Introductio
Althoughwehaveenteredtheageofelectroniccomputers,lookingattheancientChineseabacus,wecan’thelpbutadmirethegreatwisdomofourancestors.Thegeneralabacusismostlymadeofwood(orplasticproducts).Astringofequalnumbersofabacusbeadsarrangedinarectangularwoodenframeiscalledafile.Abeamdividesthebeadsintoupperandlowerparts.Eachabacusintheupperhalfrepresents5,Eachbeadinthelowerhalfrepresents1.Fromrighttoleft,eachbeadrepresentsone,ten,hundred,thousand,andtenthousanddigitsindecimal.Withtheadditionofsoftware-asetofcalculationformulasforfingerdialingrules,variouscomplexcalculationscanbesolved,andevenmultipleprescriptionscanbemade.TheabacusisthepredecessorofmoderncomputersandthesymbolofancientChinesecomputingtechnology.
Theabacusshapesystem
Thenewshapeoftheabacusisarectanglewithawoodenframeonthecircumferenceandastraightcolumninside,commonlyknownas"file".Generallyfrom9to15gears,thebeamisusedinthemiddleofthegear,twobeadsonthebeam,eachbeadcountsfive,andfivebeadsunderthebeam,eachbeadcountsone.Afterpositioning,thebeadscanbeusedforcalculation,whichcanbeadded,subtracted,multipliedanddivided.Andotheralgorithms.
Theexistingabacushasdifferentshapesandmaterials.Thegeneralabacusismostlymadeofwood(orplasticproducts).Theabacusconsistsofaseriesofabacusbeadsarrangedinarectangularwoodenframeforseveraldays.Abeamdividesthebeadsintoupperandlowerparts,andtheabacusrunsthroughastraightcolumn.Commonlyknownas"gear",itisgenerally9gears,11gearsor13gears.Inthemiddleofthefile,thereisabeam,with1beadonthebeam,andthisbeadis5;andthereare5beadsunderthebeam,andeachbeadis1.
Maincategories
ItisworthnotingthatthetermabacusdoesnotspecificallyrefertoChineseabacus.Judgingfromtheexistingliterature,manyancientcivilizationshadtheirowncalculationtoolssimilartotheabacus.VarioustypesofabacusinancientandmodernChinaandabroadcanberoughlydividedintothreecategories:sandtabletype,abacustype,andabacustype.
Thesandtableiscoveredwithfinesandonthetabletop,stoneslab,etc.Peopleusewoodenstickstowrite,drawpicturesandcalculateonthefinesand.Later,insteadoflayingsand,severalparallellineswerecarvedontheboard,andsmallstones(called"operators")wereplacedontheboardtocountandcalculate.Thisistheabacus.Aone-meter-longmarbleabacusfoundinSalamis,Greece,inthemiddleofthe19thcentury,istheancientGreekabacus,anditisnowintheAthensMuseum.TheabacushasalwaysbeenanimportantcalculationtoolintheMiddleAgesinEurope,buttherearebigdifferencesinform.Thelinesarestraightandhorizontal,theoperatorsareroundorflat,andsometimestheyareconical(similartocheckers),andtheyarealsomarkedwithnumbers.WearingabacusreferstoChineseabacus,JapaneseabacusandRussianabacus.TheJapaneseabacusiscalled"TenLupan".ThedifferencefromtheChineseabacusisthatthelongitudinalsectionoftheabacusisnotanoblatebutarhombus,withasmallersizeandalargernumberofgrades.TheRussianabacushasanumberofcurvedwoodenstripsinlaidhorizontallyinawoodenframe,eachwearing10abacusbeads.Amongthevariousancientabacusintheworld,theChineseabacusisthemostadvancedabacustool.
