A history of Arabic sciences and mathematics: 1 Founding figures and commentators in Arabic mathematics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Buch |
| Sprache: | English Arabic |
| Veröffentlicht: |
London ; New York
Routledge
2012
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Culture and civilization in the Middle East
29 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XXIII, 808 S. graph. Darst. |
| ISBN: | 9780415582179 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804148573979279360 |
|---|---|
| adam_text | CONTENTS
Editor’s Foreword.................................................. xiii
Preface........................*................................... xix
Note................................................................xxiv
CHAPTER I : BANÜ MÜSA AND THE CALCULATION OF THE VOLUME
OF THE SPHERE AND THE CYLINDER
U. INTRODUCTION....................................................... 1
1.1.1. The Banü Musa: dignitaries and learned ........................ 1
1.1.2. The mathematical works of the Banü Müsà..................... 7
1.1.3. Treatise on the measurement of plane and spherical figures:
a Latin translation and a rewritten version by al-Tüsï........ 10
L1.4. Title and date of the Banü Müsà treatise..................... 34
1.2. MATHEMATICAL COMMENTARY .......................................... 38
1.2.1. Organization and structure of the Banu Musa book............ 38
1.2.2. The area of the circle........................................ 40
1.2.3. The area of the triangle and Hero’s formula .................. 46
1.2.4. The surface area of a sphere and its volume .................. 47
1.2.5. The two-means problem and its mechanical construction ........ 60
1.2.6a. The trisection of angles and Pascal’s Limaçon.............. 66
1.2.6b. Approximating cubic roots ................................... 69
1.3. TRANSLATED TEXT: On the Knowledge of the Measurement of Plane
and Spherical Figures................................................... 73
CHAPTER II: THÀBITIBN QURRA AND HIS WORKS IN INFINITESIMAL
MATHEMATICS
2.1. INTRODUCTION...................................................... 113
2.1.1. Thâbit ibn Qurra: from Harrân to Baghdad .................... 113
2.1.2. The works of Thàbit ibn Qurra in infinitesimal mathematics .. 122
2.1.3. History of the texts and their translations ................. 124
2.2. MEASURING THE PARABOLA ........................................... 130
2.2.1. Organization and structure of Ibn Qurra’s treatise .......... 130
2.2.2. Mathematical commentary...................................... 133
2.2.2.1. Arithmetical propositions............................. 133
2.2.2.2. Sequence of segments and bounding .................... 142
2.2.2.3. Calculation of the area of a portion of a parabola... 154
2.2.3. Translated text: On the Measurement of the Conic Section
Called Parabola .................................................... 169
2.3. MEASURING THE PARABOLOID.......................................... 209
2.3.1. Organization and structure of Ibn Qurra’s treatise........... 209
2.3.2. Mathematical commentary...................................... 214
2.3.2.1. Arithmetical propositions............................. 214
2.3.2.2. Extension to sequences of segments.................... 218
2.3.2.3. Volumes of cones, rhombuses and other solids......... 223
2.3.2.4. Property of four segments ............................ 230
2.3.2.5. Arithmetical propositions............................. 231
X
CONTENTS
2.3.2.6. Sequence of segments and bounding ................... 233
2.3.2.7. Calculation of the volumes of paraboloids ........... 244
2.3.2.8. Parallel between the treatise on the area of the parabola
and the treatise on the volume of the paraboloid............. 256
2.3.3. Translated text: On the Measurement of the Paraboloids....... 261
2.4. ON THE SECTIONS OF THE CYLINDER AND ITS LATERAL
SURFACE.......................................................... 333
2.4.1. Introduction ............................................. 333
2.4.2. Mathematical commentary................................... 337
2.4.2.1. Plane sections of the cylinder ...................... 337
2.4.2.2. Area of an ellipse and elliptical sections .......... 341
2.4.2.3. Concerning the maximal section of the cylinder and
concerning its minimal sections ........................... 356
2.4.2.4. Concerning the lateral area of the cylinder and
the lateral area of portions of the cylinder lying between
the plane sections touching all sides ........................ 363
2.4.3. Translated text: On the Sections of the Cylinder and its
Lateral Surface ................................................. 381
CHAPTER III: IBN SINÀN, CRITIQUE OF AL-MÀHÀNÎ:
THE AREA OF THE PARABOLA
3.1. INTRODUCTION................................................... 459
3.1.1. Ibrahim ibn Sinan: ‘heir’ and ‘critic’.................... 459
3.1.2. The two versions of The Measurement of the Parabola:
texts and translations........................................... 463
3.2. MATHEMATICAL COMMENTARY ....................................... 466
3.3. TRANSLATED TEXTS
3.3.1. On the Measurement of the Parabola ....................... 483
3.3.2. On the Measurement of a Portion of the Parabola.............. 495
CHAPTER IV: ABÜ JATAR AL-KHÀZIN: ISOPERIMETRICS AND
ISEPIPHANICS
4.1. INTRODUCTION................................................... 503
4.1.1. Al-Khàzin: his name, life and works ...................... 503
4.1.2. The treatises of al-Khazin on isoperimeters and isepiphanics. 506
4.2. MATHEMATICAL COMMENTARY ....................................... 507
4.2.1. Introduction ............................................. 507
4.2.2. Isoperimetrics ........................................... 509
4.2.3. Isepiphanics ............................................. 524
4.2.4. The opuscule of al-Sumaysati.............................. 546
4.3. TRANSLATED TEXTS
4.3.1. Commentary on the First Book of the Almagest ................ 551
