Treść książki
Przejdź do opcji czytnikaPrzejdź do nawigacjiPrzejdź do informacjiPrzejdź do stopki
16
MarekOtisk
poratingthefirstbookoftheso-calledpseudo-Boethius’sGeometryII
14
andby
theshorttextspennedbyHermanofReichenau(Qualitermultiplicationesfiant
inabaco)
15
andLaurentofAmalfi(Dedivisione)
16
.Duringthesecondhalfof
the11
th
centuryandinthebeginningofthe12
th
century,thenumberoftextson
theuseoftheabacusaswellasthenumberofabacistsincreased.Amongthe
mostnotablewereGarlandusCompotista(Deabaco)
17
,RadulfofLaon(Liber
deabaco)
18
,AdelardusofBath(Reguleabaci)
19
,andTurchillusCompotista
(Regunculesuperabacum)
20
.
Earlierattemptsatachronologicalorderingoftheoldestabacustexts
21
have
beensignificantlyrevisedintherecentpast,thankstothemoredetailedstudies
ofthesurvivingdepictionsoftheabacusfromtheendofthe10
th
aswellasthe
11
th
century
22
.Today,theprevailingopinionisthatitwasalreadyattheendof
the10
th
centurywhentheuseofArabicnumerals(socalledghubar)beganin
Europe;however,theywereonlyusedinabacuscalculations.Thehypothesis
concerningGerbert’sinitiatingrolehasonceagainincreasedinpopularity,
sinceGerbertcouldhavecomeintocontactwithghubarnumeralsduringhis
stayintheshadowofthePyrenees
23
.This,inturn,constitutesthemainreason
astowhythisarticlefocusesprimarilyonthetwooldesttextualdescriptions
oftheabacuswrittenbeforetheyear1000,oratleastaroundthisyearatthe
latest,aswellasonacoupleoftheoldestsurvivingdrawingsofanabacus.
14
“Boethius”GeometrieII.EinmatematischesLehrbuchdesMittelaltersI,19.Ed.
M.Folkerts.Wiesbaden1970,pp.1371144.
15
HermannusContractus:Qualitermultiplicationesfiantinabaco.Ed.P.Treutlein.
“Bulletinodibibliografiaedistoriadellescienzematematicheefisiche”1877,no10,pp.6431
647.
16
LaurentiusAmalfitanus:Dedivisione.Ed.F.Newton.MonumentaGermaniae
Historica.QuellenzurGeistesgeschichtedesMittelalters.T.7.Weimar1973,pp.76180.
17
GarlandusCompotista:Deabaco.Ed.P.Treutlein.“Bulletinodibibliografiaedi
storiadellescienzematematicheefisiche”1877,no10,pp.5951607.
18
RadulphusLaudunensis:Liberdeabaco.Ed.A.Nagl.“AbhandlungenzurGe-
schichtederMathematik”1890,Nr.5,pp.851133.
19
AdelardusBathoniensis:Reguleabaci.Ed.B.Boncompagni.“Bulletinodibi-
bliografiaedistoriadellescienzematematicheefisiche”1881,no14,pp.11134.
20
TurchillusCompotista:Regunculesuperabacum.Ed.E.Narducci.“Bulletinodi
bibliografiaedistoriadellescienzematematicheefisiche”1882,no15,pp.1111163.
21
W.Bergmann:InnovationenimQuadrivium…,pp.2051206.
22
SeeforexampleM.Folkerts:FrüheDarstellungendesGerbertschenAbakus.In:Iti-
neramathematica…,pp.23143;Idem:Thenamesandformsofthenumeralsontheabacus
intheGerberttradition.In:Gerbertod’AurillacdaAbatediBobbioaPapadell’Anno1000.Atti
delCongressointernazionale.Ed.F.G.Nuvolone.Bobbio2001,pp.2451265,orCh.Bur-
nett:TheAbacusatEchternachinca.1000A.D.“SCIAMVS”2002,no3,pp.911108.
23
SeeRicherusRemensis:HistoriarumlibriIIIIIII,43.Ed.H.Hoffmann.Mo-
numentaGermaniaeHistorica.ScriptoresinFolio.T.38.Hannover2000,pp.1911192,or
AdemarusCibardi:HistoriarumlibriIIIIII,31.Ed.D.G.Waitz.MonumentaGermaniae
Historica.ScriptoresinFolio.T.4.Hannover1841,p.130.
