Founding Figures and Commentators in Arabic Mathematics. A history of Arabic sciences and mathematics 1

813 Pages·2012·5.09 MB·English

by  Roshdi Rashed

FOUNDING FIGURES AND
COMMENTATORS IN ARABIC
MATHEMATICS
Inthisuniqueinsightintothehistoryandphilosophyofmathematicsandscienceinclassical
Islamiccivilisation,theeminentscholarRoshdiRashedilluminatesthevarioushistorical,
textual and epistemic threads that underpinned the history of Arabic mathematical and
scientific knowledge up to the seventeenth century. The first of five wide-ranging and
comprehensivevolumes,thisbookprovidesadetailedexplorationofArabicmathematics
andsciencesintheninthandtenthcenturies.
ExtensiveanddetailedanalysesandannotationssupportanumberofkeyArabictexts,
which are translated here into English for the first time. In this volume Rashed focuses
on the traditions of celebrated polymaths from the ninth- and tenth century ‘School of
Baghdad’ – such as the Banu¯ Mu¯sa¯, Tha¯bit ibn Qurra, Ibra¯h¯ım ibn Sina¯n, Abu¯ Ja‘far
al-Kha¯zin, Abu¯ Sahl Wayjan ibn Rusta¯m al-Qu¯h¯ı – and eleventh-century Andalusian
mathematicians such as Abu¯ al-Qa¯sim ibn al-Samh. and al-Mu’taman ibn Hu¯d. The
Archimedean–Apolloniantraditionsofthesepolymathsarethematicallyexploredtoillus-
trate the historical and epistemological development of ‘infinitesimal mathematics’ as it
becamemoreclearlyarticulatedintheeleventh-centuryinfluentiallegacyofal-Hasanibn
al-Haytham(‘Alhazen’).
Contributingtoamoreinformedandbalancedunderstandingoftheinternalcurrentsof
thehistoryofmathematicsandtheexactsciencesinIslam,andofitsadaptiveinterpretation
andassimilationintheEuropeancontext,thisfundamentaltextwillappealtohistoriansof
ideas,epistemologistsandmathematiciansatthemostadvancedlevelsofresearch.
Roshdi Rashed is one of the most eminent authorities on Arabic mathematics and the
exact sciences. A historian and philosopher of mathematics and science and a highly
celebratedepistemologist,heiscurrentlyEmeritusResearchDirector(distinguishedclass)
attheCentreNationaldelaRechercheScientifique(CNRS)inParis,andistheDirector
oftheCentreforHistoryofMedievalScienceandPhilosophyattheUniversityofParis
(DenisDiderot,ParisVII).
NaderEl-BizriisaReaderattheUniversityofLincoln,andaChercheurAssociéatthe
CentreNationaldelaRechercheScientifiqueinParis(CNRS,UMR7219).Hehaslectured
on‘ArabicSciencesandPhilosophy’attheUniversityofCambridgesince1999.Heheld
aVisitingProfessorshipattheUniversityofLincoln(2007–2010),andsince2002hehas
beenaseniorResearchAssociateaffiliatedwithTheInstituteofIsmailiStudies,London.
[13:4031/8/20115689-Rashed-prelims.tex] JobNo:5517 Rashed:SecondLanguageAcquisition Page:i i–viii
CULTURE AND CIVILIZATION
IN THE MIDDLE EAST
GeneralEditor:IanRichardNetton
ProfessorofIslamicStudies,UniversityofExeter
This series studies the Middle East through the twin foci of its diverse cultures
andcivilizations.Comprisingoriginalmonographsaswellasscholarlysurveys,it
coverstopicsinthefieldsofMiddleEasternliterature,archaeology,law,history,
philosophy,science,folklore,art,architectureandlanguage.Whilethereisaplu-
ralityofviews,theseriespresentsseriousscholarshipinalucidandstimulating
fashion.
