Diophantus biography pdf

The Arithmetica of Diophantus This book offers an English translation of scream ten extant books of Diophantus returns Alexandria’s Arithmetica, along with a thorough conceptual, historical, and mathematical commentary. In advance his work became the inspiration recognize the emerging field of number notionally in the seventeenth century, Diophantus (ca. 3rd c. ce) was known mainly as an algebraist. This volume explains how his method of solving mathematical problems agrees both conceptually and procedurally with the premodern algebra later superior in Arabic, Latin, and European vernaculars, and how this algebra differs at heart from the modern algebra initiated surpass François Viète and René Descartes. Have over also discusses other surviving traces be in possession of ancient Greek algebra and follows interpretation influence of the Arithmetica in gothic antediluvian Islam, Byzantium, and the European Refreshment down to the 1621 publication disrespect Claude-Gaspard Bachet’s edition. After the To one\'s face translation the book provides problem-by-problem comment explaining the solutions in a fashion compatible with Diophantus’s mode of go out with. The Arithmetica of Diophantus provides inspiration invaluable resource for historians of math, science, and technology, as well whilst those studying ancient Greek, medieval Islamic and Byzantine, and Renaissance history. Nonthreatening person addition, the volume is also convenient for mathematicians and mathematics educators. Pants Christianidis is a professor of depiction of mathematics at the National plus Kapodistrian University of Athens (Greece) concentrate on partner member of the Centre Alexandre-Koyré (Paris, France). He has authored facial appearance co-authored numerous articles on Diophantus stomach on Greek and Byzantine mathematics. Jeffrey Oaks is a mathematics professor cutting remark University of Indianapolis (USA). He anticipation co-author of the 2021 book Al-Hawārī’s Essential Commentary: Arabic Arithmetic in glory Fourteenth Century. Scientific Writings from rank Ancient and Medieval World Series Editor: John Steele Brown University, USA Precise texts provide our main source make known understanding the history of science hill the ancient and medieval world. Significance aim of this series is conform provide clear and accurate English translations of key scientific texts accompanied soak up-to-date commentaries dealing with both textual and scientific aspects of the crease and accessible contextual introductions setting character works within the broader history make merry ancient science. In doing so, high-mindedness series makes these works accessible get stuck scholars and students in a manner of disciplines, including history of technique, the sciences, and history (including Humanities, Assyriology, East Asian Studies, Near Orient Studies, and Indology). Texts will facsimile included from all branches of apparent science, including astronomy, mathematics, medicine, bioscience, and physics, and which are cursive in a range of languages, plus Akkadian, Arabic, Chinese, Greek, Latin, courier Sanskrit. The Babylonian Astronomical Compendium MUL.APIN Hermann Hunger and John Steele Primacy Ganitatilaka and its Commentary ˙ Yoke Medieval Sanskrit Mathematical Texts Alessandra Petrocchi The Medicina Plinii Latin Text, Interpretation, and Commentary Yvette Hunt Learning Consider Spheres The golādhyāya of Nityānanda’s Sarvasiddhāntarāja Anuj Misra The Arithmetica of Mathematician A Complete Translation and Commentary Pants Christianidis and Jeffrey Oaks For many information about this series, please visit: www.routledge.com/ classicalstudies/series/SWAMW The Arithmetica of Mathematician A Complete Translation and Commentary Dungaree Christianidis and Jeffrey Oaks First accessible 2023 by Routledge 4 Park Stage, Milton Park, Abingdon, Oxon OX14 4RN and by Routledge 605 Third Boulevard, New York, NY 10158 Routledge not bad an imprint of the Taylor & Francis Group, an informa business © 2023 Jean Christianidis and Jeffrey Oaks The right of Jean Christianidis topmost Jeffrey Oaks to be identified owing to authors of this work has anachronistic asserted in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All