Ibn al-Haytham's geometrical methods and the philosophy of mathematics : a history of Arabic sciences and mathematics. Volume 5 / Roshdi Rashed ; translated by J.V. Field.
Ibn al-Haytham's geometrical methods and the philosophy of mathematics :
ISBN
9781351686006
1351686003
9781315168456 (ebk)
1315168456 (ebk)
9781351686013 (electronic bk. : PDF)
1351686011 (electronic bk. : PDF)
9781351685993 (electronic bk. : Mobipocket)
1351685996 (electronic bk. : Mobipocket)
9780415582193 (hbk.)
1351686003
9781315168456 (ebk)
1315168456 (ebk)
9781351686013 (electronic bk. : PDF)
1351686011 (electronic bk. : PDF)
9781351685993 (electronic bk. : Mobipocket)
1351685996 (electronic bk. : Mobipocket)
9780415582193 (hbk.)
Dil Kodu
İngilizce
Yazar
Yayın Bilgisi
London : New York : Routledge, 2017.
©2017
©2017
Fiziksel Niteleme
1 online resource (xiv, 664 pages) : illustrations
Dizi
Culture and civilization in the Middle East ; volume 55
History of Arabic sciences and mathematics ; volume 5
History of Arabic sciences and mathematics ; volume 5
Genel Not
"This book is the translation of Les Mathèmatiques infinitèsmales du IXe au XIe siècle, vol. IV: Mèthodes gèomètriques, transformations ponctuelles et philosophie des mathèmatique"--Foreword page
3.7. Variations on the same problem from Ptolemy in other writings by al-Sijzī
3.7. Variations on the same problem from Ptolemy in other writings by al-Sijzī
İçindekiler Notu
Introduction : motion and transformation in geometry -- Chapter I: The properties of the circle -- Chapter II: The analytical art in the tenth to eleventh centuries -- Analysis and synthesis : mathematical method and discipline -- The knowns : a new geometrical discipline -- Analysis and synthesis : examples of the geometry of triangles -- Chapter III: Ibn al-Haytham and the geometrisation of place -- Appendix : the Ars Inveniendi : Thabit ibn Qurra and al-Sijzi -- Thabit ibn Qurra : axiomatic method and invention -- Al-Sijzi : the idea of an Ars Inveniendi -- History of the texts -- Translated texts -- Supplementary notes -- Bibliography -- Indexes.
Cover; Half Title; Title Page; Copyright Page; Table of Contents; Foreword; Preface; Introduction: Motion and Transformations in Geometry; Chapter I: The Properties of the Circle ; Introduction; 1. The concept of homothety; 2. Euclid, Pappus and Ibn al-Haytham: on homothety; 3. Ibn al-Haytham and homothety as a point by point transformation; 4. History of the text; Mathematical Commentary; Translated Text: On the Properties of Circles; Chapter II: The Analytical Art in the Tenth to Eleventh Centuries; Introduction; 1. The rebirth of a subject; 2. Analytical art: discipline and method.
3. The analytical art and the new discipline: 'The Knowns'4. History of the texts; On Analysis and Synthesis; The Knowns; I. Analysis and Synthesis: Mathematical Method and Discipline Mathematical Commentary; 1. The double classification of Analysis and Synthesis; Preliminary propositions; Analysis and synthesis in arithmetic; Analysis and synthesis in geometry; Analysis and synthesis in astronomy; Analysis in music; 2. Applications of analysis and synthesis in number theory and in geometry; Number theory; Perfect numbers; Two indeterminate systems of equations of the first degree.
Geometrical problemsProblem in plane geometry; Problem solved with the help of transformations; Construction of a circle to touch three given circles; Auxiliary problem; Geometrical commentary on the problem; Algebraic commentary on the auxiliary problem; Translated Text: On Analysis and Synthesis; II. The Knowns: A New Geometrical Discipline; Introduction; Mathematical Commentary; 1. Properties of position and of form and geometrical transformations; 2. Invariant properties of geometrical loci and geometrical transformations; Translated Text: On the Knowns.
III: Analysis and Synthesis: Examples of the Geometry of Triangles1. On a geometrical problem: Ibn Sahl, al-Sijzī and Ibn al-Haytham; 2. Distances from a point of a triangle to its sides; 3. History of the texts; 3.1. On a Geometrical Problem; 3.2. On the Properties of the Triangle; Translated Texts:; On a Geometrical Problem; On the Properties of the Triangle in Regard to Height; Chapter III: Ibn al-Haytham and the Geometrisation of Place; History of the Text; Translated Text: On Place; Appendix: The Ars Inveniendi: Thābit Ibn Qurra and al-Sijzī
I. Thābit Ibn Qurra: Axiomatic Method and InventionII. Al-Sijzī: The Idea of an Ars Inveniendi; 1. Introduction; 2. A propaedeutic to the ars inveniendi; 3. The methods of the ars inveniendi and their applications; 3.1. Analysis and point-to-point transformation; 3.2. Analysis and variation of one element of the figure; 3.3. Analysis and variation of two methods of solution of a single problem; 3.4. Analysis and variation of lemmas; 3.5. Analysis and variation of constructions carried out using the same figure; 3.6. Variations on a problem from Ptolemy.