PREVIOUSLYPUBLISHEDBYCURZON
THEORIGINSOFISLAMICLAW
TheQur’an,theMuwatta’andMadinanAmal
YasinDutton
AJEWISHARCHIVEFROMOLDCAIRO
ThehistoryofCambridgeUniversity’sGenizahcollection
StefanReif
THEFORMATIVEPERIODOFTWELVERSHI’ISM
HadithasdiscoursebetweenQumandBaghdad
AndrewJ.Newman
QUR’ANTRANSLATION
Discourse,textureandexegesis
HusseinAbdul-Raof
CHRISTIANSINAL-ANDALUS711–1000
AnnRosemaryChristys
FOLKLOREANDFOLKLIFEINTHEUNITEDARABEMIRATES
SayyidHamidHurriez
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THEFORMATIONOFHANBALISM
Pietyintopower
NimrodHurvitz
ARABICLITERATURE
Anoverview
PierreCachia
STRUCTUREANDMEANINGINMEDIEVALARABICAND
PERSIANLYRICPOETRY
Orientpearls
JulieScottMeisami
MUSLIMSANDCHRISTIANSINNORMANSICILY
Arabic-speakersandtheendofIslam
AlexanderMetcalfe
MODERNARABHISTORIOGRAPHY
Historicaldiscourseandthenation-state
YoussefChoueiri
THEPHILOSOPHICALPOETICSOFALFARABI,AVICENNA
ANDAVERROES
TheAristotelianreception
SalimKemal
PUBLISHEDBYROUTLEDGE
1. THEEPISTEMOLOGYOFIBNKHALDUN
ZaidAhmad
2. THEHANBALISCHOOLOFLAWANDIBNTAYMIYYAH
Conflictorconcilation
AbdulHakimIAl-Matroudi
3. ARABICRHETORIC
Apragmaticanalysis
HusseinAbdul-Raof
4. ARABREPRESENTATIONSOFTHEOCCIDENT
East–WestencountersinArabicfiction
RasheedEl-Enany
[13:4031/8/20115689-Rashed-prelims.tex] JobNo:5517 Rashed:SecondLanguageAcquisition Page:iii i–viii
5. GODANDHUMANSINISLAMICTHOUGHT
Abdal-Jabba¯r,IbnS¯ına¯ andal-Ghaza¯l¯ı
MahaElkaisy-Friemuth
6. ORIGINALISLAM
MalikandtheMadhhabofMadina
YasinDutton
7. AL-GHAZALIANDTHEQUR’AN
Onebook,manymeanings
MartinWhittingham
8. BIRTHOFTHEPROPHETMUHAMMAD
DevotionalpietyinSunniIslam
MarionHolmesKatz
9. SPACEANDMUSLIMURBANLIFE
AtthelimitsofthelabyrinthofFez
SimonO’Meara
10. ISLAMANDSCIENCE
TheintellectualcareerofNizamal-Dinal-Nizaburi
RobertG.Morrison
11. IBN‘ARABΖTIMEANDCOSMOLOGY
MohamedHajYousef
12. THESTATUSOFWOMENINISLAMICLAWANDSOCIETY
Annotatedtranslationofal-T.a¯hiral-H.adda¯d’sImra’tuna¯ fi
(cid:2) (cid:2)
‘l-shar¯ı awa‘l-mujtama,withanintroduction
RonakHusniandDanielL.Newman
13. ISLAMANDTHEBAHA’IFAITH
AcomparativestudyofMuhammad‘Abduhand‘Abdul-Baha‘Abbas
OliverScharbrodt
14. COMTEDEGOBINEAUANDORIENTALISM
SelectedEasternwritings
TranslatedbyDanielO’DonoghueEditedbyGeoffreyNash
15. EARLYISLAMICSPAIN
ThehistoryofIbnal-Qu¯t.¯ıya
DavidJames
[13:4031/8/20115689-Rashed-prelims.tex] JobNo:5517 Rashed:SecondLanguageAcquisition Page:iv i–viii
16. GERMANORIENTALISM
ThestudyoftheMiddleEastandIslamfrom1800to1945
UrsulaWokoeck
17. MULLA¯ S.ADRA¯ ANDMETAPHYSICS
Modulationofbeing
SajjadH.Rizvi
18. SCHOOLSOFQUR’ANICEXEGESIS
Genesisanddevelopment
HusseinAbdul-Raof
19. AL-GHAZALI,AVERROESANDTHEINTERPRETATION
OFTHEQUR’AN
CommonsenseandphilosophyinIslam
AvitalWohlman,translatedbyDavidBurrell
20. EASTERNCHRISTIANITYINTHEMODERNMIDDLEEAST
EditedbyAnthonyO’MahonyandEmmaLoosley
21. ISLAMICREFORMANDARABNATIONALISM
ExpandingthecrescentfromtheMediterraneantothe
IndianOcean(1880s–1930s)
AmalN.Ghazal
22. ISLAMICETHICS
DivinecommandtheoryinArabo-Islamicthought
