The Archimedes Palimpsest edited by Reviel Netz, William - IRCPS

13 Pages·2013·13.91 MB·English

The Archimedes Palimpsest edited by Reviel Netz, William Noel, Natalie
Tchernetska,andNigelWilson
Cambridge:CambridgeUniversityPress,2011.2vols.Pp. .ISBN978–1–
107–01684–2.Cloth£150,$240.00
700
Reviewedby
FabioAcerbi
CNRS,UMR8560CentreAlexandreKoyré,Paris
[email protected]
Thebookisanoutcomeoftheprojectofreadingwithmoderntechniques
theso-called‘Archimedeanpalimpsest’(=CodexC),aprayer-bookorεὐχο-
λόγιονretainingbeneathitssurface-textsomewritingsofArchimedesand
Hyperides as well as portions of a commentary on Aristotle’s Categories.
The Archimedean texts were identified and read for the first time when
theDanishscholarJ.L.HeibergfirstinspectedthepalimpsestinIstanbulin
summerof1906;thenon-Archimedeanfragmentshavebeenidentifiedin
theearlierstagesofthisproject. AfterHeiberg’stravelstoIstanbul,Codex
Cwasstolenandunderwentseveralvicissitudesuntilitwasrecoveredand
thenacquiredbyananonymouscollectoratanauctionin1998. Itisnow
locatedwiththeowner.
The importance of the palimpsest can be understood immediately if one
looksattheArchimedeanmanuscripttradition. Thistradition,formostof
thetreatises,derivesfromthreeindependentsources:
(a) the 10th century Codex C standing alone, the subject of the book
underreview;
(b) the lost Codex A, which can be reconstructed from a series of apo-
graphsofitthatweremadebetweenca.1455and1January1544;
(c) theLatintranslationofWilliamofMoerbeke,achievedca.31Decem-
ber1269andbasedpartlyonCodexAand,mostimportantly,partly
onafurtherArchimedeanexemplar,CodexB,lastheardofin1311.
Therefore,onlyCodexChassurvivedamongtheArchimedeanmanuscripts
writtenbeforethe13thcentury,whilethetextscontainedinCodexAandB
canonlybereconstructedbystandardphilologicalmethods. Whatismore,
the palimpsest is our unique source for two Archimedean treatises: the
©2013InstituteforResearchinClassicalPhilosophyandScience issn1549–4497(online)
Allrightsreserved issn1549–4470(print)
Aestimatio10(2013)34–46
FabioAcerbi 35
Stomachion (of which, however, only a short fragment remains) and the
celebratedMethod,addressedtothedistinguishedAlexandrianscholarEra-
tosthenes. Codex C contains also an almost complete Greek text of On
FloatingBodies,whichotherwisecanonlybereadinWilliamofMoerbeke’s
translation. ItwasonaccountofthisnewevidencethatHeibergpublished
in1910–1915acriticaleditionofArchimedes’Operaomniawhichreplaced
hisearliereditionof1880–1881[cf.1907].
The book under review is the ‘official’ outcome in print of the project of
restoring,conserving,andreadingthepalimpsestwithmoderntechniques,
aprojectthatwasdevelopedattheWaltersArtMuseuminBaltimorewhere
thepalimpsestwaslocateduntilrecently. Theresultofthisrenewedreading
isaseriesofdigitally-processedimagesoftheleavesofthemanuscript,which
arestoredonthepalimpsestwebsite[http://www.archimedespalimpsest.org/].
Theseimagescanbedownloadedfreelyandarealsoreproducedinthebook.
AfteranintroductionbyWilliamNoel,whowasapparentlythedrivingforce
ofthewholeproject,volume1isdividedintofiveparts:
adetailedcodicologicaldescriptionofthemanuscript;1
thehistoryofthecodexfromthemakingoftheεὐχολόγιονtoHei-
berg’stravelstoIstanbultoreadtheArchimedeantexts;2
∘
amonothematicsectionbyAbigailQuandton‘ConservingtheArchi-
∘
medesPalimpsest’;
descriptions of the image-processing and organization of the data
∘
mountedonthepalimpsestwebsite;3and
apresentationofthetexts.4
∘
Volume 2 contains digitally-processed images of (almost) all leaves of the
palim∘psest(eitherrectoorversoofasinglefolioinonesingleimage)with
1 Thispartwascollectivelyauthoredby‘AbigailQuandtandtheeditors’,assistedby
S.Lucà,S.Parenti,andJ.Lowden.