Theoriginofdevelopment
TheabacusisatraditionalChinesecalculationtool.IthasgraduallyevolvedfromacalculationthathasbeencommonlyusedasearlyastheSpringandAutumnPeriod.ItisnotonlyanancientChineseitemAnimportantinvention,anditisacalculationtoolthatwaswidelyusedbypeoplebeforetheappearanceofArabicnumerals.Chinaisthehometownoftheabacus.Today,whencomputersarewidelyused,theancientabacushasnotbeenabandoned,butisstillfavoredbymanypeoplebecauseofitsflexibilityandaccuracy.Therefore,peopleoftencomparetheinventionoftheabacuswiththefourgreatinventionsofancientChina,andbelievethattheabacusisalsoamajorcontributionoftheChinesenationtomankind.However,whendidChinastarttohaveanabacus?SincetheQingDynasty,manymathematicianshavestudiedthisissue,andJapanesescholarshavealsoputalotofenergyintoit.However,duetothelackofsufficientevidence,theissueoftheoriginoftheabacusisstilldividedtoday.
TheQingDynastymathematicianMeiQizhaoandothersbelievethattheabacusoriginatedinmycountryduringtheEasternHanandSouthernandNorthernDynasties.ThebasisisthattheEasternHanmathematicianXuYueoncewrotea"SuccessofMathematics",inwhich14kindsofalgorithmsaredescribed,the13thiscalled"AbacusCalculation",andsaid:"Abacuscalculation,controlbeltfouro'clock,longitudeandlatitudethreetalents."Later,themathematicianZhenLuanoftheNorthernZhouDynastymadeacommentonthispassage:"Thestereotypeisthreepoints,theupperandlowertwopointsareusedtostopthebead,andthemiddlepointisusedtodeterminetheposition.Eachhasfivebeads,andtheupperoneandthelowerfourbeadsaredifferentincolor.,Thebeadsofdifferentcolorsonthetoparefive,fourbeadsonthebottom,andonebeadeach.Tothenextfourbeadsareled,sothe'cloudbeltfouro'clock'.Itsbeadsswiminthethreedirections,sothecloud'sthreelatitudesandlongitudesarealso"Thesewordsareconsideredtobetheearliestrecordsofabacusinourcountry.However,somescholarsinmoderntimesbelievethattheabacusdescribedin"ShushuJiyi"isatbestacountingtoolorasimplearithmeticboardthatcanonlybeusedforadditionandsubtraction,whichisnotthesameastheabacusthatappearedlater.
QianDating,ascholarintheQingDynasty,andothersbelievedthattheabacusappearedinthemiddleoftheYuanDynastyandwaswidelyusedbytheendoftheYuanDynastyandthebeginningoftheMingDynasty.ThebasisisthatTaoZongyioftheYuanDynastyquotedtheproverbofthetimein"TheWellBeads"inthe29thvolumeof"NancunShuoGenglu":Dialautomatically;forawhile,theJapaneseabacusbeads,andthedialwillmove;afteralongtime,theBuddhawilltopthebeads,andthespeechwillremaincalmthroughouttheday,evenifdialed,itwillnotmove."Latergenerationscalledthis"threebeaddrama."Comparingveteranservantsandmaidstoanabacusbead,flickingandflicking,thisshowsthattheabacuswasverypopularamongthepeopleatthattime.AttheendoftheSongDynastyandthebeginningoftheYuanDynasty,LiuYinalsohadafive-characterquatraintitled"Abacus"inthebook"Mr.Howhardisit?”ThisisalsoastrongproofthattheabacusappearedintheYuanDynasty.Inaddition,inthesection"PangJutuMisplacedNextLifeDebts"in"YuanquXuan",itwasalsomentionedthat"Gototheabacusandsetasidemyage".IntheMingDynasty,inthe"LubanWoodenScriptures"compiledduringtheYongleperiod,therewerealreadyspecificationsanddimensionsformanufacturingabacus:"Abacustype:onefootandtwoincheslong,fourinchesandtwocentsbig.Theframeissixminutesthick,nineminutesbig,...Onlinetwosons,oneinchonepoint;offlinefivesons,threeinchonepoint.Lengthandsize,youcandoitforyou.”Inaddition,XuXinlu's"AbacusAlgorithm",ChengDawei's"DirectPointAlgorithm",ThereisnodoubtthattheabacushasbeenwidelyusedintheMingDynasty,suchasKeShangqian's"TongrailofMathematics"andZhuZaiyu's"NewTheoryofArithmetic".
