VATU vamwe nge vali nakusaka kutachikiza pezo yavo chipwe yavyuma vanakusaka kulanda, veji kuzachisanga vasona vavaHindu-Arabic. Mwomwo ika? Mwomwo vatu valinangula chikuma vaze vasonekele lilimi lyaArabic mulifuchi lyaIndia vakiko vaputukile jinambala twazachisa makumbi ano jakuputukila ha 0 nakuheta ku 9 nakujinangula vatu vakumafuchi akumulauko. Lunga umwe hakachi kavo apwile Muhammad ibn-Musa al-Khwarizmi. Lunga kana asemukilile mulifuchi lize vali nakuvuluka jino ngwavo Uzbekistan mumwaka wa 780 C.E., kaha vamuvuluka ngwavo “kuluwa wamakumi aArabic.” Mwomwo ika vamuvulukila ngocho?

## “MUTU WATETE KULINANGULA MAKUMI MULILIMI LYAARABIC”

Al-Khwarizmi atuvile jila yakuzachishilamo jinambala jakufwana nge 10, na 100 namwakuwanyina makumi. Mumukanda wenyi waThe Book of Restoring and Balancing asonekelemo jila yakuwanyinamo makumi kana. Mulilimi lyaArabic lizu al-jabr lyalumbununa Kitab al-jabr wa’l-muqabala, muChingeleshi lyalumbununa algebra. Muka-kusoneka vyasayasi walijina lyaEhsan Masood ambile ngwenyi, algebra “apwa makumi amalemu chikuma aze akundwiza kunangula chasayasi chosena.” *

Muka-kusoneka umwe walunga ambile ngwenyi, “vaka-shikola vavavulu vali nakuyayavala ngwavo kachi al-Khwarizmi kanehele makumi kanako. Oloze al-Khwarizmi ambile ngwenyi anehele makumi kana mangana ashiwise mwakulavila vyuma mukusekasana, nahakulipangila luheto, mwakupimina vyuma, navyeka vyangana.

Omu mwahichile myaka makulukaji, malunga valinangula makumi vakufwana nge Galileo naFibonacci navakwavo veka vaKumulauko, vasangejekele al-Khwarizmi ngwavo alingile kanawa kutuva jila yakuwanyinamo makumi kana. Jila yize Al-Khwarizmi alumbunwinemo makumi yakafwile vatu veka valinangule chikuma makumi akufwana nge arithmetic, natrigonometry. Echi chakafwile vaka-kulinangula veka vakumulauko valilongese makumi eka navyamumelu. (angles, triangles and advance studies in astronomy). *

Algebra: “Apwa makumi amalemu chikuma”

Vatu vaze vakavangijilenga kunangula chaal-Khwarizmi vatachikijile jijila jeka jajihya jamwakuzachishila jinambala jakufwana nge 10 chipwe 100 nakulinangula nawa jila yayihya yamwakuwanyina kusuhwa nakukuluka chachuma. Vaka-kutunga jizuvo vakuMututuko vazachishilenga jila kana mumyaka yakunyima shimbu kanda vakwavo vaKumulauko vatachikize jila kana. Kutwala muze vanangwileko vakwavo vaMuzilemu vamulifuchi lyavo vaze vapwile matunduke navafunge.

## MAKUMI AARABIC NAWATANDA

Omu mwahichile lwola, milimo yaal-Khwarizmi vayalumwine mulilimi lyaLatin. Mutu uze atachikiza chikuma makumi wakulifuchi lyaItaly walijina lyaFibonacci (c. 1170-1250), uze nawa vavulukile ngwavo Leonardo wamunganda yaPisa atandakanyishile jinambala jaHindu-Arabic kumulauko walifuchi kana. Alinangwile makumi kana omu apwilenga muungeji wenyi wakuya kuMediterranean, kaha kutwala muze asonekele mukanda waBook of Calculation.

Kunangula chaAl-Khwarizmi chambachile myaka yayivulu numba vatu vachitachikize. Oloze jijila anangwililemo makumi kana yinatande jino musayasi namuchinyingi chakutunga makina, keshi nge mukusekasana kahako.

^ par. 5 Algebra yamakumbi ano yazachisa vasona vakufwana nge x chipwe y vaze vemanyinako jinambala jize katwatachikijile hakusoneka makumi. Chakutalilaho, likumi lya x + 4 = 6 linalumbununa ngwavo nge 6 navafumisamo 4 nayipwa 2. Kulumbununa nge x yikiko 2.

^ par. 7 Vaka-kulinangula vyamumelu vakiko vaputukile mwakupimina jimbango (angles and triangles). VaIzilamu vaze valinangula chikuma vapwile nakuzachisa makumi kana mangana vawane kuchihela kuze vavuluka ngwavo Mecca. VaMuzilemu veji kulombanga oku vanatalisa chameso kuMecca. Kweseka nachisemwa chavaMuzilemu nge mutu nafu hakumufunda veji kumutalisa kuMecca. Kaha nawa hakujiha kanyama veji kutalisa kuMecca.