Quadrivium · IV
Geometry
An art in the old sense: it makes something. Its constructions are built in the imagination and judged by reason, and their conclusions admit no exceptions — for most minds, the first meeting with necessity.
I. What the Studium has
Construct, see, and justify.
Open full Euclid Book I module →ABC
Construction 1 of 4
A single straight line lying level across the board, its ends lettered A and B.
II. From the Seven Pillars
Imagination and the Art of Geometry: the six lectures on this art in the Institute’s certificate course, given on artsofliberty.org and heard there.
- 1The Quadrivium: Training Ground for the Imagination
- 2Geometry as Liberal Art and Science
- 3The Principles of Geometry
- 4A Tale of Two Triangles
- 5Ratio and Proportion
- 6Mathematics as Mediator
III. In the galleries
- Philosophy and the Seven Liberal ArtsFrom the Hortus Deliciarum of Herrad of Landsberg, Twelfth century
- The School of AthensRaphael, 1511
- The Seven Liberal ArtsFrancesco Pesellino, Painted in the artist’s lifetime, 1422–1457
- The Seven Liberal Arts Persecuted by Pluto and BacchusJost Amman, Sixteenth century
- The Seven Liberal ArtsVirgilius Solis, Sixteenth century
- Philosophy Presenting the Seven Liberal Arts to BoethiusCoëtivy Master (Henri de Vulcop), 1460–1470
IV. In the Library
- Euclid’s ElementsEuclid · Primary Source
- The equilateral triangleArts of Liberty Studium · Teaching Tool
V. In the Atlas
- QuadriviumNumber, form, harmony, heavens
- Euclid’s ElementsConstruction ordered by proof
- Ratio & ProportionA relation across the four arts
- PlatoDialogue and ascent
- BoethiusThe liberal arts transmitted
Continue the inquiry
Explore sources, people, and connected ideas.
Resource libraryOpen the geometry collection →Tradition AtlasTrace proof, ratio, and motion →Teacher StudioTurn this art into a lesson →