Quadrivium
The medieval curriculum of arithmetic, geometry, music, and astronomy, taught as the four mathematical arts following the trivium.
Arithmetic: The study of numbers, their properties, and operations. It supplied the quadrivium’s study of number considered in itself.
Plato: An ancient Greek philosopher whose writings shaped Western metaphysics, epistemology, and political thought. His dialogues linked mathematical study with knowledge of an intelligible order.
Abacus: A counting device that uses movable pieces or beads to represent numbers and perform calculations. Abacus practice made the quadrivium’s arithmetic useful for routine computation.
Liberal arts: A tradition of education in disciplines intended to cultivate intellectual capacities and civic judgment. The quadrivium became the mathematical half of this broader educational tradition.
Geometry: The study of shapes, space, and their properties. It treated number through magnitude and spatial relations.
Republic (Plato): A dialogue by Plato exploring justice, political life, education, and the philosopher’s role. Its education plan connects arithmetic, geometry, harmonics, and astronomy with philosophical training.
Euclid's Elements: A mathematical treatise presenting geometry and number theory through definitions, propositions, and proofs. Its geometry became a major source for teaching the quadrivium’s spatial mathematics.
Medieval university: A European institution of higher learning that developed from the twelfth century onward. University arts faculties taught quadrivial subjects as part of foundational study.
Music theory: The study of musical structures, including rhythm, pitch, and harmony. Medieval music studied numerical relations embodied in sound.
Pythagoreanism: An ancient Greek philosophical and religious tradition associated with Pythagoras and mathematical explanations of nature. Its account of numerical harmony helped shape the quadrivium’s mathematical outlook.