2 In succession: ‘The Making of the Euchologion’ by A. Quandt, ‘The Strange and
EventfulHistoryoftheArchimedesPalimpsest’byJ.Lowden,and‘ItineraArchime-
dea:OnHeiberginConstantinopleandArchimedesinCopenhagen’byE.Petersen.
3 In succession: ‘Imaging and Image-Processing Techniques’ by W.A.Christens-
Barry, R.L.Easton, Jr., and K.T.Knox; ‘Imaging with X-Ray Fluorescence’ by U.
Bergmann;and‘ThePalimpsestDataSet’byD.Emery,A.Lee,andM.B.Toth.
4 In succession: ‘The Palimpsest in Context’ by N.Tchernetska and N.Wilson, and
‘ThePlaceofCodexCinArchimedesScholarship’byR.Netz.
36 Aestimatio
facingtranscription. Theorderoftheimagesissuchastoprovideacontinu-
ousreadingoftheworksinthepalimpsest;thefoliationofCodexCbeing
therebyperturbed,thereadercanlocatespecificfoliosbyresortingtothe
useful‘ConcordanceofFoliations’thatclosesvolume1. Whentheoriginal
foliosaretoodamagedtoproducereadableimages,thesearereplacedby
Heiberg’s photographs or, if none of these was available, by scans of his
criticaleditionofArchimedes[!]. (Inthelattercase,Ihavebeenunableto
findindicationsastowhatthefacingtranscriptioncorrespondsto.)
Thetranscriptionshavebeencarriedoutbyahostofscholars. Inthecase
oftheHyperidestexts,thejobwasdonewellbeforethepublicationofthe
book.5 The Archimedean writings were transcribed by Nigel Wilson and
RevielNetz.
TheArchimedesPalimpsesthasseveralmerits: itpresentsallimagesina
handyformat,thoughformorerefinedinvestigationstheimagesstoredon
thewebsitearebetter(‘weighingin’atover250Mbeach). Further,itcollects
in a single publication the transcriptions and an introduction to the non-
Archimedeantexts,explainsindetailtheimage-processingtechniques,and
offersamostinterestingexpositionoftheactionsandtechniquesthatwere
usedtoconservethepalimpsest. Mostchaptersofthebookarepleasantto
readandevenentertaining. Itis, however, lesssatisfyingifonewishesto
useitforscholarlypurposes.
Letussayfirstthattheonlymaterialofanyvalueaboutthenon-Archimedean
texts is the transcriptions. The scanty and quite generic information on
thesetextspresentedinthesection‘ThePalimpsestinContext’(21/ pages
2
onHyperides,3pagesonthecommentaryonAristotle’sCategories)does
notevenprovideafullbibliographicalrecordinthefirstcase,and,inthe
second,consistsinnomorethananinconclusivediscussionofauthorship
andsomepaleographicalnotes.
So let us then turn to Archimedes. I shall focus first on the ‘diacritic and
punctuation’sectionat1.46–47. Therearefourpiecesofinformationinit
requiringcomment.
(1) Regardingthepresenceofan‘unexplainedabbreviation’inSpiral
Lines,prop.24,onereadsthat‘therequiredtextisτριπλαϲίωνἔϲτω’.
5 Seethebibliographyappendedattheendofthisreview.
FabioAcerbi 37
Infact,itissimply«τριπλαϲίων»,asthetranscriptionat2.173hasit.
Theabbreviationisclearlyvisibleeveninthefacingimage: itisa
«Γ»withasuperimposed«π». Theexplanationisstraightforward: in
mathematicalmanuscripts,«Γ»(usually,«Γ̅»)isthecardinal‘three’,
«Γ΄»istheordinal‘third’orthealiquotpart‘1/’,«Γ»withasuperim-
3
posed«κ»standsfortheadverb«τριάκ̲ιϲ»,6«Γ»withasuperimposed
«π»standsfor«τριπ̲λαϲίων».7
(2) It is reported that the sign for «ἔϲτω» is ‘fairly rare but not totally
unknown’. Hundreds of instances of it can be found in reading
mathematical manuscripts [see also 40n13 below]. Where do we
havetosetthethresholdforasign’sbeingnolonger‘fairlyrare’?
(3) A variant of the sign for «ἔϲται» in the Method8 is described as ‘a
semicirclewithtwodots’. Itissaidtobe‘exceptionallyrare’onthe
groundsofevidencethatweowetoG.Vitellianddatingto1885.9
More details would have been welcome, as some strokes of the
palimpsest’ssignmightnolongerbevisibleandinsensiblydifferent
variantsofitareattested: fouroccurrencesofonesuchvariantoccur
inthefirstfolioofVat.gr.218[seeFigure1].
