Sourcebook in the mathematics of Medieval Europe and North Africa:
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton and Oxford
Princeton University Press
[2016]
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xvi, 574 Seiten Illustrationen, Diagramme 27 cm |
| ISBN: | 9780691156859 |
Internformat
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| 245 | 1 | 0 | |a Sourcebook in the mathematics of Medieval Europe and North Africa |c edited by Victor J. Katz ; Menso Folkerts, Barnabas Hughes, Roi Wagner, J. Lennart Berggren |
| 246 | 1 | 3 | |a Mathematics of Medieval Europe and North Africa |
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Datensatz im Suchindex
| _version_ | 1804176538171604992 |
|---|---|
| adam_text | Titel: Sourcebook in the mathematics of medieval Europe and North Africa
Autor: Katz, Victor J
Jahr: 2016
Contents
Preface xi
Permissions xiii
General Introduction 1
Chapter 1. The Latin Mathematics of Medieval Europe 4
Menso Folkerts and Barnabas Hughes
Introduction 4
I Latin Schools, 800-1140 6
1-1. Brief Selections 6
1. The Quadrivium of Martianus Capella 6
2. The Quadrivium of Cassiodorus 9
3. The Quadrivium of Isidore of Seville 10
4. A New Creation: Rules for Addition of Signed Numbers 11
I-2. Numbering 12
1. Roman numerals 12
2. Finger reckoning 13
3. Isidore of Seville, Liber numerorum (Book of Numbers) 18
4. Hindu-Arabic numerals 20
I-3. Arithmetic 22
1. Boethius, De institutione arithmetica (Introduction to Arithmetic) 22
2. Computus 29
3. Gerbert sjump 36
4. Pandulf of Capua, Liber de calculatione 39
1-4. Geometry 44
1. Gerbert, Geometry 44
2. Gerbert: Area of an equilateral triangle 48
3. Units of measurement 49
vi Contents
4. Franco of Liege, De quadratura circuli 50
5. Hugh of St. Victor, Practica geometriae 53
I-5. Recreational Mathematics 55
1. Number puzzles 55
2. Thought problems 57
3. The Josephus Problem 58
4. The most important medieval number game: the Rithmimachia 59
II. A School Becomes a University: 1140-1480 64
II-1. Translations 66
1. Translators and translations 66
2. Translations . A practical illustration 70
11-2. Arithmetic 75
1. Al-Khwarizmi, Arithmetic 75
2. Leonardo of Pisa (Fibonacci), Liber abbaci (Book on Calculation) 79
3. John of Sacrobosco, Algorismus vulgaris 85
4. Johannes de Lineriis, Algorismus de minuciis 93
5. Jordanus de Nemore (Nemorarius), De elementis arithmetice artis 96
6. Combinatorics and probability, De Vetula 100
II-3. Algebra 103
1. Al-Khwarizmt, Algebra 103
2. Leonardo of Pisa, Liber abbaci (Book on Calculation) 106
3. Leonardo of Pisa, Book of Squares 112
4. Jordanus de Nemore, De numeris datis (On Given Numbers) 116
5. Nicole Oresme, Algorismus proportionum (Algorithm of Ratios) 119
6. Nicole Oresme, De proportionibus proportionum (On the Ratio of
Ratios) 121
II-4. Geometry 123
1. Banu Musa ibn Shakir, The Book of the Measurement of Plane and
Spherical Figures 123
2. Abu Bakr, Liber mensurationum (On Measurement) 126
3. Leonardo of Pisa, De practica geometrie (Practical Geometry) 130
4. John of Murs, De arte mensurandi 140
5. Jordanus de Nemore, Liber philotegni 143
6. Dominicus de Clavasio, Practica geometriae 146
II-5. Trigonometry 148
1. Ptolemy, On the Size of Chords in a Circle 149
2. Leonardo of Pisa, De practica geometrie (Practical Geometry) 153
3. Johannes de Lineriis, Canones 155
4. Richard of Wallingford, Quadripartitum 157
5. Geoffrey Chaucer, A Treatise on the Astrolabe 160
6. Regiomontanus, On Triangles 162
Contents vii
11-6. Mathematics of the infinite 173
1. Angle of contingence 174
2. Thomas Bradwardine, Tractatus de continuo (On the Continuum) 178
