Ibn al-Haytham’s theory of conics, geometrical constructions and practical geometry. A history of Arabic sciences and mathematics 3 PDF
Preview Ibn al-Haytham’s theory of conics, geometrical constructions and practical geometry. A history of Arabic sciences and mathematics 3
IBN AL-HAYTHAM’S THEORY OF CONICS, GEOMETRICAL CONSTRUCTIONS AND PRACTICAL GEOMETRY This book provides a unique primary source on the history and philosophy of mathematics and science from the medieval Arab world. The present text is complemented by two preceding volumes of A History of Arabic Sciences and Mathematics, which focused on founding figures and commentators in the ninthandtenthcenturies,andthehistoricalandepistemologicaldevelopmentof ‘infinitesimal mathematics’ as it became clearly articulated in the oeuvre of Ibn al-Haytham. Thisvolumeexaminestheincreasingtendency,aftertheninthcentury,toexplain mathematical problems inherited from Greek times using the theory of conics. RoshdiRashedarguesthatIbnal-Haythamcompletesthetransformationofthis ‘areaofactivity’intoapartofgeometryconcernedwithgeometricalconstructions, dealingnotonlywiththemetricalpropertiesofconicsectionsbutalsowithways ofdrawingthemandpropertiesoftheirpositionandshape. Includingextensivecommentaryfromoneoftheworld’sforemostauthorities onthesubject,thisbookcontributesamoreinformedandbalancedunderstanding of the internal currents of the history of mathematics and the exact sciences in Islam,andoftheiradaptiveinterpretationandassimilationintheEuropeancon- text.Thisfundamentaltextwillappealtohistoriansofideas,epistemologistsand mathematiciansatthemostadvancedlevelsofresearch. 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) in Paris, and is the Director of the Centre for History of Medieval Science and PhilosophyattheUniversityofParis(DenisDiderot,ParisVII).Healsoholdsan HonoraryProfessorshipattheUniversityofTokyoandanEmeritusProfessorship attheUniversityofMansourahinEgypt. J. V. Field is a historian of science and is a Visiting Research Fellow in the Department of History of Art and Screen Media, Birkbeck, University of London,UK. 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 andcivilisations.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 Conflictorconciliation 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 (cid:2) Annotatedtranslationofal-T.a¯hiral-H.adda¯d’sImra’tuna¯ fi‘l-shar¯ı awa (cid:2) ’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 ExpandingthecrescentfromtheMediterraneantotheIndianOcean (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 TheAkhbarmajmu’a DavidJames 27. INSPIREDKNOWLEDGEINISLAMICTHOUGHT Al-Ghazali’stheoryofmysticalcognitionanditsAvicennianfoundation AlexanderTreiger 28. SHI’ITHEOLOGYINIRAN Thechallengeofreligiousexperience OriGoldberg 29. FOUNDINGFIGURESANDCOMMENTATORSINARABIC MATHEMATICS AhistoryofArabicsciencesandmathematics,Volume1 RoshdiRashed(translatedbyRogerWareham,withChrisAllenandMichael Barany,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) 34. GHAZALI’SPOLITICSINCONTEXT YazeedSaid 35. ORIENTALISMREVISITED Art,LandandVoyage EditedbyIanRichardNetton 36. IBNAL-HAYTHAM’STHEORYOFCONICS,GEOMETRICAL CONSTRUCTIONSANDPRACTICALGEOMETRY AhistoryofArabicsciencesandmathematics,Volume3 RoshdiRashed,translatedbyJ.V.Field IBN AL-HAYTHAM’S THEORY OF CONICS, GEOMETRICAL CONSTRUCTIONS AND PRACTICAL GEOMETRY A history of Arabic sciences and mathematics Volume 3 Roshdi Rashed Translated by J. V. Field Firstpublished2013 byRoutledge 2ParkSquare,MiltonPark,Abingdon,OX144RN SimultaneouslypublishedintheUSAandCanada byRoutledge 711ThirdAvenue,NewYork,NY10017 RoutledgeisanimprintoftheTaylor&FrancisGroup,aninformabusiness ©2013RoutledgeandCAUS TherightofRoshdiRashedtobeidentifiedasauthorofthisworkhasbeen assertedbyhiminaccordancewithsections77and78oftheCopyright, DesignsandPatentsAct1988. Allrightsreserved.Nopartofthisbookmaybereprintedorreproducedor utilisedinanyformorbyanyelectronic,mechanical,orothermeans,now knownorhereafterinvented,includingphotocopyingandrecording,orin anyinformationstorageorretrievalsystem,withoutpermissioninwriting fromthepublishers. Trademarknotice:Productorcorporatenamesmaybetrademarksor registeredtrademarks,andareusedonlyforidentificationandexplanation withoutintenttoinfringe. BritishLibraryCataloguinginPublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary LibraryofCongressCataloginginPublicationData TheLibraryofCongresshascatalogedvolume1ofthistitleunderthe LCCN:2011016464 ISBN:978-0-415-58215-5(hbk) ISBN:978-0-203-59770-5(ebk) TypesetinTimesNewRoman byCenveoPublisherServices Thisbookwaspreparedfrompress-readyfilessuppliedbytheeditor CONTENTS Foreword .................................................................................. xiii Preface ..................................................................................... xv INTRODUCTION: CONIC SECTIONS AND GEOMETRICAL CONSTRUCTIONS .......................................................................... 1 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 BANª MªSÆ’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 Banº Mºsæ ..................... 273 CHAPTER III: PROBLEMS OF GEOMETRICAL CONSTRUCTION ............... 289 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-Sijzî against Abº al-Jºd ............................... 300 3.1.4. The lemmas for the construction of the heptagon: the division of a segment ....................................................................... 314 3.1.4.1. Archimedes’ division (D ) .............................................. 315 1 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-Qºhî and al-∑æghænî ............................. 321 3.1.4.1.3.1. Al-Qºhî: the first treatise .................................... 321 3.1.4.1.3.2. Al-∑æghænî(cid:3)..................................................... 326 3.1.4.1.3.3. Al-Qºhî: the second treatise .............................. 333 3.1.4.2. The range studied by Abº al-Jºd and al-Sijzî (D ) ................... 341 2 3.1.4.3. Abº al-Jºd’s range (D ) ................................................. 351 3 3.1.4.4. Comparing the ranges: Abº al-Jºd, al-Shannî, Kamæl al-Dîn ibn Yºnus ........................................................... 353 3.1.4.5. Ibn al-Haytham’s ranges (D and D ) ................................. 360 4 5
Description:The list of books you might like