Cover; Half Title; Title Page; Copyright Page; Table of Contents; Foreword; Preface; Introduction: Motion and Transformations in Geometry; Chapter I: The Properties of the Circle ; Introduction; 1. The concept of homothety; 2. Euclid, Pappus and Ibn al-Haytham: on homothety; 3. Ibn al-Haytham and homothety as a point by point transformation; 4. History of the text; Mathematical Commentary; Translated Text: On the Properties of Circles; Chapter II: The Analytical Art in the Tenth to Eleventh Centuries; Introduction; 1. The rebirth of a subject; 2. Analytical art: discipline and method.
3. The analytical art and the new discipline: 'The Knowns'4. History of the texts; On Analysis and Synthesis; The Knowns; I. Analysis and Synthesis: Mathematical Method and Discipline Mathematical Commentary; 1. The double classification of Analysis and Synthesis; Preliminary propositions; Analysis and synthesis in arithmetic; Analysis and synthesis in geometry; Analysis and synthesis in astronomy; Analysis in music; 2. Applications of analysis and synthesis in number theory and in geometry; Number theory; Perfect numbers; Two indeterminate systems of equations of the first degree.
Geometrical problemsProblem in plane geometry; Problem solved with the help of transformations; Construction of a circle to touch three given circles; Auxiliary problem; Geometrical commentary on the problem; Algebraic commentary on the auxiliary problem; Translated Text: On Analysis and Synthesis; II. The Knowns: A New Geometrical Discipline; Introduction; Mathematical Commentary; 1. Properties of position and of form and geometrical transformations; 2. Invariant properties of geometrical loci and geometrical transformations; Translated Text: On the Knowns.
III: Analysis and Synthesis: Examples of the Geometry of Triangles1. On a geometrical problem: Ibn Sahl, al-Sijzī and Ibn al-Haytham; 2. Distances from a point of a triangle to its sides; 3. History of the texts; 3.1. On a Geometrical Problem; 3.2. On the Properties of the Triangle; Translated Texts:; On a Geometrical Problem; On the Properties of the Triangle in Regard to Height; Chapter III: Ibn al-Haytham and the Geometrisation of Place; History of the Text; Translated Text: On Place; Appendix: The Ars Inveniendi: Thābit Ibn Qurra and al-Sijzī
I. Thābit Ibn Qurra: Axiomatic Method and InventionII. Al-Sijzī: The Idea of an Ars Inveniendi; 1. Introduction; 2. A propaedeutic to the ars inveniendi; 3. The methods of the ars inveniendi and their applications; 3.1. Analysis and point-to-point transformation; 3.2. Analysis and variation of one element of the figure; 3.3. Analysis and variation of two methods of solution of a single problem; 3.4. Analysis and variation of lemmas; 3.5. Analysis and variation of constructions carried out using the same figure; 3.6. Variations on a problem from Ptolemy.
Özet, vb.
"This fifth volume of A History of Arabic Sciences and Mathematics is complemented by four preceding volumes which focused on the main chapters of classical mathematics: infinitesimal geometry, theory of conics and its applications, spherical geometry, mathematical astronomy, etc. This book includes seven main works of Ibn al-Haytham (Alhazen) and of two of his predecessors, Thābit ibn Qurra and al-Sijzī: The circle, its transformations and its properties; Analysis and synthesis: the founding of analytical art; A new mathematical discipline: the Knowns; The geometrisation of place; Analysis and synthesis: examples of the geometry of triangles; Axiomatic method and invention: Thābit ibn Qurra; The idea of an Ars Inveniendi: al-Sijzī. Including extensive commentary from one of the world's foremost authorities on the subject, this fundamental text is essential reading for historians and mathematicians at the most advanced levels of research."--Provided by publisher
Konu
Alhazen, __ 965-1039.
Sijzī, Aḥmad ibn Muḥammad, __ -1084 or 1085.
Thābit ibn Qurrah al-Ḥarrānī, __ -901.
Science __ Arab countries __ History.
Mathematics __ Arab countries __ History.
Science, Medieval.
Mathematics, Medieval.
Science __ Arab countries __ Philosophy __ History.
Mathematics __ Arab countries __ Philosophy __ History.
HISTORY / Middle East / General __ bisacsh
MATHEMATICS / History & Philosophy __ bisacsh
Sijzī, Aḥmad ibn Muḥammad, __ -1084 or 1085.
Thābit ibn Qurrah al-Ḥarrānī, __ -901.
Science __ Arab countries __ History.
Mathematics __ Arab countries __ History.
Science, Medieval.
Mathematics, Medieval.
Science __ Arab countries __ Philosophy __ History.
Mathematics __ Arab countries __ Philosophy __ History.
HISTORY / Middle East / General __ bisacsh
MATHEMATICS / History & Philosophy __ bisacsh
Diğer Yazarlar
Veritabanı
