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Ibn Al-Haytham's Theory of Conics, Geometrical Constructions...

Ibn Al-Haytham's Theory of Conics, Geometrical Constructions and Practical Geometry: A History of Arabic Sciences and Mathematics Volume 3TitoloIbn Al-Haytham's Theory of Conics, Geometrical Constructions and Practical Geometry: A History of Arabic Sciences and Mathematics Volume 3
AutoreRashed, Roshdi
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€ 94,44   Spedizioni gratuite in Italia
(Prezzo € 111,11 Risparmio € 16,67)
CategoriaMathematics: History & Philosophy
History: Middle East
History: Medieval
RilegaturaHardcover
Dati776 p.
Anno2013
EditoreRoutledge
CollanaCulture and Civilization in the Middle East
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Indice e argomenti trattati
Forewordxiii
Prefacexv
Introduction: Conic Sections And Geometrical Constructions1
Chapter I Theory Of Conics And Geometrical Constructions: 'Completion Of The Conics'
1.1 Introduction
9
1.1.1 Ibn Al-Haytham And Apollonius' Conics
9
1.1.2 The Eighth Book Of The Conics
10
1.1.3 The Completion Of The Conics: The Purpose Of The Enterprise
27
1.1.4 History Of The Text
32
1.2 Mathematical Commentary
38
1.3 Translated Text: On The Completion Of The Conics
171
Chapter II Correcting The Band Musa's Lemma For Apollonius' Conics
2.1 Introduction
247
2.2 Mathematical Commentary
248
2.3 History Of The Text
269
2.4 Translated Text: On A Proposition Of The Banu Musa
273
Chapter III Problems Of Geometrical Construction289
3.1 The Regular Heptagon
289
3.1.1 Introduction
289
3.1.2 The Traces Of A Work By Archimedes On The Regular Heptagon
292
3.1.3 A Priority Dispute: Al-Sijzi Against Abu Al-Jud
300
3.1.4 The Lemmas For The Construction Of The Heptagon: The Division Of A Segment
314
3.1.4.1 Archimedes' Division (D1)
315
3.1.4.1.1 First Stage: The Division In The Text Attributed To Archimedes
316
3.1.4.1.2 Second Stage: Ibn Sahl
318
3.1.4.1.3 Third Stage: Al-Quhi And Al-Saghani
321
3.1.4.1.3.1 Al-Quhi: The First Treatise
321
3.1.4.1.3.2 Al-Saghani
326
3.1.4.1.3.3 Al-Quhi: The Second Treatise
333
3.1.4.2 The Range Studied By Abu Al-Jud And Al-Sijzi (D2)
341
3.1.4.3 Abu Al-Jud's Range (D3)
351
3.1.4.4 Comparing The Ranges: Abu Al-Jud, Al-Shanni, Kamal Al-Din Ibn Yunus
353
3.1.4.5 Ibn Al-Haytham's Ranges (D4 And D5)
360
3.1.4.5.1 Triangle (1, 3, 3) And Ibn Al-Haytham's Range (D5)
361
3.1.4.5.2 Triangle (3, 2, 2) And The Range Of Type D3
362
3.1.4.5.3 Triangle (1, 5, 1) And Ibn Al-Haytham's Range (D4)
363
3.1.4.5.4 Triangle (1, 2, 4) And The Range D1
363
3.1.5 Two Supplementary Constructions: Nasr Ibn 'Abd Allah And An Anonymous Author
364
3.1.5.1 Nasr Ibn 'Abd Allah
364
3.1.5.2 An Anonymous Text
369
3.1.6 Ibn Al-Haytham's Two Treatises On The Construction Of The Heptagon
370
3.1.6.1 On The Determination Of The Lemma For The Side Of The Heptagon
370
3.1.6.2 On The Construction Of The Heptagon
383
3.2 Division Of The Straight Line
412
3.3 On A Solid Numerical Problem
418
3.4 History Of The Texts Of Ibn Al-Haytham
422
3.4.1 On The Construction Of The Regular Heptagon
422
3.4.2 Treatise On The Determination Of The Lemma Of The Heptagon
426
3.4.3 The Division Of The Straight Line Used By Archimedes
428
3.4.4 On A Solid Numerical Problem
429
3.5 Translated Texts
431
3.5.1 A Lemma For The Side Of The Heptagon
433
3.5.2 On The Construction Of The Heptagon In A Circle
441
3.5.3 On The Division Of The Straight Line Used By Archimedes
461
3.5.4 On A Solid Numerical Problem
465
Chapter IV Practical Geometry: Measurement469
4.1 Introduction
469
4.2 Mathematical Commentary
472
4.2.1 Treatise On The Principles Of Measurement
472
4.2.2 A Stereometric Problem
497
4.3 History Of The Texts
503
4.3.1 On The Principles Of Measurement
503
4.3.2 On Knowing The Height Of Upright Objects
506
4.3.3 On The Determination Of The Height Of Mountains
509
4.4 Translated Texts
511
4.4.1 On The Principles Of Measurement
513
4.4.2 On Knowing The Height Of Upright Objects
565
4.4.3 On The Determination Of The Height Of Mountains
567
Appendix I: A Research Tradition: The Regular Heptagon569
1.1 History Of The Texts
569
1.2 Translated Texts
585
1.2.1 Book Of The Construction Of The Circle Divided Into Seven Equal Parts By Archimedes
587
1.2.2 Treatise By Abu Al-Jud Muhammad Ibn Al-Layth On The Construction Of The Heptagon In The Circle
605
1.2.3 Treatise By Abu Al-Jud Muhammad Ibn Al-Layth On The Account Of The Two Methods Of Al-Quhi And Al-Saghani
615
1.2.4 Book By Al-Sijzi On The Construction Of The Heptagon
629
1.2.5 Solution By Al-Quhi For The Construction Of The Regular Heptagon In A Given Circle
639
1.2.6 Treatise On The Construction Of The Side Of The Regular Heptagon Inscribed In The Circle By Abu Sahi Al-Quhi
651
1.2.7 Treatise By Al-Saghani For 'Adud Al-Dawla
661
1.2.8 Book On The Discovery Of The Deceit Of Abu Al-Jud By Al-Shanni
671
1.2.9 On The Determination Of The Chord Of The Heptagon By Nasr Ibn 'Abd Allah
689
1.2.10 Synthesis For The Analysis Of The Lemma On The Regular Heptagon Inscribed In The Circle (Anonymous)
693
1.2.11 Treatise On The Proof For The Lemma Neglected By Archimedes, By Kamal Al-Din Ibn Yunus
697
Appendix II: Sinan Ibn Al-Fath And Al-Qabisi: Optical Mensuration703
Sinan Ibn Al-Fath: Extracts From Optical Mensuration
704
Al-Qabisi: Fragment On Optical Mensuration
707
Supplementary Notes
I On The Completion Of The Conics
709
II A Neusis To Divide The Straight Line Used By Archimedes
712
III Al-Quhi: The Lemma To Archimedes' Division Of A Straight Line
714
Addenda (Vol. 2) Al-Hasan Ibn Al-Haytham And Muhammad Ibn Al-Haytham: The Mathematician And The Philosopher729
Bibliography735
Indexes
Index Of Names
745
Subject Index
748
Index Of Works
753
Index Of Manuscripts
758

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