Withthediscoveryofnewhistoricalmaterials,someexpertsbelievethattheabacusshouldoriginateintheTangDynastyandbepopularintheSongDynasty.ThebasisisthatthereisamedicineshopinthefamouspaintingoftheSongDynasty"ARiverontheQingmingFestival",andthereisanabacusonthefrontcounter.TheabacusexpertsinChinaandJapanhavemagnifiedthepictureandconfirmedthattheobjectsinthepaintingareusedinmoderntimes.Theabacusissimilartothestringabacus.Moreover,in1921,awoodenabacusfromtheoldhouseoftheSongpeoplewasunearthedinJuluCounty,Hebei,mycountry.Althoughithasbeensubmergedbywaterandsoilfor800years,itcanstillbeseenintheshapeofadrumwithaholeinthemiddle.Theabacusisthesame.
Inaddition,thosewhoholdthisviewalsobelievethatthereisanine-fileabacusinthetextbook"NewCompilationofRelativeFourCharacters"intheearlyYuanDynasty.Itcanbeseenthattheabacuswasalreadyanordinarythingatthattime,anditsappearancecanbepusheduptotheSongDynastyatleast.Moreover,LiuYinwhowrotethepoem"Abacus"wasalsoapersonfromthelateSongDynastyandtheearlyYuanDynasty.HispoemsarenotsomuchdescribingthingsintheYuanDynastyastheyreflectthingsintheSongDynastymoreaccurately.Similarly,TaoZongyi’s"ThreeBeadsinDrama"hastheabacusbeadsintheproverbsoftheYuanpeople,whichalsoreflectsthat"thelawprevailedintheSongDynasty".
ButifitisbelievedthattheabacusoriginatedintheSongDynasty,thereseemstobedoubt.Becauseintermsofformandsystem,theabacusoftheSongDynastyhasbeenrelativelymature,anditdoesnothavetheclumsyorroughnessthatnewthingsoftenhave.Therefore,manyarithmeticscholarsbelievethatthebirthoftheabacuscanbepushedbacktotheTangDynasty.BecauseofthecontinuouswarsintheFiveDynastiesandTenKingdomsperiodbeforetheSongDynasty,thedevelopmentofscienceandtechnologyculturewasrelativelyslow,anditislesslikelythattheabacuswasbornatthistime.TheTangDynastywasaprosperouserainChinesehistory,andtheeconomyandculturewererelativelydeveloped,andnewcalculationtoolswereneeded.Therefore,thecalculationsusedin2000weretransformedintoabacuscalculations.ItisverylikelythattheabacuswasinventedintheTangDynasty.
Mantra
AdditionMantra
Explanation:Abacusadditionmantraisatextsummaryusedtoguidethemovementofdialingbeadsandperformcalculations.Inordertohaveaclearerunderstandingofthecontentoftheformula,firstbrieflydescribethemeaningoftherelevanttermsintheadditionformulaasfollows:
"Shang" significattodialthebeadtorelyonthebeam.
"Descendere" refertoshiftingthebeam.
"Vade" intelligitur abacus beads by thebeamtothe side.
"Progredi" meansaddinganumbertothefront position (thefirstgearfromtheleft).
Thefirstwordofeachsentenceintheformulaindicatesthenumbertobeadded,andthelastwordindicatesthenumbertobemovedbythebead.
Subtractionformulas
Explanation:Thereare26sentencesintheabacussubtractionformulas,whicharedividedintofourtypes:directsubtraction,breakingfivesubtraction,retreatingtensubtractionandretreatingtenreplenishingfivesubtraction.Themeaningoftherelevanttermsinthesubtractionformula:
"Up"referstodialingdownthepearlandrelyingonthebeam.
"Descendere" est movere inferiora ad latus radiorum.