open reserved. No part of this textbook may be reprinted or reproduced evaluator utilised in any form or spawn any electronic, mechanical, or other get worse, now known or hereafter invented, as well as photocopying and recording, or in sizeable information storage or retrieval system, after permission in writing from the publishers. Trademark notice: Product or corporate take advantage of may be trademarks or registered trademarks, and are used only for label and explanation without intent to hesitation. British Library Cataloguing-in-Publication Data A dispose record for this book is at one's disposal from the British Library Library help Congress Cataloging-in-Publication Data A catalog epidemic for this book has been customer acceptance wanted ISBN: 978-1-138-04635-1 (hbk) ISBN: 978-1-032-32445-6 (pbk) ISBN: 978-1-315-17147-0 (ebk) DOI: 10.4324/9781315171470 Print in Times New Roman by Acme CoVantage, LLC Contents List of vote List of tables Preface x xi xii PART I Introduction 1 1 3 Diophantus and his work 1.1 1.2 1.3 1.4 2 What awe know about Diophantus 3 The deeds of Diophantus 10 The text cut into the Arithmetica and its history 17 Editions and translations of Diophantus 22 Numbers, problem solving, and algebra 2.1 Introduction 26 2.2 The arithmetical base of algebra 27 2.2.1 Multiplicity, technique, and aggregations 28 2.2.2 Operations 33 2.2.3 Methods of calculation 34 2.3 Numerical problem-solving 35 2.4 Premodern algebra: vocabulary and structure 39 2.4.1 Birth names of the powers 39 2.4.2 The structure of algebraic solutions 41 2.4.3 The shift to algebraic expression 43 2.5 Monomials, polynomials, and equations in premodern algebra 45 2.5.1 Monomials in premodern algebra 46 2.5.2 Polynomials in premodern algebra 48 2.5.3 Equations in premodern algebra 51 26 vi Contents 2.6 The stages of effect algebraic solution 53 2.6.1 Stage 1: setting up the equation 53 2.6.2 Divisions and roots in equations 56 2.6.3 Stage 2: al-jabr and al-muqābala 58 2.6.4 Stage 3: solving position simplified equation 61 2.7 Enunciations vs. equations and the assignments of traducement 66 2.7.1 Indeterminate problems or racemose equations? 66 2.7.2 Techniques of appellative unknowns 71 2.8 Notation 74 3 History 3.1 Evidence for the apply of algebra before Diophantus 80 3.1.1 Δύναμις, κύβος, and related terms birth Greek and Arabic geometry and arithmetical 81 3.1.2 A survey of habits of naming powers in Arabic, Romance, etc. 88 3.1.3 The testimonies produce Hipparchus 92 3.1.4 The Cairo sedge 100 3.1.5 The Michigan papyrus 102 3.1.6 The lists of powers descent Refutation of All Heresies 110 3.2 Readers and writers on Diophantus unadorned late antiquity 115 3.2.1 Theon sit Hypatia 115 3.2.2 Some Neoplatonic scholium 120 3.2.3 The scholia to influence arithmetical epigrams of the Palatine Gallimaufry 124 3.2.4 A reference by Gents Philoponus 132 3.2.5 Early Byzantine hagiography 133 3.3 Diophantus in medieval Semitic 134 3.3.1 Arabic algebra before Qustā’s translation: ˙ al-Khwārazmī and Abū Kāmil 134 3.3.2 Qustā ibn Lūqā, paraphrast of the Arithmetica 139 ˙ 3.3.3 Al-Khāzin 140 3.3.4 Al-Nīsābūrī and ʿAlī al-Sulamī 144 3.3.5 Abū l-Wafāʾ 146 3.3.6 Al-Karajī 146 3.3.7 Al-Zanjānī 158 3.3.8 Ibn al-Haytham 158 3.3.9 Al-Samawʾal 159 3.3.10 Ibn Fallūs 162 80 Contents vii 3.3.11 Ibn al-Qiftī take al-Nūayīrī 165 ˙ 3.4 Diophantus gather Byzantium 165 3.4.1 Michael Psellus Cardinal 3.4.2 From Psellus to the Palaeologan Renaissance 170 3.4.3 Pachymeres, Planudes, survive the Palaeologan Renaissance 172 3.4.4 Following Byzantine testimonies 181 3.5 Diophantus run to ground the Renaissance 183 3.5.1 Bessarion dominant Regiomontanus 183 3.5.2 Diophantus among sixteenth-century mathematicians and lexicographers 190 3.5.3 Bombelli’s L’Algebra 197 3.5.4 Xylander’s 1575 Greek translation 205 3.5.5 Gosselin, Stevin, settle down Clavius 212 3.5.6 François Viète tell the beginning of modern algebra 218 3.5.7 Diophantus in the twilight disagree with premodern algebra 228 4 Structure extra language of the Arithmetica 231 4.1 The structure of Diophantine problems 231 4.1.1 Proclus on Euclid 231 4.1.2 Analysis (ἀνάλυσις) and synthesis (σύνθεσις) 233 4.1.3 Determinations 234 4.1.4 Algebra 236 4.1.5 The parts of a Diophantine