3. John Duns Scotus, Indivisibles and Theology 180
4. Does light travel instantaneously or over time? 182
5. Nicole Oresme, Questiones super geometriam Euclidis (Questions on the
Geometry of Euclid) 184
II-7. Statics, Dynamics, and Kinematics 185
1. Robert Grosseteste, De lineis, angulis etfiguris {On lines, angles and
figures) 185
2. Jordanus de Nemore, De ratione ponderis {On the Theory of Weights) 186
3. Thomas Bradwardine, Tractatus de proportionibus 189
4. William Heytesbury, Regule solvendi sophismata {Rules for Solving
Sophisms) 191
5. Giovanni di Casali, De velocitate motus alterationis {On the Velocity of
Motion of Alteration) 194
6. Nicole Oresme, De configurationibus qualitatum et motuum {On the
Configurations of Qualities and Motions) 197
III. Abbacist Schools: 1300-1480 207
III-1. Foreign Exchange 208
III-2. Geometry 209
lli-3. Algebra 210
1. Gilio da Siena, A Lecture in Introductory Algebra 210
2. Paolo Girardi, Libro di Ragioni 211
3. Jacobo da Firenze, Tractatus algorismi 212
4. Master Dardi, New equations solved 213
Sources 216
References 221
Chapter 2. Mathematics in Hebrew in Medieval Europe 224
Roi Wagner
Introduction 224
I. Practical and Scholarly Arithmetic 227
1. Abraham ibn Ezra, Sefer Hamispar {The Book of Number) 227
2. Aaron ben Isaac, Arithmetic 235
3. Immanuel ben Jacob Bonfils, On decimal numbers and fractions 237
4. Jacob Canpanton, Bar Noten Ta am 239
5. Elijah Mizrahi, Sefer Hamispar {The Book of Number) 244
6. Levi ben Gershon, Ma ase Hoshev {The Art of the Calculator) 253
viii Contents
II. Numerology, Combinatorics, and Number Theory 268
1. Abraham ibn Ezra, Sefer Haehad (The Book of One) 269
2. Abraham ibn Ezra, Sefer Haolam (Book of the World) 271
3. Levi ben Gershon, Ma ase Hoshev (The Art of the Calculator) 273
4. Levi ben Gershon, On Harmonic Numbers 277
5. Qalonymos ben Qalonymos, Sefer Melakhim (Book of Kings) 283
6. Don Benveniste ben Lavi, Encyclopedia 284
7. Aaron ben Isaac, Arithmetic 285
III. Measurement and Practical Geometry 286
1. Abraham ibn Ezra (?), Sefer Hamidot (The Book of Measure) 287
2. Abraham bar Hiyya, Hibur Hameshiha Vehatishboret (The Treatise on
Measuring Areas and Volumes)
3. Rabbi Shlomolshaqi (Rashi), On the Measurements of the
Tabernacle Court
4. Simon ben Semah, Responsa 165 concerning Solomon s Sea
5. Levi ben Gershon, Astronomy
IV. Scholarly Geometry
1. Levi ben Gershon, Commentary on Euclid s Elements
2. Levi ben Gershon, Treatise on Geometry
3. Qalonymos ben Qalonymos, On Polyhedra
4. Immanuel ben Jacob Bonfils, Measurement of the Circle
5. Solomon ben Isaac, On the Hyperbola and Its Asymptote
6. Abner of Burgos (Alfonso di Valladolid), Sefer Meyasher Aqov
(Book of the Rectifying of the Curved) 345
V Algebra 354
1. Quadratic word problems 354
2. Simon Motot, Algebra 358
3. Ibn al-Ahdab, Igeret Hamispar (The Epistle of the Number) 362
Sources 374
References 376
Chapter 3. Mathematics in the Islamic World in
Medieval Spain and North Africa 381
J. Lennart Berggren
Introduction 381
I. Arithmetic 385
1. Ibn al-Banna , Arithmetic 385
2. All b. Muhammad al-Qalasadl, Removing the Veil from the Science of
Calculation 398
3. Muhammad ibn Muhammad al-Fullam al-Kishnawi, On magic squares 407
296
313
315
320
326
326
335
337
339
340
Contents
II. Algebra
1. Ahmad ibn al-Banna Algebra
2. Muhammad ibn Badr, An Abridgement of Algebra
III. Combinatorics
1. Ahmad ibn Mun im, Fiqh al-hisab (On the Science of Calculation)
2. Ibn al-Banna on Combinatorics, Raising the Veil
3. Shihab al-DIn ibn al-Majdl, On enumerating polynomial equations
IV. Geometry
1. Abu Abd Allah Muhammad ibn Abdun, On Measurement
2. Abu al-Qasim ibn al-Samh, The Plane Sections of a Cylinder and the
