Ibn al-Haytham and analytical mathematics. A history of Arabic sciences and mathematics 2

465 Pages·2013·2.38 MB·English

by  Roshdi Rashed

R I
o b
s n CULTURE AND CIVILIZATION IN THE MIDDLE EAST
h
d a
i
R l-
a H
sh a
e y
d t
h
a
m
a
n
d
A
n
a
l
y
t
i
c
a
l
M
a
t
h
e
m
a
ti Ibn al-Haytham and Analytical
c
s
Mathematics
A history of Arabic sciences and mathematics
Volume 2
Roshdi Rashed
Translated by Susan Glynn and Roger Wareham
aninformabusiness
ISBN 978-0-415-58218-6
,!7IA4B5-ficbig!
www.routledge.com
IBN AL-HAYTHAM AND
ANALYTICAL MATHEMATICS
Thisvolumeprovidesauniqueprimarysourceonthehistoryandphilosophyof
mathematics and the exact sciences in the medieval Arab world. The second of
five comprehensive volumes, this book offers a detailed exploration of Arabic
mathematicsintheeleventhcenturyasembodiedinthelegacyofthecelebrated
polymathal-Hasanibnal-Haytham.
Extensiveanalysesandannotationsfromtheeminentscholar,RoshdiRashed,
supportanumberofkeyArabictextsfromIbnal-Haytham’streatisesininfinitesi-
malmathematics,translatedhereintoEnglishforthefirsttime.Rashedshowshow
Ibnal-Haytham’sworksdemonstratearemarkablemathematicalcompetencein
mathematical subjects like the quadrature of the circle and of lunes, the calcu-
lation of the volumes of paraboloids, the problem of isoperimetric plane figures
andsolidfigureswithequalsurfaceareas,alongwiththeextractionofsquareand
cubicroots,etc.
The present text is complemented by the first volume of A History of Arabic
SciencesandMathematics,whichfocusedonfoundingfiguresandcommentators
in the ninth- and tenth-century Archimedean–Apollonian mathematical ‘School
of Baghdad’. This constellation of works illustrates the historical and epistemo-
logical development of ‘infinitesimal mathematics’ as it became clearly articu-
latedintheoeuvreofIbnal-Haytham.
Contributing to a more informed and balanced understanding of the internal
currentsofthehistoryofmathematicsandtheexactsciencesinIslam,andofits
adaptiveinterpretationandassimilationintheEuropeancontext,thisfundamental
textwillappealtohistoriansofideas,epistemologistsandmathematiciansatthe
mostadvancedlevelsofresearch.
Roshdi Rashed is one of the most eminent authorities on Arabic mathematics
and the exact sciences. A historian and philosopher of mathematics and science
andahighlycelebratedepistemologist,heiscurrentlyEmeritusResearchDirector
(distinguishedclass)attheCentreNationaldelaRechercheScientifique(CNRS)
inParis,andistheformerDirectoroftheCentreforHistoryofArabicandMedieval
ScienceandPhilosophyattheUniversityofParis(DenisDiderot,ParisVII).He
alsoholdsanHonoraryProfessorshipattheUniversityofTokyoandanEmeritus
ProfessorshipattheUniversityofMansourahinEgypt.
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
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
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
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
27. INSPIREDKNOWLEDGEINISLAMICTHOUGHT
Al-Ghazali’stheoryofmysticalcognitionanditsAvicennianfoundation
AlexanderTreiger
28. SHI’ITHEOLOGYINIRAN
Thechallengeofreligiousexperience
OriGoldberg
29. FOUNDINGFIGURESANDCOMMENTATORSINARABIC
MATHEMATICS
AhistoryofArabicsciencesandmathematics,Volume1
RoshdiRashed(translatedbyRogerWareham,withChrisAllenand
MichaelBarany,underthesupervisionofNaderEl-Bizri)
30. THEMUSLIMCONQUESTOFIBERIA
MedievalArabicnarratives
NicolaClarke
31. ANGELSINISLAM
Jalalal-Dinal-Suyuti’sal-Haba’ikfiakhbaral-mala’ik
StephenBurge
32. THEOLOGICALAPPROACHESTOQUR’ANICEXEGESIS
Apracticalcomparative–contrastiveanalysis
HusseinAbdul-Raof
33. IBNAL-HAYTHAMANDANALYTICALMATHEMATICS
AhistoryofArabicsciencesandmathematics,Volume2
RoshdiRashed,translatedbySusanGlynnandRogerWareham
IBN AL-HAYTHAM AND
ANALYTICAL
MATHEMATICS
A history of Arabic sciences and mathematics
Volume 2
Roshdi Rashed
Translated by Susan Glynn and Roger Wareham
Firstpublished2013
byRoutledge
2ParkSquare,MiltonPark,Abingdon,OX144RN
SimultaneouslypublishedintheUSAandCanada
byRoutledge
