Imvelaphi yoMthetho weL'Hôpital

UGuillaume-François-Antoine Marquis de l'Hôpital, uMarquis de Sainte-Mesme, uComte d'Entremont et Seigneur d'Ouques-la-Chaise, owaziwa kakhulu njengoGuillaume L'Hôpital, wazalwa ngo-1661 eParis kwintsapho enelifa elinamandla lomkhosi. Nangona kunjalo, ngokuchasene neminqweno yosapho lwakhe kunye nembono ebanzi yobuhandiba eFransi, wayeyithanda imathematika kwasebuncinaneni bakhe. Ebudeni benkonzo yakhe yasemkhosini, wazenza ngathi uphumle ententeni yakhe waza endaweni yoko wafunda ijometri. UBernard de Fontenelle wabhala ngaye kwi-eulogy ye-L'Hôpital:

Kuba kufuneka kuvunywe ukuba isizwe samaFrentshi, nangona siziphatha kakuhle njengazo naziphi na ezinye, sisekwelo hlobo loburhalarhume apho sizibuza ukuba ingaba inzululwazi, ithathwe kwinqanaba elithile, ayihambelani nobuhandiba, nokuba ayilunganga na ukungazi nto. … Ndibabonile ngokobuqu abanye babo babesebenza ngaxeshanye, bemangaliswe kakhulu kukuba indoda eyayiphila njengabo yayiyenye yeengcali zezibalo ezikhokelayo eYurophu.

UL’Hôpital wawushiya umkhosi waseFransi ngenxa yokungaboni kakuhle, nangona kwakusithiwa ufuna ukwenza imathematika ixesha elizeleyo. Ngoku amashumi amabini anesine, waya kwiBandla leOratory kwisangqa sikaNicolas Malebranche (iqela elihlanganisana ukuze kuxoxwe kunye nobudlelwane,) elalihlalwa ngoosonzululwazi bezibalo abaphambili kunye nezazinzulu zaseParis. Apho, wadibana noJohann Bernoulli, umntakwabo omncinci kunye nomncinci kaJakob Bernoulli, owayefundise uLeibniz ebusheni bakhe kwaye wayesele ethathwa njengengqondo yezibalo. UL'Hôpital wayengoyena mfundi unomdla kaBernoulli kwaye kungekudala wamhlawula ukuba amfundise ngasese, endaweni yoko.

U-L'Hôpital ungenise isisombululo sengxaki kwikhosi uBernoulli awayemnike yona kuChristiaan Huygens ngaphandle kokutsho ukuba yayingeyena. Kuyaqondakala ukuba, kungekho bungqina buchasene noko, uHuygens wacinga ukuba uL’Hôpital uyenzile. UBernoulli wayenomsindo kwaye waqhawula imbalelwano yakhe rhoqo kunye ne-L'Hôpital kangangeenyanga ezintandathu-kodwa wophula ukuthula xa uL'Hôpital emcela ukuba afumane "ukufumanisa" okungakumbi malunga neeponti ezingamakhulu amathathu (kunye nokwandayo). Ucele umhlohli wakhe ukuba naye amnike amalungelo akhethekileyo kwimpumelelo yakhe kunye nezifundo. UBernoulli waphendula ngokukhawuleza ukuba akayi kuphinda apapashe nantoni na ebomini bakhe ukuba u-L'Hôpital wayefuna.

Ethatha kwizinto ezifunyenwe nguBernoulli kunye namanqaku aphuma kwiimfundiso zakhe, uL’Hôpital wapapasha eya kuba yincwadi yokuqala yesibali: Analyse de infiniment petits pour l’intelligence des lignes courbes (Uhlahlelo lweZixa eziNcinane ngokuNgapheliyo zoKuqondwa kweeCwaves.) Kuyo, uchaza indlela yokumisela umda:

1. Nika ukuba izixa ezibini, umahluko wazo osisixa esingenasiphelo, zinokuthathwa (okanye zisetyenziswe) ngokungakhathaliyo; okanye (eyinto enye) ukuba umyinge owandisiweyo okanye owehlisiwe kuphela ngobungakanani obuncinci obungenasiphelo bunokuthi buthathwe njengobuhlala bufana.

2. Vumela ukuba igophe lithathwe njengokudityaniswa kwenani elingenasiphelo lemigca emincinci ethe ngqo; okanye (eyinto enye) njengepolygon yenani elingenasiphelo lamacala, ngalinye lincinci ngokungenasiphelo, elimisela ukugoba kwegophe ngeeengile abazenzayo enye kwenye.

