The Arithmetica of Diophantus : a complete translation and commentary / Jean Christianidis, Jeffrey Oaks.

Format:

Book

Author/Creator:

Christianidis, Jean, author.

Oaks, Jeffrey, author.

Series:

Scientific Writings from the Ancient and Medieval World

Language:

English

Subjects (All):

Diophantus, of Alexandria.

Diophantus.

Diophantus, of Alexandria--Influence.

Mathematics, Greek--Early works to 1800.

Mathematics, Greek.

Physical Description:

1 online resource (891 pages)

Edition:

First edition.

Place of Publication:

Abingdon, Oxon, England ; New York, New York : Routledge, [2023]

Summary:

"This volume offers an English translation of all ten extant books of Diophantus of Alexandria's Arithmetica, along with a comprehensive conceptual, historical, and mathematical commentary. Before his work became the inspiration for the emerging field of number theory in the seventeenth century, Diophantus (ca. 3rd c. CE) was known primarily as an algebraist. This volume explains how his method of solving arithmetical problems agrees both conceptually and procedurally with the premodern algebra later practiced in Arabic, Latin, and European vernaculars, and how this algebra differs radically from the modern algebra initiated by François Viète and René Descartes. It also discusses other surviving traces of ancient Greek algebra and follows the influence of the Arithmetica in medieval Islam, Byzantium, and the European Renaissance down to the 1621 publication of Claude-Gaspard Bachet's edition. After the English translation the book provides problem-by-problem commentary explaining the solutions in a manner compatible with Diophantus's mode of thought. The Arithmetica of Diophantus provides an invaluable resource for historians of mathematics, science, and technology, as well as those studying ancient Greek, medieval Islamic and Byzantine, and Renaissance history. In addition, the volume is also suitable for mathematicians and mathematics educators"-- Provided by publisher.

Contents:

Cover

Half Title

Series

Title

Copyright

Contents

List of figures

List of tables

Preface

Part I Introduction

1 Diophantus and his work

1.1 What we know about Diophantus

1.2 The works of Diophantus

1.3 The text of the Arithmetica and its history

1.4 Editions and translations of Diophantus

2 Numbers, problem solving, and algebra

2.1 Introduction

2.2 The arithmetical foundation of algebra

2.2.1 Multiplicity, species, and aggregations

2.2.2 Operations

2.2.3 Methods of calculation

2.3 Numerical problem-solving

2.4 Premodern algebra: vocabulary and structure

2.4.1 The names of the powers

2.4.2 The structure of algebraic solutions

2.4.3 The shift to algebraic language

2.5 Monomials, polynomials, and equations in premodern algebra

2.5.1 Monomials in premodern algebra

2.5.2 Polynomials in premodern algebra

2.5.3 Equations in premodern algebra

2.6 The stages of an algebraic solution

2.6.1 Stage 1: setting up the equation

2.6.2 Divisions and roots in equations

2.6.3 Stage 2: al-jabr and al-muqābala

2.6.4 Stage 3: solving the simplified equation

2.7 Enunciations vs. equations and the assignments of names

2.7.1 Indeterminate problems or indeterminate equations?

2.7.2 Techniques of naming unknowns

2.8 Notation

3 History

3.1 Evidence for the practice of algebra before Diophantus

3.1.1 Δύναμις, κύβος, and related terms in Greek and Arabic geometry and arithmetic

3.1.2 A survey of ways of naming powers in Arabic, Italian, etc.

3.1.3 The testimonies about Hipparchus

3.1.4 The Cairo papyrus

3.1.5 The Michigan papyrus

3.1.6 The lists of powers in Refutation of All Heresies

3.2 Readers and writers on Diophantus in late antiquity

3.2.1 Theon and Hypatia

3.2.2 Some Neoplatonic scholia.

3.2.3 The scholia to the arithmetical epigrams of the Palatine Anthology

3.2.4 A reference by John Philoponus

3.2.5 Early Byzantine hagiography

3.3 Diophantus in medieval Arabic

3.3.1 Arabic algebra before Qusṭā's translation: al-Khwārazmī and Abū Kāmil

3.3.2 Qusṭā ibn Lūqā, translator of the Arithmetica

3.3.3 Al-Khāzin

3.3.4 Al-Nīsābūrī and ʿAlī al-Sulamī

3.3.5 Abū l-Wafāʾ

3.3.6 Al-Karajī

3.3.7 Al-Zanjānī

3.3.8 Ibn al-Haytham

3.3.9 Al-Samawʾal

3.3.10 Ibn Fallūs

3.3.11 Ibn al-Qift˙ī and al-Nūayīrī

3.4 Diophantus in Byzantium

3.4.1 Michael Psellus

3.4.2 From Psellus to the Palaeologan Renaissance

3.4.3 Pachymeres, Planudes, and the Palaeologan Renaissance

3.4.4 Later Byzantine testimonies

3.5 Diophantus in the Renaissance

3.5.1 Bessarion and Regiomontanus

3.5.2 Diophantus among sixteenth-century mathematicians and lexicographers

3.5.3 Bombelli's L'Algebra

3.5.4 Xylander's 1575 Latin translation

3.5.5 Gosselin, Stevin, and Clavius

3.5.6 François Viète and the beginning of modern algebra

3.5.7 Diophantus in the twilight of premodern algebra

4 Structure and language of the Arithmetica

4.1 The structure of Diophantine problems

4.1.1 Proclus on Euclid

4.1.2 Analysis (ἀνάλυσις) and synthesis (σύνθεσις)

4.1.3 Determinations

4.1.4 Algebra

4.1.5 The parts of a Diophantine problem

4.2 The language of Diophantine problems

4.2.1 The names of the unknowns and their notation

4.2.2 Assigning values to given numbers

4.2.3 Assigning algebraic names to sought-after numbers

4.2.4 The language of the operations

4.2.5 The statement of the equation

4.2.6 Simplifying the equation

4.2.7 The language of fractions

4.2.8 Other technical terms in the Greek algebra of Diophantus

5 The didactic aspect of the Arithmetica

Part II Translation.

Book I

Book II

Book III

Book IV (Arabic)

Book V (Arabic)

Book VI (Arabic)

Book VII (Arabic)

Book IVG

Book VG

Book VIG

Part III Commentary

Book I

Part IV Appendices

Appendix 1: Reconstitution of the text of four missing problems from the fifth Greek book by Evangelos S. Stamatis

Appendix 2: Techniques of solving indeterminate problems by algebra

Appendix 3: Lexicon and conventions

Appendix 4: Conspectus of problems

Bibliography

Index.

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-315-17147-3

1-351-69497-9

9781315171470

OCLC:

1346854008