Figure1.Thesignfor«ἔϲται»inVat.gr.218,f.1
Inaddition,itisquestionablethatwhatcanbeseeninthe250Mb
digital image can be termed without hesitation ‘a semicircle with
twodots’: Heibergreadorguessedthestandardsignfor«ἐϲτι»(an
oblique straight stroke with two dots in the same positions as the
6 The Cod.Matrit.4678 (Diophantus) offers many occurrences of this abbreviation,
andforseveralnumeraladverbs.
7 Or «τριπλάϲιοϲ». On what grounds, then, did the editors choose the former? Of
course, the fact that this is the reading of the other branch of the Archimedean
traditionshouldnotinterferewithatranscriptionofCodexC.
8 Atf.158r,col.1,line6=2.120=Heiberg1910–1915,2.500.4.
9 ThesigncanbefoundinLaur.Plut.32.9andisrecordedinAllen1889andCereteli
1904.
38 Aestimatio
implied one for «ἔϲται») and I suspect that his reading should be
retained.
(4) An abbreviation closing propositions 3 and 4 of the Method that
lookslike«Ο̅Ι̅»andapparentlystandsforthecanonical«ὅπερἔδει
δεῖξαι».10Thisisleftunexplained: theauthorsrecall,justtodismiss
theconnection,thatthe‘combinationofthefirstandlastlettersof
thewordsabbreviatedremindsoneofnominasacra’. Yetthebar
onf.63visquitedistantfromtheunderlyinglettersincomparison
with the location it has when it marks denotative letters. Maybe
the copyist only found in his exemplar, and misunderstood, the
residualhorizontalstrokeofasuperimposed«π»,whichwasinfact
a canonical abbreviation for «ὅπερ» [see, e.g., Ephrem’s Euclid in
Laur.Plut.28.3]followedbysomediacriticalsignthathemisreadfor
an «Ι». Ending a proposition with a simple «ὅπερ» + sign11 is not
uncommon,aswegatherfromPappus’Vat.gr.218[seeAddendum,
p.44]
Turningfromthe‘diacriticandpunctuation’sectiontothesectionon‘codex
CandArchimedeanscholarship’,Igivethreeexamplesofitsunreliability,
bearingrespectively: onthetreatmentofthe‘Archimedeanscholarship’in
question,ontheevidencecomingfromthefigures,andonthatcomingfrom
thetranscription.
First,NetzassertsthatOntheSphereandtheCylinder‘iswritteninpure
Koinedialect,notracesremainingofDoric’[1.277]. Thisisstrictlyspeaking
false, as already noted by Heiberg [1879, 69–70], since the word «τῆνοϲ»
is Doric [f.109v, col. 2, line 2 = 2.190 = Heiberg 1910–1915, 1.4.15]. Netz
suggeststhatthistreatisewasoriginallywritten‘in(someversion)ofDoric,
whichthenbecomeskoinicizedinthemilieuofEutocius’,andassertsthat
thisis‘thecommunisopinio,totheextentthatanyoneotherthan[he]has
opinionsonthematter’[1.278]. ContrarytowhatNetzsuggests,thisreallyis
acommunisopinio,sinceithasbeenpartofArchimedeanscholarlyfolklore
sinceHeiberg’s‘PhilologischeStudienzugriechischenMathematikern’[1883,
543–544]. Still,thereareseriousproblemswiththisview. Ontheonehand,
the Archimedean lemmata accompanying the Eutocean commentary On
10 At ff.63v, col.2, line 30 = 2.84 = Heiberg 1910–1915, 2.454.7; 44v, col.1, line 36 =
2.88,whichwasnotreadbyHeiberg.
11 Onf.44vofthepalimpsest,theabbreviationisfollowedbytheusualsign‘:—’.
FabioAcerbi 39
Figure2.ThediagramofSpiralLinesprop.13inMarc.gr.305,f.70r
Figure3.ThediagramofSpiralLinesprop.13inLaur.Plut.28.4,f.79v
40 Aestimatio
the Sphere and the Cylinder are in Koine; on the other hand, Eutocius
himselfassertsthathehadrecoveredwhathetooktobealostArchimedean
appendixtoOntheSphereandtheCylinderbecauseitretainedinpartthe
author’s ‘beloved Doric dialect’, and that he set out to rewrite it. Since a
similarclaimisnotmadeconcerningthemaintextofOntheSphereand
theCylinder,onemaysubmitthatthedoricismsofthistreatisewerelost
beforeEutociusbeganhiscommentaryonitbutthathetookitasobvious
thattheArchimedesshouldhavewrittenhistreatiseinDoric.