Determination of Their Areas
3. Abu Abd Allah Muhammad ibn Mu adh al-Jayyani, On ratios
4. Al-Mu taman ibn Hud, Kitab al-Istikmal (Book of Perfection)
5. Muhyl al-DTn ibn Abl al-Shukr al-Maghribl, Recension of Euclid s
Elements
V. Trigonometry
1. Abu Abd Allah Muhammad ibn Mu adh al-Jayyani, Book of Unknowns
of Arcs of the Sphere
2. Abu Abd Allah Muhammad ibn Mu adh al-Jayyani, On Twilight and the
Rising of Clouds
3. Abu Abd Allah Muhammad ibn Mu adh al-Jayyani, On the qibla
4. Ibrahim ibn al-Zarqalluh, On a universal astrolabe
5. Abu Muhammad Jabir ibn Aflah, Correction of the Almagest
Sources
References
Appendices
Appendix 1. Byzantine Mathematics
1. Maximus Planudes, The Great Calculation According to the Indians
2. Manuel Moschopoulos, On Magic Squares
3. Isaac Argyros, On Square Roots
4. Anonymous fifteenth-century manuscript on arithmetic
Sources
Appendix 2. Diophantus Arithmetics, Book I, #24
Appendix 3. From the Ganitasarasangraha of Mahavira
Appendix 4. Time Line
Editors and Contributors
Index
|
| any_adam_object | 1 |
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| discipline | Mathematik |
| era | Geschichte 800-1500 gnd |
| era_facet | Geschichte 800-1500 |
| format | Book |
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| spelling | Sourcebook in the mathematics of Medieval Europe and North Africa edited by Victor J. Katz ; Menso Folkerts, Barnabas Hughes, Roi Wagner, J. Lennart Berggren Mathematics of Medieval Europe and North Africa Princeton and Oxford Princeton University Press [2016] © 2016 xvi, 574 Seiten Illustrationen, Diagramme 27 cm txt rdacontent n rdamedia nc rdacarrier Geschichte 800-1500 gnd rswk-swf Mittelalter (DE-588)4129108-6 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Europa (DE-588)4015701-5 gnd rswk-swf Nordafrika (DE-588)4042482-0 gnd rswk-swf (DE-588)4135952-5 Quelle gnd-content Europa (DE-588)4015701-5 g Nordafrika (DE-588)4042482-0 g Mathematik (DE-588)4037944-9 s Mittelalter (DE-588)4129108-6 s Geschichte 800-1500 z DE-604 Katz, Victor J. 1942- (DE-588)1023186675 edt HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029150293&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sourcebook in the mathematics of Medieval Europe and North Africa Mittelalter (DE-588)4129108-6 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4129108-6 (DE-588)4037944-9 (DE-588)4015701-5 (DE-588)4042482-0 (DE-588)4135952-5 |
| title | Sourcebook in the mathematics of Medieval Europe and North Africa |
| title_alt | Mathematics of Medieval Europe and North Africa |
| title_auth | Sourcebook in the mathematics of Medieval Europe and North Africa |
| title_exact_search | Sourcebook in the mathematics of Medieval Europe and North Africa |
| title_full | Sourcebook in the mathematics of Medieval Europe and North Africa edited by Victor J. Katz ; Menso Folkerts, Barnabas Hughes, Roi Wagner, J. Lennart Berggren |
| title_fullStr | Sourcebook in the mathematics of Medieval Europe and North Africa edited by Victor J. Katz ; Menso Folkerts, Barnabas Hughes, Roi Wagner, J. Lennart Berggren |
| title_full_unstemmed | Sourcebook in the mathematics of Medieval Europe and North Africa edited by Victor J. Katz ; Menso Folkerts, Barnabas Hughes, Roi Wagner, J. Lennart Berggren |
| title_short | Sourcebook in the mathematics of Medieval Europe and North Africa |
| title_sort | sourcebook in the mathematics of medieval europe and north africa |
| topic | Mittelalter (DE-588)4129108-6 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Mittelalter Mathematik Europa Nordafrika Quelle |
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