Fetela boitsebisong

Fetela lethathamong la tse ka hare

LITŠOANTŠO TSA MEHLENG EA KHALE

Al-Khwarizmi

Al-Khwarizmi

BATHO ba bangata ba sebelisa lipalo tse tloaelehileng ha ba kala boima ba ntho e itseng kapa ba bala litšenyehelo tsa korosari. Ho tlile joang hore batho ba sebelise lipalo tseo? Lipalo tsena tse tloaelehileng, e leng noto ho ea ho robong, li qalile India ’me li ’nile tsa sebelisoa ho ea fihla linaheng tsa Bophirimela ka lebaka la litsebi tsa mehleng ea khale tse neng li ngola ka Searabia. Ea tsebahalang ka ho fetisisa ho tsona ke Muhammad ibn-Musa al-Khwarizmi. E ka ’na eaba o hlahetse naheng eo kajeno e bitsoang Uzbekistan hoo e ka bang ka 780 C.E., ’me o bitsoa “mohale oa thuto ea lipalo tsa Searabia.” Ke hobane’ng ha a fuoe tlotla eo?

“MOHALE OA THUTO EA LIPALO TSA SEARABIA”

Al-Khwarizmi o ile a ngola ka mokhoa oo li-decimal, e leng lipalo tse nang le khutlo li ka sebelisoang kateng, a ba a hlakisa tsela ea ho sebetsa lipalo. O ile a hlalosa mokhoa ona bukeng ea hae e bitsoang The Book of Restoring and Balancing. Lentsoe la Senyesemane algebra le nkiloe ho lentsoe al-jabr le tsoang sehloohong sa Searabia se reng Kitab al-jabr wa’l-muqabala. Mongoli oa saense e leng Ehsan Masood o re Algebra e nkuoa e le “thulusi ea bohlokoa ka ho fetisisa ea lipalo e kileng ea etsoa le hore e tšehetsa saense ka hohle.” *

Mongoli e mong o ile a bua ka bosoasoi ’me a re: “Liithuti tse ngata tsa likolo tse phahameng li re [al-Khwarizmi] a ka be a sa ka a itšoenya.” Le hoja ba cho joalo, al-Khwarizmi eena o ile a re sepheo sa hae e ne e le ho etsa mekhoa ea ho nolofatsa lipalo litabeng tsa khoebo, ho arola mafa, ho potiela le tse ling.

Lilemo tse lekholo hamorao, litsebi tsa lipalo tsa linaheng tsa Bophirimela tse akarelletsang Galileo le Fibonacci, li ile tsa hlompha al-Khwarizmi ka lebaka la tsela e hlakileng eo a neng a hlalosa li-equation ka eona. Tsela eo Al-Khwarizmi a neng a hlalosa ka eona e ile ea etsa hore ho hlahe lithuto tse ling tsa algebra, arithmetic le trigonometry. Trigonometry e ne e thusa liithuti tsa linaheng tsa Bochabela bo Hare hore li lekanye likhutlo le mahlakore a likhutlo-tharo le ho ntšetsa pele lithuto tsa astronomy. *

Algebra: “Thulusi ea bohlokoa ka ho fetisisa e kileng ea etsoa”

Batho ba sebelisang mokhoa o neng o sebelisoa ke al-Khwarizmi, ba ithutile litsela tse ncha tsa ho sebelisa decimal fractions le ho qapa mekhoa e mecha ea ho lekanya bophara ba sebaka le boholo ba sona. Haesale litsebi tsa meralo ea ho haha tsa Bochabela bo Hare le liahi li sebelisa mekhoa e tsoetseng pele joaloka eo le pele ho litsebi tse ling tsa linaheng tsa Bophirimela, tse ileng tsa tseba ka eona nakong ea Lintoa tsa Bolumeli. Hamorao ha litsebi tseo li khutlela linaheng tsa habo tsona, li ile tsa sebelisa tsebo eo li e fumaneng, li thusoa ke batšoaruoa ba rutehileng ba Maislamo le bajaki.

THUTO EA LIPALO EA SEARABIA EA TSEBAHALA

Ka mor’a nako, mosebetsi oa al-Khwarizmi o ile oa fetoleloa ho Selatine. Setsebi sa thuto ea lipalo e leng Fibonacci (c. 1170-1250), ea boetseng a tsejoa ka lebitso la Leonardo oa Pisa, o tumme haholo ka ho tsebahatsa lipalo tse tloaelehileng linaheng tsa Bophirimela. O ile a ithuta ka tsona ha a ntse a hahlaula linaheng tsa Mediterranean eaba ka mor’a moo o ngola buka e bitsoang Book of Calculation.

Litlhaloso tsa Al-Khwarizmi li nkile lilemo tse makholo hore li tsebahale. Leha ho le joalo, mekhoa ea hae le lithuto tsa lipalo tse amanang le eona ke karolo ea bohlokoa saenseng le theknolojing hammoho le litabeng tsa khoebo le liindasteri.

^ ser. 5 Ho algebra ea mehleng ea kajeno, palo e sa tsejoeng e emeloa ke litlhaku tse kang x kapa y. Mohlala oa sena ke equation ea x + 4 = 6. Ha u tlosa 4 ka mahlakoreng a mabeli equationeng ena u tla fumana hore x ke 2.

^ ser. 7 Litsebi tsa linaleli tsa Bagerike ke tsona tse qalileng mosebetsi oa ho lekanya mahlakore le likhutlo tsa likhutlo-tharo. Litsebi tsa Maislamo li ne li sebelisa trigonometry ho tseba hore na Mecca e hōle hakae. Mamosleme a rata ho rapela a shebile Mecca. Ho latela setso sa ’ona, ha bafu ba patoa ba lokela ho shebisoa Mecca le bo-ralilakha ba Maislamo, ba sheba teng ha ba bolaea liphoofolo bakeng sa nama.