Second,theevidencefromthefiguresistreatedunreliably. Letusconsider
the nearly incredible 12-line paragraph at 1.284, inclusive of footnote 51.
Theaimistoshowthat‘[a]ncientdiagramsseemtowishtoemphasizethe
impossibilityofanimpossiblecase’envisagedinaproofbyreductio. A‘very
clearexample’isallegedlyprovidedbythefigureassociatedwithSpiralLines
prop.13andsaidbyNetztobe‘[his]reconstruction’ofadiagramrepresenting
asabrokenstraightlinetheimpossibletangentattwopointsofaspiral. The
figurepresentedbyNetzcannotbetermeda‘reconstruction’becauseitis
attested exactly as it is reproduced, in Codex C (with the omission of the
letters«Ε»and«Ζ»)andintwoapographsofValla’slostCodexA,namely,
inMarc.gr.305,f.70r[seeFigure2,left],andPar.gr.2361,p.204. WhatNetz
omitstosayisthattheothertwoapographsofCodexA[Laur.Plut.28.4,f.
79v, andPar.gr.2360, f.51r]andWilliamofMoerbeke’stranslationinVat.
Ottob.lat.1850,12whichmostprobablyderivesfromCodexAitself,havetwo
figuresdifferentfromtheonejustseenbutsimilartoeachother: theseare
reproducedfromthefirstmanuscriptasFigure3andfromthesecondas
Figure4below.13
12 And in the margin of Marc.gr.305, as we see again in Figure 2. Note that it is
a figure with Latin lettering, identical with the one in the Vat.Ottob.gr.1850; this
phenomenonisuniqueinMarc.gr.305.
13 InFigure3,IhaveincludedalsoastretchoftextfromSpiralLinesprop.14inorder
toshowfourconsecutiveoccurrencesofthesignfor«ἔϲτω»discussedunderpoint2
above; these are all contained in the three lines centered on the horizontal stroke
ontheleftmargin. Thereadercaneasilyestimatebyextrapolationhowmanyoc-
currencesofthissignarefoundinLaur.Plut.28.4,writteninanimitativescriptby
JohannesScutariotesinabout1491–1492[Rollo2012].
FabioAcerbi 41
Figure4.ThediagramofSpiral
Linesprop.13inPar.gr.2360,f.51r
It follows from this that Codex A had two figures, a ‘weird’ and a more
‘regular’one. The‘regular’diagramwasadded,probably,inthemarginsat
somestageofthetradition,simplybecausetheformerdoesnotrepresent
the‘impossible’configurationsupposedinSpiralLinesprop.13: thereduc-
tio proves that straight lines ΖΕ and ΘΑ intersect each other somewhere
betweenΘandΑ,whichissubsequentlyshowntobeimpossible. Asacon-
sequence,the‘weird’diagramdoesnotevenrepresentthe‘impossiblecase’:
itissimplyandplainlywrong. Furthermore,onemightaskwhatisa‘weird’
behaviorofastraightlineandwhatisamore‘regular’one. Netzexpendsa
rhetoricalquestionandanexclamationmarktohighlightthe‘contortions’
that the (broken) line ‘has to go through’! Well, just one ‘contortion’, the
pointofinflexion. Still,itisdebatablewhichisthelinethathashadtogo
throughmore‘contortions’,whetheritis
theoneinFigure2(left)—recallthatforaGreekgeometerabroken
straightlineremainsjustasingle,thoughbroken,straightline,
theoneinFigure3: atangentthatcrossesacurve—quiteanimpossi-
∘
bleobjectafterall,or
theoneinFigure4: the‘straightline’thathasacurvedportion,asit
∘
partlycoincideswiththespiral—thisisHeiberg’sfigure.
Butth∘isisnottheendofthestory. Itremainstoreadfootnote51;Iquoteit
infull,insertingmycommentsinitalics:
42 Aestimatio
ThefigureitselfisidenticalinCodicesAandC;[Thisisfalse,aswehavejust
seen.] however, CodexA[Itshouldbe‘CodexC’.] omitstheletters«Ε»and
«Ζ»(onceagainweseeanerrorinthemathematicalexecution[Whatdoesthis
mean?] ofCodexC;notthatCodexAisfreeofsuchmistakes). Thisdiagramin
Heibergisnotonlygeometricallydifferent[Ofcourse,sincehechosetheother
figurethatisattestedinthemanuscripts.] butalso,nearlyuniquely,containsa
misprint: ΟforΘ. [ThereisnomisprintinHeiberg’sedition: Netzapparently
hasinhishandsthephototypesetreproductionmadein1972ofthe1913
volume. Suchreproductions,asoftenhappens,tendtofadeoutsomedetails
oftheletters. Inthereprintof1972,thehorizontalstrokeofthe«Θ»,which
featuresasitshouldintheoriginalfigureof1913,hasnearlydisappeared,the
outcomebeingan«Ο»withanirregularinternaloutline. Itiseasytocheck
thisbylookingatthesamefigureinHeiberg1880–1881,2.56,acompletescan
ofwhichisavailableonline. Ofcourse,Heibergrecycledtheclichésofthe
diagramsfromhisfirsteditiontothesecond.]