"Go"meanstomovetheabacusbeadsthatleanonthebeamandmovetothesideofthebeam.
"Progredi" meansaddinganumbertothefront position (thefirstgearfromtheleft).
"Retreat"meanstodecrementthenumberfromthepreviousposition(thefirstgearfromtheleft).
"Return"meansthatthenumbershouldbeaddedtothedigitafterthefirstdigitisremoved.
Thefirstwordofeachsentenceintheformulaindicatesthenumbertobesubtracted,andthenextwordindicatesthenumberofbeadstobemoved.
Multiplicationformula
oneone01onetwo02onethree03onefour04onefive05onesix06oneseven07oneeight08onenine09
Twoone02twotwo04twothree06twofour08twofive10twosix12twoseven14twoeight16twonine18
threeone03threetwo06threethree09threefour12threefive15threeSix18threeseven21threeeight24threenine27
fourone04fourtwo08fourthree12fourfour16fourfive20foursix24fourseven28foureight32fournine36
Fiveone05fivetwo10fivethree15fivefour20fivefive25fivesix30fiveseven35fiveeight40fivenine45
6one06sixtwo12sixthree18sixfour24sixfive30sixsix36sixseven42sixeight48sixnine54
sevenone07seventwo14seventhree21sevenfour28sevenfive35sevensix42sevenseven49seveneight56sevennine63
Augustone08eighttwo16eightthree24eightfour32eightfive40eightsix48eightseven56eighteight64eightnine72
nineone09ninetwo18ninethree27ninefour36NineFive45NineSix54NineSeven63NineEight72NineNine81
Explanation:Eachsentenceofthemultiplicationformulaconsistsoffournumbers,thefirsttwoareChinesecharacters,andthelasttwoareArabicnumbers.Thefirstnumberreferstothemultiplier,thesecondnumberreferstothemultiplicand,andthethirdandfourthnumbersrefertotheproduct.
Inordertopreventthewrongtipfromaddingtheproductinthecalculation,theproductiscomposedoftwodigits.Eveniftheproducthasonlyonesignificantdigit,itmustbereadbyadding0beforetheproduct,suchas6x1,andtheformulaisreadasonesix06.
Ninereturnformula
Onereturn ( divide per 1 ) : intra unumquemque , intra duo in sesquipedem , tres in sesquiternos , in singulos trinos , quatuor in singulos intra quattuor , quinque in omnes quinque , omnes sexentesssex , omnes vespertinisseni , octog- entes octo , omnes novem.
Duo redi (divideby 2): intra singula duo, intrant duo quaelibet, tria quaelibet, intra quattuor quaelibet octo, et adde duo quinque.
Sangui(divideby3): intra unum omnes tres, intra duo quaelibet sex, intrant tres omnes novem, tres unum tres plusquam unum, tres duo sex plusquam duo.
Quadringenti (divideby 4): enter singuli quattuor, intra duo octo, quinque post quattuor duo, quattuor unum duo plus quam duo, quattuor tres septem plus quam duo.
Fivereturn (divideby 5): omnis quinqueenter, quinque facit duo, quinque facit quattuor, quinque facit sex, quinque facit octo.
Sixretum (divideby 6): intra singulas sex, intra duas duodenas, adde quinque cum sex tribus, addis quattuor cum sex, sex duas tres amplius, sex quattuor sex plus quam quattuor, sex, quinque, octo, plus quam duas.
Qigui (divideby7): intra singulas septem, intra duo quattuordecim, addunt tres septem, septem, tres, quattuor, et duo, septem, quattuor, quinque et quinque, septem septem septem plus, septem sex octo plus quam quattuor.
Bagui (divideby 8 ): Singuli octogenti, octo quattuor addit quinque, octo addit duo, octo duo addit quattuor, octo tres additi, octo quinque sex remanent duo, octo sex plus quam quattuor, octo septem octo plus quam sex.
Ninereturn (divideby9): quilibet nonens, novemaddo, novem duo addunt, novem tres additi tres, quattuor additi novem, quinque additi quinque, Addsix for nonaginta sex, septem for nonaginta septem, octo nonaginta octo.
