Mathematics and Philosophy at the Turn of the First Millennium : Abbo of Fleury on Calculus / Clelia V. Crialesi.

Format:

Book

Author/Creator:

Crialesi, Clelia V., 1991- author.

Contributor:

Taylor & Francis eBooks

Series:

Global Perspectives on the History of Natural Philosophy.

Global Perspectives on the History of Natural Philosophy

Language:

English

Subjects (All):

Mathematics--History.

Mathematics.

Physical Description:

1 online resource : illustrations.

Place of Publication:

London : Routledge, 2025.

Contents:

IntroductionChapter 1Abbo and His Time: European History and Mathematics 1. Politics and (Religious) Culture 2. Liberal Arts 3. Mathematics 3.1 Speculative Arithmetic 3.2 Practical ArithmeticChapter 2Victorious' 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 CommentatorChapter 3A 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 pondereChapter 4Henology 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 CalculusChapter 5The 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 voxChapter 6Arithmetic 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 RulesChapter 7Physics 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 ThingsConclusions

Notes:

Electronic reproduction. London Available via World Wide Web.

Online resource; title from PDF title page (Taylor & Francis, viewed March 17, 2025).

ISBN:

9781032643472

1032643471

9781040331859

1040331858

9781040331842

104033184X

Publisher Number:

90101641404

Access Restriction:

Restricted for use by site license.