711ThirdAvenue,NewYork,NY10017
RoutledgeisanimprintoftheTaylor&FrancisGroup,aninformabusiness
©2013RoutledgeandCAUS
Therightoftheeditorstobeidentifiedastheauthorsoftheeditorial
material,andoftheauthorsfortheirindividualchapters,hasbeenasserted
inaccordancewithsections77and78oftheCopyright,Designsand
PatentsAct1988.
Allrightsreserved.Nopartofthisbookmaybereprintedorreproducedor
utilisedinanyformorbyanyelectronic,mechanical,orothermeans,now
knownorhereafterinvented,includingphotocopyingandrecording,orin
anyinformationstorageorretrievalsystem,withoutpermissioninwriting
fromthepublishers.
Trademarknotice:Productorcorporatenamesmaybetrademarksor
registeredtrademarks,andareusedonlyforidentificationandexplanation
withoutintenttoinfringe.
BritishLibraryCataloguinginPublicationData
AcataloguerecordforthisbookisavailablefromtheBritishLibrary
LibraryofCongressCataloginginPublicationData
TheLibraryofCongresshascatalogedvolume1ofthistitleunderthe
LCCN:2011016464
ISBN978-0-415-58218-6(hbk)
ISBN978-0-203-08434-2(ebk)
TypesetinTimesNewRoman
byCenveoPublisherServices
Thisbookwaspreparedfrompress-readyfilessuppliedbytheeditor.
Printed and bound in Great Britain by
TJ International Ltd, Padstow, Cornwall
CONTENTS
Foreword ................................................................................. xi
Preface .................................................................................... xiii
Note ....................................................................................... xv
INTRODUCTION: IBN AL-HAYTHAM AND HIS WORKS ON INFINITESIMAL
MATHEMATICS
1. Ibn al-Haytham: from Basra to Cairo .............................................. 1
2. Al-Îasan ibn al-Îasan and MuÌammad ibn al-Îasan:
mathematician and philosopher ......................................................... 11
3. The works of al-Îasan ibn al-Haytham on infinitesimal mathematics ......... 25
CHAPTER I: THE QUADRATURE OF LUNES AND CIRCLES
1.1. INTRODUCTION ....................................................................... 39
1.2. MATHEMATICAL COMMENTARY ................................................ 42
1.2.1. Treatise on lunes ................................................................. 42
1.2.2. Treatise on the quadrature of the circle ........................................ 46
1.2.3. Exhaustive treatise on the figures of lunes .................................... 49
1.3. TRANSLATED TEXTS
1.3.1. Treatise on Lunes ............................................................... 93
1.3.2. Treatise on the Quadrature of the Circle .................................... 99
1.3.3. Exhaustive Treatise on the Figures of Lunes .............................. 107
CHAPTER II: CALCULATION OF VOLUMES OF PARABOLOIDS AND SPHERES
AND THE EXHAUSTION METHOD
2.1. INTRODUCTION ....................................................................... 143
2.2. MATHEMATICAL COMMENTARY ................................................ 144
2.2.1. Calculation of volumes of paraboloids ........................................ 144
2.2.2.1. Arithmetical lemmas ................................................... 144
2.2.2.2. Volume of a paraboloid of revolution ................................ 151
2.2.2.3. The volume of the second species of paraboloid ................... 160
2.2.2.4. Study of surrounding solids .......................................... 164
2.2.3. Calculation of the volume of a sphere ......................................... 168
2.3. TRANSLATED TEXTS:
2.3.1. On the Measurement of the Paraboloid ...................................... 177
2.3.2. On the Measurement of the Sphere .......................................... 221
2.3.3. On the Division of Two Different Magnitudes as Mentioned
in the First Proposition of the Tenth Book of Euclid’s Elements .............. 235
CHAPTER III: THE PROBLEMS OF ISOPERIMETRIC AND ISEPIPHANIC
FIGURES AND THE STUDY OF THE SOLID ANGLE
3.1. INTRODUCTION ....................................................................... 239