Treść książki
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28
MarekOtisk
as(uncia,duellaand,ontwooccasions,sicilicus),the[Pa]focusesonscripu-
lusanditsrelationtoasor,inthecaseofsmallervalues,itaddsmutualvalues
scripulus1obolusandobolus1cerates1calcus.Whileabacus[Pa]doesnot
includethehexameteronGerbert’sintroductionoftheghubarnumeralstothe
LatinWest,itplacesthevaluesdeterminedbythenumberfiveinsertedintothe
particularcolumn,i.e.thesemi-valuesofthedecimalscalesbytheborderline
betweenthesecondandthirdhorizontalsection.Here,thescribemadeaner-
ror,since,inthethirdcolumnontheleft(10
24
),hewrotethesamecharacters
asforthedecimalvaluesinsteadofthehalf-value(correctly,itshouldread
VCCCC).Furthermore,nearthedividinglinebetweenthefirstandsecond
ˉˉˉˉˉ
horizontalsections,aheadofthemarkingsofthecolumnswithvaluesofhundreds
ofthousands,the[Pa]abacusexpressesthevaluesofthecolumnswiththehelp
oftheRomannumeralforfive(scales10
1
to10
5
)andthescaleofunits(10
0
)as
twicethevalueofthesemis.Anothererrorinthe[Pa]abacusisthefactthatthe
symbolsC,DandMarewritteninthefirstthreecolumnsontheright,dedi-
catedtocalculationswithfractionsandthereforedevoidoftheneedforwritten
decimalvalues.Finally,itisnecessarytomentionthatinthesmallestarches,the
western-Arabicnumeralsareincludedin[Pa]andomittedin[B].Itseems,there-
fore,thatthedrawingofthe[Pa]abacuswasstronglyinspiredby[B];however,
itisnotonlyitsvariation,astheauthorof[Pa]addedoramendedsomeimpor-
tantorinterestinginformation,thoughnotalwaysinthecorrectway.
Thelastmanuscriptanalysedinthearticleisacomputisticmanuscriptfrom
St.John’sCollege,Oxford,datingbacktothefirstquarterofthe12thcentury.It
containsaparticularlydecorativedrawingofa27-columnabacus[J](Oxford,
St.John‘sCollege,MS17,48v149r)46.Ofalltheabacusesdiscussedinthisar-
ticle,thisistheyoungest,yet,atthesametime,itrepresentsaverypreciselyex-
ecutedcomputingtool.Apartfromthecolumnsforcalculationswithfractions,
italsocommunicatesallotherinstructionalinformation(seeplate8):everyco-
lumnismarkedwiththevalueofthedecimalscale;thetriadofcolumns(with
thecharactersC,DandM/S)isalwaysroofedbyalargearch(asin[E],[B],
[P],and[Pa])withtwoothersmallerarchesinside1onelargerthantheother,
roofingtwocolumns,andthesecondsmallerarchforunits(justasinBernelius’
description);inthesmallestarch,thewestern-Arabic,Greek,andRomannume-
ralsareinscribedwiththenamesofHindu-Arabicnumeralsabove.Althoughthe
columnsdedicatedtocalculationswithfractionsdonotdisplayRomanfractions,
theirsymbols,names,andsomeoftheirratiosarewritteninthebottomsection
46
Abacusisavailableonline:http://digital.library.mcgill.ca/ms-17/folio.php?p=48v;resp.
http://digital.library.mcgill.ca/ms-17/folio.php?p=49r.Foritsanalysis,interpretationincl.pho-
tocopiesseeG.R.Evans:DifficillimaetArdua:theoryandpracticeintreatisesontheaba-
cus,95011150.“JournalofMedievalHistory”1977,no3,pp.21138;orIdem:Schoolsand
scholars:thestudyoftheabacusinEnglishSchoolsc.9801c.1150.“TheEnglishHistorical
Review”1979,no94,pp.71189.
