Ja ku birimwo

Ja ku rutonde rw'ibirimwo rwa kabiri

Ja ku rutonde rw’ibirimwo

Ivyabona vya Yehova

Ikirundi

Be maso!  |  Rusama 2015

 KAHISE KATWIGISHA IKI?

Al-Khwarizmi

Al-Khwarizmi

Igihe abantu bariko barapima ibilo bafise canke baharura amahera y’ivyo basumye, benshi bakoresha ibiharuro vy’abahindu n’Abarabu. Kubera iki vyitwa gutyo? Muri iki gihe, turakoresha ibiharuro ubusa gushika kw’icenda. Biboneka ko ivyo biharuro vyatanguriye mu Buhindi, mu nyuma bishika i Buraya biciye ku bahinga ba kera bandika mu carabu. Umwe muri bo ni umugabo yitwa Muhammad ibn-Musa al-Khwarizmi. Ashobora kuba yavukiye ahasigaye hitwa Uzbekistani nko mu 780 inyuma ya Kristu. Yiswe “igihangange mu biharuro vy’Abarabu.” Kubera iki yiswe gutyo?

“IGIHANGANGE MU BIHARURO VY’ABARABU”

Al-Khwarizmi yaranditse ibijanye n’ingene abantu bashobora guharura bafatiye ku macumi, arasigura neza yongera aramenyekanisha cane uburyo bwo gukora ibiharuro bimwebimwe vy’ubupfindo. Ubwo buryo yabusiguye mu gitabu yanditse (The Book of Restoring and Balancing). Ijambo al-jabr riboneka mw’izina ry’icarabu ry’ico gitabu (Kitab al-jabr wa’l-muqabala) ni ryo ryakomotseko ijambo ry’igifaransa algèbre. Umwanditsi w’ivya siyansi yitwa Ehsan Masood avuga yuko ibiharuro vyitwa algèbre ari “bwo buryo bwo gukora ibiharuro buhambaye gusumba ubundi bwose bumaze kwiyumvirwa, bukaba bufasha mu mice yose y’ubuhinga bwa siyansi.” *

Umwanditsi umwe yavuze atera inkuru ati: “Abanyeshure benshi bo mu mashure yisumbuye bari gushima ko [al-Khwarizmi] atazana ivyo biharuro.” Ariko al-Khwarizmi yavuze ko intumbero yiwe yari iyo gusigurira abantu uburyo  bworoshe bwo guharura bokoresha mu rudandaza, mu vyo kugabura intoranwa, mu vyigwa bijanye n’amatohoza, no mu bindi.

Mu binjana vyakurikiye, abahinga mu biharuro b’Abanyaburaya, ushizemwo Galilée na Fibonacci, baremera cane al-Khwarizmi kubera ko yasiguye neza ibijanye n’ibiharuro vy’ubupfindo. Ivyo Al-Khwarizmi yasiguye vyaraciriye inzira ibindi vyigwa vyagizwe muri vya biharuro vyitwa algèbre, mu vy’uguharura ibitigiri (arithmétique) no mu biharuro bijanye n’ingero z’inyabutatu (trigonométrie). Ibiharuro bijanye n’ingero z’inyabutatu vyarafashije abahinga bo mu Karere k’ibihugu vy’Abarabu gupima imfuruka z’inyabutatu n’impande zazo, biranabafasha gutera imbere mu vyigwa bijanye n’ibisyo vyo mu kirere. *

Ibiharuro vyitwa algèbre ni “bwo buryo bwo gukora ibiharuro buhambaye gusumba ubundi bwose bumaze kwiyumvirwa”

Abisunze ivyo al-Khwarizmi yanditse baratanguje ubuhinga bushasha bwo gukoresha ibice vy’ibitigiri, baranateza imbere uburyo bushasha bwo gupima uburinganire bw’ikintu n’ubwuzure bwaco (uburiba). Abafundi n’abahinga mu vy’ubwubatsi bo mu bihugu vy’Abarabu barakoresheje ubwo buhinga buteye imbere, bagenzi babo b’Abanyaburaya bataranabumenya. Abanyaburaya bagiye kubumenya mu gihe ca za ntambara z’abakirisu n’abisilamu zabera muri Palestina. Basubiye iwabo bajanye ubwo buhinga, bafashijwe n’abisilamu bize bari bagizwe imbohe. Barafashijwe kandi n’abimukira bize.

IBIHARURO VY’ABARABU BIKWIRAGIRA

Ivyo al-Khwarizmi yanditse vyahavuye bishirwa mu kilatini. Umuhinga mu biharuro w’Umutaliyano yitwa Fibonacci (uwitwa kandi Léonard de Pise, akaba yabayeho mu 1170-1250), ni we ahanini avugwa ko yakwiragije ibiharuro vy’abahindu n’Abarabu i Buraya. Yamenye ivyo biharuro igihe yagira ingendo mu karere k’Ikiyaga Mediterane, araheza yandika igitabu yise Igitabu c’ibiharuro (mu kilatini).

Vyasavye imyaka amajana kugira ivyo al-Khwarizmi yasiguye bimenyekane cane. Ariko ubuhinga yakoresha be n’ibiharuro bijanye na bwo, bisigaye ari vyo nkingi y’ubuhinga bwa siyansi n’ubundi buhinga bwa none, tutibagiye ivy’ubudandaji n’amahinguriro.

^ par. 5 Mu biharuro vyitwa algèbre vyo mu gihe ca none, ibitigiri bitazwi vyandikwa hakoreshejwe indome, nka a canke b. Nk’akarorero, umuntu arashobora kwandika ngo a + 4 = 6. Ukuyemwo igiharuro 4 twateranije na a, ugaca ufata 6 ugakuramwo 4 nyene, uca usanga a ingana na 2.

^ par. 7 Abahinga mu vy’ibisyo vyo mu kirere b’Abagiriki barabaye imboneza mu vyo gupima imfuruka z’inyabutatu n’impande zazo. Ingero z’inyabutatu zarafasha abahinga b’abisilamu kumenya aho Maka igisagara cabo ceranda giherereye. Abisilamu bakunda gusenga baraba i Maka. Imigenzo yabo isaba ko uwapfuye ahambwa araba i Maka, abayangayanga b’abisilamu na bo bagakerera ibitungwa ari yo baraba.