Thesis ID: CBB001560724

Quadrivial Pursuits: Case Studies in the Conceptual Foundation of the Mathematical Arts in the Late Middle Ages (2012)


Newsome, Daniel (Author)

New York, City University of
Dauben, Joseph

Publication Date: 2012
Edition Details: Advisor: Dauben, Joseph
Physical Details: 394 pp.
Language: English

The quadrivium, the four mathematical disciplines of the Middle Ages, described the structure of the medieval cosmos, both macrocosm and microcosm. Arithmetic and music were the mathematics of Platonic counting numbers. Geometry and astronomy were the mathematics of continuous magnitude. All four disciplines worked in concert to describe a cohesive and harmonious universe, which in the late Middle Ages incorporated everything from Aristotelian elemental theory to astrology. This dissertation describes the early philosophical formulation of these disciplines from Pythagorean and Platonic roots and the foundation of the quadrivium itself in the mathematical writings of Boethius in the early sixth century. This dissertation then examines the mathematical philosophy of three late medieval authors who were proficient in the quadrivial arts: Nicole Oresme (ca. 1320-1382), Prosdocimo de' Beldomandi (ca. 1375-1428), and Leon Battista Alberti (1404-1472). All three demonstrate that the Boethian quadrivial philosophy continued to be relevant in the late 14 th and early 15th centuries, but all three studies point to a significant fault line in the metaphysical structure of the quadrivium itself--the distinction between discrete and continuous, the quadrivial distinction between arithmetic and geometry.


Description On the mathematical philosophy of Nicole Oresme, Prosdocimo de' Beldomandi, and Leon Battista Alberti. Cited in ProQuest Diss. & Thes. (2012). ProQuest Doc. ID 961699542.

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Authors & Contributors
Ulivi, Elisabetta
Biard, Joël
Busard, H. L. L.
Bosemberg, Zoe
Sarnowsky, Jürgen
Furlan, Francesco
Bollettino di Storia delle Scienze Matematiche
Revue d'Histoire des Sciences
Journal Electronique d'Histoire des Probabilités et de la Statistique
Historia Mathematica
Mitteilungen und Forschungsbeiträge der Cusanus-Gesellschaft (Inhaltsverzeichnisse)
Asclepio: Archivo Iberoamericano de Historia de la Medicina
Franz Steiner Verlag
Presses Universitaires du Septentrion
Cornell University Press
Sage Publications
Oresme, Nicole
Alberti, Leon Battista
Buridan, Jean
Albert of Saxony
Bradwardine, Thomas
Time Periods
14th century
15th century
13th century
16th century
Florence (Italy)
Great Britain
Pisa (Italy)
Oxford University
Kerala School of Astronomy and Mathematics (India)
Université de Paris

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