the three evils to which human life is subject. Wisdom against ignorance, virtue against vice, necessity against infirmity; for the rooting out of these three evils these three remedies were sought; and for finding these three remedies every art and every discipline was invented. For wisdom the theoretical was invented, for virtue the practical was invented, for necessity the mechanical was invented. These three were first in use, but afterwards, on account of eloquence, logic was invented. Which, though last in invention, ought nevertheless to be first in doctrine. There are, then, four principal sciences from which all others descend: theoretical, practical, mechanical, logical.
The theoretical is divided into theology, physics, mathematics. Theology treats of the invisible causes of visible things; mathematics of the invisible forms of visible things. And this mathematics is divided into four sciences. The first is arithmetic, which treats of number, that is of discrete quantity by itself. The second is music, which treats of proportion, that is of discrete quantity in relation to something. The third is geometry, which treats of space, that is of continuous immovable quantity. The fourth is astronomy, which treats of motion, that is of continuous movable quantity. The element of arithmetic is unity. The element of music is the unison. The element of geometry is the point. The element of astronomy is the instant. The practical is divided into solitary, private, public. The solitary teaches how each one may order his own life with honorable morals and adorn it with virtues. The private teaches how those of the household are to be ruled, and those who are related by the affection of the flesh. The public teaches how the whole people and nation ought to be governed by its rulers. The solitary pertains to individuals, the private to fathers of families, the public to rulers of cities. The mechanical treats of human works, and this is divided into seven. The first is wool-working, the second armament, the third navigation, the fourth agriculture, the fifth hunting, the sixth medicine, the seventh the theatrical. Logic is divided into grammar and the art of discoursing. The method of discoursing is divided into the probable, the necessary and the sophistical. The probable is divided into dialectic and rhetoric. The necessary pertains to philosophers, the sophistical to sophists. In these four parts of philosophy such an order ought to be kept in teaching that logic be placed first, ethics second, the theoretical third, the mechanical fourth. For first eloquence must be acquired; then, as Socrates says in the Ethics, the eye of the heart must be cleansed by the study of virtue, that afterwards in the theoretical it may be keen-sighted for the investigation of truth. Last follows the mechanical, which by itself is in every way ineffective unless it is supported by the reason of the preceding.