1st Edition
Mathematics and Philosophy at the Turn of the First Millennium Abbo of Fleury on Calculus
Introduction
Chapter 1
Abbo and His Time: European Culture and Mathematics
1. Politics and Religious Culture
2. Liberal Arts
3. Mathematics
3.1 Speculative Arithmetic
3.2 Practical Arithmetic
Chapter 2
Victorious’ Calculus and Abbo’s Explanatio
1. Contents of the Calculus
1.1 Praefatio de ratione calculi
1.2 Multiplication Tables
1.3 Supplementary Tables and Texts
2. Victorious, scripulorum calculator: the Calculus and the Reckoning of Easter
3. Two Hypothesis on the Arrival of the Calculus at Fleury
3.1 Hypothesis A: Lupus of Ferrière
3.2 Hypothesis B: Columbanus and the Abbey of Bobbio
4. Abbo’s Explanatio: Manuscripts and Critical Editions
5. Contents of the Explanatio
5.1 The Prologue (Section I)
5.2 The Theological Premise (Section II)
5.3 The Commentary on on Victorius’s Praefatio (Section III)
5.4 The Commentary on Victoriuous’s Multiplication Tables (Section IV)
5.5 On Qualitative Physics (Section V)
6. The Pedagogical Aim and the Role of the Commentator
Chapter 3
A Theological Premise: Number, Measure, and Weight
1. Augustine and Wisdom 11:21
2. Claudianus Mamertus’ De statu animae
3. Arithmetical Readings of Wisdom 11: 21: Hrabanus Maurus and John Scotus Eriugena
4. Abbo’s Tractatus de numero, mensura et pondere
Chapter 4
Henology
1. Neopythagorean Elements: Unity and the Flow of Numbers
2. The Highest Good, individuum, and Unity
3. The Lambda Diagram: a Quadrivial Henology
4. Unity as Ontological Principle
5. Unity as the Object of Arithmetic and Calculus
Chapter 5
The Composition of Reality
1. Natural Compounds
1.1 The Arithmology of Natural Compounds
1.2 Natural Compounds and Change: the Phases of the Moon
2. Artificial Compounds
2.1 The Five Kinds of Inequality Ratios
2.2 Two trinae regulae for Arithmetical Ratios
3. Ontological Composition: the Case of the Earth in Genesis 1:2
4. Division of Abstract Entities: the Case of the Units of Time
5. Divisibility and Corporality: the Case of the vox
Chapter 6
Arithmetic and Calculus
1. Fractions: Ounces and minutiae
2. Representing Integer Numbers
3. Calculus by Fingers or the loquela digitorum
4. Calculus by Tables
5. Multiplication Rules
Chapter 7
Physics Before the Physics
1. The Early Medieval Concern for Natural Phaenomena
2. Scientific Literature in the Early Medieval Fleury Area
3. Qualitative Physics: from Astronomy to Physiology
4. The Natural Power of Things
Conclusions
Biography
Clelia V. Crialesi is a Marie Skłodowska-Curie Fellow at SPHERE-CNRS (France). Formerly, she was an FWO Research Fellow at KU Leuven (Belgium) and a Mellon Fellow at PIMS (Canada). Her research focuses on premodern mathematical thought, with publications ranging from Boethian number theory to Euclidean geometry in the late medieval continuum debate.
