EZASENDULO
U-Al-Khwarizmi
LAPHO abantu bekala isisindo noma ingqikithi yesamba sokudla abakuthengile, abaningi basebenzisa indlela yokubhala izinombolo ebizwa ngokuthi iHindu-Arabic. Kungani ibizwa ngokuthi “iHindu-Arabic”? Kubukeka sengathi isimiso esivamile sezinombolo esisebenzisa u-0 kuya ku-9, sasungulwa eNdiya, nokuthi emazweni aseNtshonalanga safika ngezazi zangenkathi ephakathi ezazibhala ngesi-Arabhu. Owayevelele kuzo kwakuyindoda egama layo linguMuhammad ibn-Musa al-Khwarizmi. U-al-Khwarizmi, okungenzeka wazalelwa ezweni manje elibizwa nge-Uzbekistan, cishe ngo-780 C.E., ubizwa ngokuthi “iqhawe elikhulu lezibalo zesi-Arabhu.” Kungani athola lolo dumo?
“IQHAWE LEZIBALO ZESI-ARABHU”
U-al-Khwarizmi wabhala ngendlela yokusebenzisa izinombolo eziqala ku-0 kuya ku-9, waphinde wayenza yacaca futhi yaziwa indlela yokuxazulula izinkinga ezithile zezibalo. Le ndlela wayichaza encwadini yakhe ethi, The Book of Restoring and Balancing. Igama lesiNgisi elithi algebra lisuselwa kwelithi ‘al-jabr’ elithathwe esihlokweni sesi-Arabhu sale ncwadi esithi Kitab al-jabr wa’l-muqabala. Ongumbhali wezesayensi u-Ehsan Masood uthi, i-algebra ibhekwa “njengethuluzi lezibalo elibaluleke kunawo wonke ake asungulwa, futhi elisekela yonke imikhakha yezesayensi.”a
Encokola, omunye umlobi uthi, “Izizukulwane eziningi zabafundi basemabangeni aphakeme, zifisa sengathi ngabe [u-al-Khwarizmi] akazange azihluphe.” Nakuba kungase kube njalo, u-al-Khwarizmi wathi umgomo wakhe kwakuwukuchaza izindlela zokubala, ukuze kusetshenzwe kalula kwezentengiselwano, emkhakheni wezokuhlukanisa amafa, ekwenzeni ucwaningo, nakweminye imikhakha.
Emakhulwini eminyaka kamuva, izazi zezibalo zaseNtshonalanga, ezihlanganisa uGalileo noFibonacci, zamethulela isigqoko u-al-Khwarizmi ngenxa yezincazelo zakhe ezicacile ngokuphathelene nendlela yokuxazulula izibalo. Izincazelo zika-al-Khwarizmi zavulela indlela izifundo ezengeziwe ze-algebra, i-arithmetic kanye ne-trigonometry. I-trigonometry yenza izazi zaseMpumalanga Ephakathi zakwazi ukukala ama-engela nezinhlangothi zonxathathu nokuthuthukisa izifundo zesayensi yezinkanyezi.b
I-Algebra: “Ithuluzi lezibalo elibaluleke kunawo wonke ake asungulwa”
Labo abasebenzisa ucwaningo luka-al-Khwarizmi, basungula izindlela ezintsha zokusebenzisa indlela yokubhala izinombolo ayezisungulile futhi basungula namasu amasha okuthola ubungako bendawo nokuthi okuthile kungamumatha into engakanani. Abaklami nabakhi bezindlu baseMpumalanga Ephakathi basebenzisa lezo zindlela ezithuthukisiwe esikhathini eside ngaphambi kokuba zisetshenziswe ozakwabo baseNtshonalanga, bona abaqala ukujwayelana nazo phakathi neziMpi Zenkolo. Kamuva, basizwa amaSulumane ayizifundiswa ayethunjiwe nayevela kwamanye amazwe ekusabalaliseni lolu lwazi kwelakubo.
UKUSABALALA KWEZIBALO ZESI-ARABHU
Ngokuhamba kwesikhathi, umsebenzi ka-al-Khwarizmi wahunyushelwa nasolimini lwesiLatini. Isazi sezibalo esingumNtaliyane uFibonacci (owazalwa cishe ngo-1170-1250), esiphinde saziwe ngoLeonardo wasePisa, kuthiwa yisona esenza indlela yokubhala izinombolo ezibizwa ngeHindu-Arabic yaziwa naseNtshonalanga. Safunda ngayo phakathi nokuvakashela kwaso eMedithera futhi ngemva kwalokho sabhala incwadi yaso ethi Book of Calculation.
Kwathatha amakhulu eminyaka ngaphambi kokuba izincazelo zika-al-Khwarizmi zaziwe kabanzi. Kodwa namuhla imisebenzi yakhe kanye nezibalo ezihlobene nayo sekuwumgogodla wesayensi nezobuchwepheshe, ngisho nakwezentengiselwano nasemikhakheni yezezimboni.
a Kuyi-algebra yanamuhla, izinombolo ezingaziwa zimelelwa izinhlamvu zamagama ezifana no-x no-y. Isibonelo salokho isibalo esithi x + 4 = 6. Uma ususa u-4 nhlangothi zombili, lokho kuyobonisa ukuthi u-x ulingana no-2.
b Izazi zezinkanyezi ezingamaGreki, zasungula indlela yokulinganisa izinhlangothi nama-engela onxantathu. Izazi ezingamaSulumane zasebenzisa i-trigonometry ukuze zithole ukuthi iMecca ingakuphi. AmaSulumane ayathanda ukuthandaza ebheke ngakuyo. Ngokwesiko lawo, abafileyo kudingeka babheke ngaseMecca lapho bengcwatshwa, nezisebenzi zasezilaheni ezingamaSulumane nazo kumelwe zibheke eMecca lapho zihlaba izilwane.