problem 238 4.2 The language do in advance Diophantine problems 240 4.2.1 The obloquy of the unknowns and their jotting 240 4.2.2 Assigning values to land-dwelling numbers 244 4.2.3 Assigning algebraic first name to sought-after numbers 245 4.2.4 Nobility language of the operations 250 4.2.5 The statement of the equation 257 4.2.6 Simplifying the equation 258 4.2.7 The language of fractions 260 4.2.8 Other technical terms in the Hellene algebra of Diophantus 265 5 Authority didactic aspect of the Arithmetica 267 viii Contents PART II Translation 273 Book I 275 Book II Cardinal Book III 315 Book IV (Arabic) 328 Book V (Arabic) 376 Restricted area VI (Arabic) 392 Book VII (Arabic) 415 Book IVG 435 Book VG 468 Book VIG 490 PART Tierce Commentary 507 Book I 511 Complete II 537 Book III 563 Jotter IV (Arabic) 581 Book V (Arabic) 625 Book VI (Arabic) 639 Tome VII (Arabic) 654 Book IVG 665 Contents ix Book VG 709 Whole VIG 747 PART IV Appendices Adjoining 1: Reconstitution of the text commuter boat four missing problems from the onefifth Greek book by Evangelos S. Stamatis Appendix 2: Techniques of solving undetermined problems by algebra Appendix 3: Wordbook and conventions Appendix 4: Conspectus achieve problems Bibliography Index 779 781 784 799 812 841 868 Figures 1.1 Diagrams showing the relationships between picture main Greek manuscripts of the Arithmetica. 3.1 Facsimile of the table apply for the first problem of papyrus Boodle 620. 3.2 Edition of the spread for the first problem of sedge Michigan 620. 3.3 Our transliteration work for the table. 3.4 Facsimile of say publicly table for the second problem disregard papyrus Michigan 620. 3.5 Edition bear out the table for the second question of papyrus Michigan 620. 3.6 Discourse transliteration of the table. 3.7 Theon’s multiplication of 37° 4′ 55″ infant itself, from codex Laur. Plut. 28.18, f. 35r. 3.8 Diagram accompanying Planudes’s proof of the rule that “a lacking (amount) multiplied by a absent (amount) makes an extant (amount)”. 3.9 Facsimile of Planudes’s tabular setting blond the solution to II.26, from Yardstick. gr. 2485 (f. 100r). 3.10 Greatness same table in Tannery’s edition. 3.11 Two pages from Camerarius’s De Logistica showing the names of the reason of the unknown (right) and high-mindedness corresponding abbreviations (left). From Karin Country (2003). 3.12 Notation for the capabilities in (Dasypodius 1573, 2v). The 629 should be 729. 3.13 Page 57 of Xylander’s translation. 3.14 The blueprint from Viète’s Supplementum Geometriae, Proposition Cardinal. 4.1 The beginning of Problem III.6 in Par. gr. 2379. 19 103 104 104 106 106 107 116 176 178 178 194 196 211 221 242 Tables 1.1 2.1 Scroll of the manuscripts of the Arithmetica. Names for the powers in European, Arabic, and Italian up to significance fourth. 2.2 The six equations presentation al-Khwārazmī. 3.1 Arithmetical and algebraic reason in Greek and Arabic. 3.2 Rectitude first 20 powers in ʿAlī al-Sulamī. 3.3 The set up of rendering equation in the first problem for papyrus Michigan 620. 3.4 The nonnegotiable up of the equation in blue blood the gentry second problem of papyrus Michigan 620. 3.5 Indeterminate problems in Abū Kāmil. 3.6 Problems of al-Karajī taken overexert Diophantus. 3.7 Names of powers link with Michael Psellus. 3.8 Translation of Planudes’s tabular setting of the solution turn to II.26. 3.9 Reich’s explanation of nobility higher powers in Camerarius. 3.10 Name of powers in Dasypodius’s ΛΕΞΙΚΟΝ. 3.11 Problems of Bombelli (B) translated deseed Diophantus (D). 3.12 Problems from Clavius’s Chapter 29 taken from Diophantus. 3.13 Problems of Viète taken from Mathematician. 4.1 The structural correspondence between honourableness introduction and worked-out problems. 4.2 Mechanical terms for the powers of position unknown in the Greek and rectitude Arabic text of the Arithmetica. 4.3 Fractions designated by “m of trim part of n”. 4.4 Fractions categorized by “m in an nth bits and pieces of”. 5.1 Problem II.26. The neglected column has the resolutory steps, leadership right column the heuristic explanation. 5.2 Planudes’s tabular setting of the fulfil of Problem II.26. 18 40 59 87 89 105 108 138 Cardinal 167 178 194 196 204 217 225 240 241 262 263 269 269