Overview

At the turn of the first millennium, scientific and philosophical knowledge was far from dormant. Arithmetic, with its diverse calculation techniques and number theory, served as a bridge to philosophy, theology, and the study of the physical world. Even something as simple as a series of multiplication tables could unlock a profound knowledge of both the divine realm and natural phenomena. Such is the case with Abbo of Fleury’s Commentary on the Calculus. Mathematics and Philosophy at the Turn of the First Millennium sheds light on Abbo’s original philosophical system anchored in two central doctrines, which serve as a compass to navigate it: the theory of unity (henology) and the theory of composition. Yet, the Commentary on the Calculus covers much more. The present study, thus, explores an eclectic range of topics – from water clocks to barleycorns, constellations to human voice, synodic month to the human lifespan, and numbers to God. Abbo’s work is an ambitious attempt to tie together the study of both the visible and invisible realms, what can be measured and what cannot, what can be quantified and what exceeds quantification. Scholars and students of the history of philosophy and mathematics will be introduced to a pivotal figure from an often overlooked era. They will be provided with fresh insights into the spread of Neopythagorean doctrines in the early Middle Ages, as they learn how these ideas were transmitted through arithmetic texts and harmonised with theology and natural philosophy. They will also get to know the medieval fraction system and calculus practices.

Full Product Details

Author:   Clelia V. Crialesi
Publisher:   Taylor & Francis Ltd
Imprint:   Routledge
Weight:   0.570kg
ISBN:  

9781032643458

ISBN 10:   1032643455
Pages:   210
Publication Date:   31 March 2025
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Introduction Chapter 1 Abbo and His Time: European History 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 Time 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 Wisd. 11:21 2. Claudianus Mamertus’ De statu animae 3. Arithmetical Readings of Wisd. 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 Gen. 1:2 4. Division of Non-Material 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

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Author Information

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.

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