XA ABANTU bezijonga esikalini okanye bejonga amaxabiso okutya badla ngokusebenzisa amanani esiHindu nesiArabhu. Kutheni besebenzisa la manani nje? Kungenxa yokuba amanani esiwasebenzisa namhlanje aqala kwiqanda ukuya kwisithoba, kubonakala ukuba aqala ukusetyenziswa eIndiya, aza kamva aziswa eNtshona ngabaphengululi ababebhala ngesiArabhu. Omnye wabo babetshotsha phambili ekusebenziseni la manani yayinguMuhammad ibn-Musa al-Khwarizmi. Ual-Khwarizmi ekusenokwenzeka ukuba wazalelwa kwindawo ngoku ebizwa ngokuba yiUzbekistan ngonyaka ka-780, waziwa ngokuba “ngungqondo-ngqondo wezibalo zesiArabhu.” Kwenzeka njani ukuba abe yindumasi kwizibalo?

## “UNGQONDO-NGQONDO WEZIBALO ZESIARABHU”

Kwincwadi yakhe ethi The Book of Restoring and Balancing, ual-Khwarizmi wabhala ngendlela amanani anokusetyenziswa ngayo nangendlela anokunceda ngayo ekusombululeni izibalo ezinzima. Igama lesiNgesi elithi algebra lisuka kwelesiArabhu elithi al-jabr elithatyathwe kwisibizo esithi Kitab al-jabr wa’l-muqabala. Umbhali wezesayensi uEhsan Masood uthi, ialgebra “sesona sixhobo sezibalo sakhe sabaluleka kwezakha zakho nesixhasa isayensi.” *

Omnye umbhali uthi, “Abafundi abaninzi abakumabanga aphakamileyo bavakalelwa kukuba [ual-Khwarizmi] ngewayengazange azidube.” Kodwa yena ual-Khwarizmi wathi injongo yakhe kukwenza lula izibalo kwezoshishino, ekwahlulweni kwamafa, ekusikweni komhlaba, nezinye izinto.

Kwiminyaka kamva, oongqondo-ngqondo bezibalo baseNtshona abaquka uGalileo noFibonacci babemhlonela gqitha ual-Khwarizmi ngenxa yobuchule bakhe kwizibalo. Ual-Khwarizmi wanceda ekuvelisweni kwezifundo zealgebra, zearithmetic kunye nezetrigonometry. Itrigonometry yanceda abaphengululi bakuMbindi-Mpuma ukuba bakwazi ukubala ubude, ububanzi nokuphakama kwezinto, yaza yanceda nasekwenzeni lula ukufunda ngeenkwenkwezi. *

Ialgebra: “Sesona sixhobo sezibalo sakhe sabaluleka kwezakha zakho”

Abo baqhubeka nokusebenzisa iindlela zika-al-Khwarizmi zokubala beza nezinye ezintsha zokubala ubude nobubanzi bezinto. Amagcisa okwakha akuMbindi-Mpuma aqala ukuzisebenzisa ezi ndlela zokubala ngaphambili lee kunamagcisa aseNtshona awazifunda ngexesha leeMfazwe Zonqulo. Kamva, aye afundiswa ngakumbi ngezi ndlela zizifundiswa ezingamaSilamsi, ezazifudukele nezazithinjelwe eNtshona.

## UKUSASAZEKA KWEZIBALO ZAMA-ARABHU

Ekuhambeni kwexesha, izibalo zika-al-Khwarizmi zaguqulelwa ngesiLatin. Abantu abaninzi bathi izibalo zesiHindu nesiArabhu zasasazwa kwelaseNtshona yingcali yezibalo yaseItali uFibonacci, okwabizwa ngokuba nguLeonardo wasePisa (owayephila phakathi kweminyaka yee-1170 neyee-1250). UFibonacci wafunda ngazo xa wayekhenketha amazwe agudle uLwandlekazi iMeditera, waza kamva wabhala incwadi ethi Book of Calculation.

Kwathatha iminyaka emininzi ngaphambi kokuba zidume iindlela zika-al-Khwarizmi zokubala. Kodwa ngoku, zibaluleke gqitha kwisayensi nakwiteknoloji, singasathethi ke kwezoshishino.

^ isiqe. 5 Kwialgebra yangoku, kudla ngokusetyenziswa u-x okanye u-y kwindawo yamanani angaziwayo. Masizekelise ngesi sibalo: x + 4 = 6. Xa sithabatha u-4 ku-6 kuphuma u-2, nto leyo ethetha ukuba u-x = 2.

^ isiqe. 7 Izazi ngeenkwenkwezi zaseGrisi zaba zezokuqala ukubala ubude, ububanzi nokuphakama kwezinto. Abaphengululi abangamaSilamsi basebenzisa itrigonometry ukuze bazi icala ekulo iMecca, esesona sixeko singcwele kunqulo lwamaSilamsi. AmaSilamsi athanda ukujonga kwicala ekulo iMecca xa ethandaza. Isithethe sawo sifuna ukuba isidumbu sijongise ngaseMecca xa singcwatywa, ibe ajongisa ngakuyo naxa exhela.