Figure5
Third,theevidencefromthetranscribedtextistreatedunreliably. Theentire
interpretationoftheStomachion,14aworkpreservedonlyinthepalimpsest,
asdealingwithcombinatorics‘hangson’readinga«πλῆθοϲ»thatHeiberg
‘missed’[1.316n78]. Threeimagesareadducedat1.293asevidenceforthere
beingsuchaword[seeFigure5]. Ichallengeanyonetoseeit. Heiberghad
about15workingdaystoreadthepalimpsestinIstanbul;hewasgranted
nomorethansixhoursaday—still,onthewaybackfromhislastjourney,
hewrotetoacolleagueofhisinCopenhagenthat,afterall,itisdangerous
tostare too longatletters: theytend togeneratewholewords. Staringat
digitalimagesapparentlyhasthesameeffect. Butthereismoretotheissue.
Netzonlysaysat1.316n77thattheclausecontainingthecrucialwordmust
be corrected to accommodate for the presence of «πλῆθοϲ» («ὀλίγον» for
the palimpsest’s «ὀλίγων»); the correction is tacitly included in the clause
14 IurgethereaderconversantwithItaliantolookatMorelli2009.
FabioAcerbi 43
whenthisisdiscussedat1.293butthe‘official’transcriptionat2.285,has
«ὀλίγων»—thankfully.
The goal of the ‘transcription’ of the Greek text is ‘to produce the best
reconstructionpossibleofthereadinginthecodexasitexistedinthetenth
century’;therefore,it
wasmadeonthebasisofimagesofCodexC,Heiberg’sreadingofthemanuscript
astheycanbededucedfromhiscriticaledition ,andontheimmediatetextual
contextofthecharactersnolongervisible. [2.vii]
Howcanthisbecalleda‘transcription’? Anyre…adingcanbejustifiedresting
onsuchprinciples. Thesehavealsotheharmlessbutdisturbingconsequence
ofmakingtheauthorsencumbertheirapparatuswith100sofdoricismsre-
storedbyHeiberginhiscriticaltextofthestill‘unkoinicized’treatises.15To
giveanextremeexample,theapparatustothetranscriptionon2.19[ff.14v+
19r]counts113items,108ofwhicharepseudo-variantsindicatingrestored
doricisms: 27«ποτί»insteadof«πρόϲ»,41«τᾶϲ»insteadof«τῆϲ»,andsoon.
InthetranscriptionoftheinscriptionsandsubscriptionsoftheArchimedean
treatises,thereisalsoamistake: oneofthecrossessurroundingtheinscrip-
tion of On the Sphere and the Cylinder at f.109r, col.2, is taken for an
abbreviationofanarticle«τῆϲ»,sothatat2.189,wereadtheungrammati-
caltitle«ΑΡΧΙΜΗΔΟΥϹ(ΠΕΡΙ)Τ(ΗϹ)ϹΦΑΙΡΑϹ(ΚΑΙ)ΚΥΛΙ(Ν)ΔΡΟΥ».16
Further,severalfiguresaredrawnincorrectly;ineachcase,theerroneous
diagramquiteappropriatelycountsasaseparativevariantwithrespectto
the‘readings’attestedinthetraditionofthelostcodexA,therebyenhancing
theallegeddivergencebetweenAandC.17
15 Heiberglistedalloftheseinterventionsat1910–1915,2.x–xviii.
16 IowetheexampleoftheinscriptionofOntheSphereandtheCylindertoD’Alessan-
droandNapolitani2012.
17 RecallthatoneofthedisturbingfeaturesofCodexCisthatitstextquiteoftencoin-
cideswithA’s: asHeibergputit,CodexC
saepius,quamexspectaueris,cumAinerroribusconspirat,nonmodoinlacu-
nis ,sedetiaminerroribusminoribus . [1910–1915,3.lxxxix]
Forfurtherdetailsconcerningtheincorrectlyreportedfigures,seeagainD’Alessan-
droand…Napolitani2012. …