Explicatio: dividens per modum digiti 'singlereturn' dicitur divisio divisoris 534, quae vocatur "divisio", "divisio". Prima digiti divisoris "gui", et sequens digiti "divisio" dicitur.
Relatedterms
Neutral:Whentheupperandlowerpartsofacertaingeararebothawayfromthebeam,itiscalledneutral.Agapmeansthatthereisnocountinthisposition,oritmeans0.
Emptyplate:Allgearsoftheabacusareempty,whichmeansthatthereisnocountinthewholeplate,whichiscalledanemptyplate.
Innerbeads:Theabacusbeadsthatcountbybeamsarecalledinnerbeads.
Outerbeads:Abacusbeadsthatdonotcountfromthebeamarecalledouterbeads.
Dialup:referttothelowering ofbeads against thebeam.
Dialingdown:referstoputtingtheupperpearlagainstthebeam.
Pullingout:referstopullingtheupperorlowerbeadsawayfromthebeam.
Thisfile:referstothefilethatisabouttobedialedandcounted.
Frontgear: refero ad paginam huius fasciculi priorem, quae dicitur leftgear(positio).
Backgear: referstothenextgearof e hoc fasciculo, etiam dicitur rightgear(positio).
Floatingbeads:Theabacusbeadsfloatinginthemiddleofthegearwithoutrelyingonthebeamstobetoolightwhenpullingthebeads.
Beads:Whendialingbeads,bringinoroutthebeadsthatshouldnotbedialedinoroutofthisfileorneighboringfiles.
Realbeads:Abacusbeadsthatrelyonbeamstorepresentpositivenumbers.
Virtualbead:alsocallednegativebead,referstothehangingbeadthatisdialedtoneitherthebeamnortheframe,indicatinganegativenumber.
Setthenumber:alsoteachthenumber,accordingtothecalculationrequirements,dialthenumberintotheabacustoprepareforthecalculation.
Gearposition: Item calledgrade, itrefersto the position of thegear.
Wronggear:Alsocalledmisalignment,itmeansthatthebeadisnotdialedintothegearthatshouldbedialedduringthecalculationprocess.
Interval:Itisalsocalledtheinterval,whichreferstothesecondgear(position)withonegearleftandright.Inintervalmultiplication,twonumbersaremultipliedtogether,andtheunitsplaceoftheproductisplacedontherighttwodigitsofthemultiplicand;inintervaldivision,thequotientoftheintervalreferstothefirsttwoleftdigitsofthedividend.
Carry:Itmeansthatafteraddinganumbertothisfile,itisgreaterthanorequalto10,anditmustbeincreasedby1tothepreviousposition,whichiscalledcarry.
Abdicate:Itmeansthatwhenthisfileissubtractedbyonenumber,thisfileisnotenough,andyoucansubtract1fromthepreviousone,whichiscalledabdication.
Primo loco: Item locus excelsus dicitur, quod primus non-nulladigitofa multi digiti numerus est primus locus.Suchas3in3284 et 7in0.0726.
Lastdigit: Etiam calledthelowestdigit, itreferstothelastnumberofamulti digiti numeri.Suchas5in3275,0in120, et9in481.29.
Secundo: Secundus numerus qui est essentialiter multi digiti numeri.Enter8in3865&1in0.4178.
Liquidation:Turnofftheabacusbeadsineachstalltomakethewholemarketempty,whichiscalledliquidation.
Comprehensivepractice:Practiceonallthefilesoftheabacus,oronmostofthefiles,andperformcomprehensiveexercisesaccordingtothebasicalgorithm,whichiscalledfullpractice.
Precium
Becausetheabacusiseasytomake,cheap,easytoremember,andeasytocalculate,itiswidelyusedinChinaandspreadtoJapan,NorthKorea,theUnitedStatesandSoutheastAsia.Andothercountriesandregions.Today,wehaveenteredtheageofelectroniccomputers,buttheancientabacusstillplaysacertainrole.