Mariamal-Attar
23. MUSLIMFORTRESSESINTHELEVANT
BetweenCrusadersandMongols
KateRaphael
24. BEINGHUMANINISLAM
Theimpactoftheevolutionaryworldview
DamianHoward
25. THEUAEANDFOREIGNPOLICY
Foreignaid,identitiesandinterests
KhalidS.Almezaini
26. AHISTORYOFEARLYAL-ANDALUS
TheAkhba¯rmajmu¯’a
DavidJames
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27. INSPIREDKNOWLEDGEINISLAMICTHOUGHT
Al-Ghazali’stheoryofmysticalcognitionanditsAvicennianfoundation
AlexanderTreiger
28. SHI’ITHEOLOGYINIRAN
Thechallengeofreligiousexperience
OriGoldberg
29. FOUNDINGFIGURESANDCOMMENTATORSINARABIC
MATHEMATICS
AhistoryofArabicsciencesandmathematics,Volume1
RoshdiRashed(translationseditedbyNaderEl-Bizri)
30. THEMUSLIMCONQUESTOFIBERIA
MedievalArabicnarratives
NicolaClarke
31. ANGELSINISLAM
Jalalal-Dinal-Suyuti’sal-Haba’ikfiakhbaral-mala’ik
StephenBurge
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FOUNDING FIGURES
AND COMMENTATORS
IN ARABIC
MATHEMATICS
A history of Arabic sciences and mathematics
Volume 1
Roshdi Rashed
Edited by
Nader El-Bizri
Translated by Roger Wareham, with Chris Allen
and Michael Barany
[13:4031/8/20115689-Rashed-prelims.tex] JobNo:5517 Rashed:SecondLanguageAcquisition Page:vii i–viii
Firstpublished2012
byRoutledge
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SimultaneouslypublishedintheUSAandCanada
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©2012RoutledgeandCentreforArabUnityStudies
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[13:4031/8/20115689-Rashed-prelims.tex] JobNo:5517 Rashed:SecondLanguageAcquisition Page:viii i–viii
CONTENTS
Editor’s Foreword ........................................................................ xiii
Preface...................................................................................... xix
Note ........................................................................................xxiv
CHAPTER I : BANª MªSÆ AND THE CALCULATION OF THE VOLUME
OF THE SPHERE AND THE CYLINDER
1.1. INTRODUCTION ....................................................................... 1
1.1.1. The Banº Mºsæ: dignitaries and learned ...................................... 1
1.1.2. The mathematical works of the Banº Mºsæ ................................... 7
1.1.3. Treatise on the measurement of plane and spherical figures:
a Latin translation and a rewritten version by al-™ºsî ........................ 10
1.1.4. Title and date of the Banº Mºsæ treatise ....................................... 34
1.2. MATHEMATICAL COMMENTARY ................................................ 38
1.2.1. Organization and structure of the Banº Mºsæ 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: THÆBIT IBN QURRA AND HIS WORKS IN INFINITESIMAL
MATHEMATICS
2.1. INTRODUCTION ....................................................................... 113
2.1.1. Thæbit ibn Qurra: from Îarræn to Baghdad ................................... 113
2.1.2. The works of Thæbit 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