4.3.2. The Surface of any Circle is Greater than the Surface
of any Regular Polygon with the Same Perimeter (al-Sumaysati)....... 577
CHAPTER V: AL-QÜHÏ, CRITIQUE OF THÀBIT:
VOLUME OF THE PARABOLOID OF REVOLUTION
5.1. INTRODUCTION................................................... 579
5.1.1. The mathematician and the artisan......................... 579
CONTENTS
xi
5.1.2. The versions of the volume of a paraboloid................. 583
5.2. MATHEMATICAL COMMENTARY ........................................ 588
5.3. TRANSLATION TEXTS
5.3.1. On the Determination of the Volume of a Paraboloid ........ 599
5.3.2. On the Volume of a Paraboloid.............................. 609
CHAPTER VI: IBN AL-SAMH: THE PLANE SECTIONS OF A CYLINDER AND
THE DETERMINATION OF THEIR AREAS
6.1. INTRODUCTION.................................................. 615
6.1.1. Ibn al-Samh and Ibn Qurra, successors to al-Hasan ibn Musa. 615
6.1.2. Serenus of Antinoupolis, al-Hasan ibn Musa, Thabit ibn Qurra
and Ibn al-Samh ................................................ 618
6.1.3. The structure of the study by Ibn al-Samh ................. 622
62, MATHEMATICAL COMMENTARY ....................................... 623
6.2.1. Definitions and accepted results .......................... 623
6.2.2. The cylinder ............................................ 626
6.2.3. The plane sections of a cylinder .......................... 627
6.2.4. The properties of a circle ................................ 628
6.2.5. Elliptical sections of a right cylinder ................... 632
6.2.6. The ellipse as a plane section of a right cylinder......... 639
6.2.7. The area of an ellipse..................................... 645
6.2.8. Chords and sagittas of the ellipse......................... 653
6.3. TRANSLATED TEXT: On the Cylinder and its Plane Section.......... 667
CHAPTER VII: IBN HUD: THE MEASUREMENT OF THE PARABOLA
AND THE ISOPERIMETRIC PROBLEM
7.1. INTRODUCTION ................................................. 721
7.1.1. Kitab al-lstikmal, a mathematical compendium............. 721
7.1.2. Manuscript transmission of the texts....................... 727
7.2. THE MEASUREMENT OF THE PARABOLA ................................ 729
7.2.1. Infinitesimal property or conic property................... 729
7.2.2. Mathematical commentary on Propositions 18-21 ............. 733
7.2.3. Translation: Kitab al-lstikmal........................... 749
7.3. THE ISOPERIMETRIC PROBLEM .................................... 755
7.3.1. An extremal property or a geometric property .............. 755
7.3.2. Mathematical commentary on Propositions 16 and 19.......... 758
7.3.3. Translation: Kitab al-lstikmal........................... 764
SUPPLEMENTARY NOTES
The Formula of Hero of Alexandria according to Thabit ibn Qurra. 767
Commentary of Ibn Abi Jarrada on The Sections of the Cylinder
by Thabit ibn Qurra............................................. 767
BIBLIOGRAPHY....................................................... 779
INDEXES
Index of names.................................................. 793
Subject index................................................... 797
Index of works.................................................. 805
|
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| edition | 1. publ. |
| era | Geschichte 500-1700 gnd |
| era_facet | Geschichte 500-1700 |
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| id | DE-604.BV039700801 |
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| indexdate | 2024-07-10T00:09:17Z |
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| isbn | 9780415582179 |
| language | English Arabic |
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| series | Culture and civilization in the Middle East |
| series2 | Culture and civilization in the Middle East |
| spelling | Rashed, Roshdi 1936- Verfasser (DE-588)120250446 aut A history of Arabic sciences and mathematics 1 Founding figures and commentators in Arabic mathematics Roshdi Rashed ; edited by Nader El-Bizri 1. publ. London ; New York Routledge 2012 XXIII, 808 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Culture and civilization in the Middle East 29 Culture and civilization in the Middle East ... Includes bibliographical references and index Geschichte 500-1700 gnd rswk-swf Islam (DE-588)4027743-4 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Islam (DE-588)4027743-4 s Mathematik (DE-588)4037944-9 s Geschichte 500-1700 z b DE-604 Bizri, Nader el- 1966- (DE-588)1016969317 edt (DE-604)BV039699811 1 Erscheint auch als Online-Ausgabe 978-0-203-63659-6 Culture and civilization in the Middle East 29 (DE-604)BV022955619 29 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024549352&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rashed, Roshdi 1936- A history of Arabic sciences and mathematics Culture and civilization in the Middle East Islam (DE-588)4027743-4 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4027743-4 (DE-588)4037944-9 |
| title | A history of Arabic sciences and mathematics |
| title_auth | A history of Arabic sciences and mathematics |
| title_exact_search | A history of Arabic sciences and mathematics |
| title_full | A history of Arabic sciences and mathematics 1 Founding figures and commentators in Arabic mathematics Roshdi Rashed ; edited by Nader El-Bizri |
| title_fullStr | A history of Arabic sciences and mathematics 1 Founding figures and commentators in Arabic mathematics Roshdi Rashed ; edited by Nader El-Bizri |
| title_full_unstemmed | A history of Arabic sciences and mathematics 1 Founding figures and commentators in Arabic mathematics Roshdi Rashed ; edited by Nader El-Bizri |
| title_short | A history of Arabic sciences and mathematics |
| title_sort | a history of arabic sciences and mathematics founding figures and commentators in arabic mathematics |
| topic | Islam (DE-588)4027743-4 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Islam Mathematik |
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