De quadrivio.
What Mathematics Studies
Mathematics concerns abstract quantity, which divides into continuous magnitude and discrete multitude.
Since, as was said above, it properly belongs to mathematics to attend to abstract quantity, we must look for its species within the divisions of quantity. Abstract quantity is nothing other than visible form impressed on the mind according to linear dimension, which consists in imagination, and it has two parts: one continuous, such as a tree or a stone, which is called magnitude; the other discrete, such as a flock or a population, which is called multitude.
Number and Magnitude
Multitude is either absolute or relative, and magnitude is either movable or immovable.
Again, some kinds of multitude exist in themselves, such as three, four, or any other number; others exist in relation to something else, such as double, half, sesquialter, sesquitertius, or any such ratio. Of magnitude, some kinds are movable, such as the sphere of the world; others are immovable, such as the earth.
The Four Disciplines
Arithmetic, music, geometry, and astronomy each govern one branch of quantity, completing the division of mathematics.
Arithmetic, then, studies the kind of multitude that exists in itself, while music studies the kind that exists in relation to something else. Geometry offers knowledge of immovable magnitude. But knowledge of movable magnitude is claimed by the expertise of astronomical discipline. Mathematics, therefore, is divided into arithmetic, music, geometry, and astronomy.
Read the original Latin
Cum igitur, ut supradictum est, ad mathematicam proprie pertineat abstractam attendere quantitatem, in partibus quantitatis species eius quaerere oportet. quantitas abstracta nihil est aliud nisi forma visibilis secundum lineamentarem dimensionem animo impressa, quae in imaginatione consistit, cuius geminae sunt partes: una continua, ut arbor, lapis, quae magnitudo dicitur, alia discreta, ut grex, populus, quae multitudo appellatur. rursus multitudinis alia sunt per se, ut tres, quattuor, vel quilibet alter numerus, alia ad aliquid ut duplum, dimidium, sesquialterum, sesquitertium, vel quodlibet tale. magnitudinis vero alia sunt mobilia, ut sphaera mundi, alia immobilia, ut terra. multitudinem ergo quae per se est arithmetica speculatur, illam autem quae ad aliquid est, musica. immobilis magnitudinis geometria pollicetur notitiam. mobilis vero scientiam astronomicae disciplinae peritia vindicat. mathematica igitur dividitur in arithmeticam, musicam, geometriam, astronomiam.
Didascalicon de Studio Legendi (On the Study of Reading) companion
Hugh said begin with small daily portions. Start tomorrow.
Chosen Portion serves one short, ordered devotional reading each day — the medieval lectio pattern, free on iOS.
Hugh taught that formation comes from ordered, incremental daily reading, and Chosen Portion is that ordered daily portion delivered to your phone.
- A curated daily portion in 2-3 minutes, no decision fatigue about what to read
- Progress through complete historic works in order, the way Hugh prescribed
- Free app plus a weekly email unpacking one reading in depth