Nangona inganikezelwanga ngokusesikweni njengeencwadi zezifundo zecalculus zangoku, njengakwiCandelo 4.4 leStewart’s Calculus: Early Transcendentals, elichaza:

njengomthetho we-L'Hôpital (ecatshulwe kwincwadi ethi L'Hospital,) ingxelo yakhe yantlandlolo kunye nokuphindaphinda kwanamhlanje kuyafana ngokwengqiqo. Xa i-L'Hôpital ithetha ngeeyantlukwano ezincinci ezingenasiphelo, oku kufana nokumelwa kwemida. Ingcamango "yemigca emincinci emincinci ngokuthe tye" imele ukuqonda kwejometri yokwahlula kwaye ingukhokho wengcamango yethu yangoku ye-derivative. Ngokubanzi, njengoko kwiCandelo 4.4., i-original theorem ye-L'Hôpital ithi iifom ezingapheliyo zingasombululwa ngokufumana imisebenzi yenguqu yenguqu.

Abaxhasi bakaJohann Bernoulli bathi wanyanzelwa ukuba anikezele kwintando yezidwangube. Ngaphandle kwesivumelwano sokuqala sikaBernoulli ngenxa yokuphelelwa yimali, ilungiselelo laqhubeka ixesha elide kwi-professorship yakhe eyimpumelelo eGroningen. UBernoulli wathi incwadi kaL'Hôpital “yayiyeyakhe” kuphela emva kokusweleka komfundi wakhe wangaphambili. Ngelo xesha, igama likaBernoulli lalimdaka emva kwemiqolo emininzi kunye nomntakwabo omdala. Ngelo xesha, yayiyinto eqhelekileyo yokuhlawula iinkonzo ezivela kwiingcali eziphezulu ezifana nezopolitiko kunye namagqwetha, kwaye abaninzi babemjonga uL'Hôpital njengengcali yezibalo enobuchule ngokwakhe.

Enye inqaku lokuqala lamathandabuzo kwingqibelelo yomsebenzi we-L'Hôpital yayisisisombululo sakhe kwingxaki ye-brachistochrone (eyenziwe nguJohann Bernoulli ngo-1696, ingxaki malunga negophe lokuhla ngokukhawuleza):

Ingxaki eNtsha apho iingcali zeMathematika zimenywe ukuba ziyisombulule: Ukuba amanqaku A kunye no-B anikwe kwinqwelo-moya ethe nkqo, ukwabela isuntswana elihambahambayo elingu-M indlela i-AMB apho, isihla phantsi kobunzima bayo, idlula ukusuka kwindawo A ukuya kwindawo B kwelona xesha lifutshane.

Kwacetyiswa ukuba impendulo kaL'Hôpital kumbuzo yayingekho eyakhe, mhlawumbi loo mfundisi-ntsapho uBernoulli ngokwakhe.

Ekugqibeleni, i-L'Hôpital yayinobuchule bokudibanisa iimfundiso zikaJohann Bernoulli kwaye yapapasha i-opus ebalulekileyo kwicandelo elikhula ngokukhawuleza lokubala, elenza ukuba uphuhliso lufikeleleke kubaphulaphuli abaninzi. Nangona kunjalo, umsebenzi wakhe awuyi kubambelela kwimigangatho yangoku yokuthembeka kwezemfundo, kwaye kunokuthiwa wasebenzisa kakubi isikhundla sakhe sezemali ukuba abe ngusaziwayo wezemfundo kwiFransi yenkulungwane yeshumi elinesixhenxe ngaphandle kobuchule bokwenene boontanga bakhe.

References

“Acta Eruditorum. 1696.” Internet Archive, Lipsiae : Apud J. Grossium et J.F. Gletitschium, 1 Jan. 1696, archive.org/details/s1id13206630.

Katz, Victor J. A History of Mathematics. 3rd ed., Pearson Education Limited, 2014.

L’Hospital, Guillaume François Antoine De, and M. Varignon. Analyse Des Infiniments Pettits, Pour l’intelligence Des Lignes Courbes. ALL-Éditions, 1988.

O’Connor, J J, and E F Robertson. “Guillaume François Antoine Marquis de L’Hôpital.” Maths History, University of St. Andrews School of Mathematics and Statistics, Dec. 2008, mathshistory.st-andrews.ac.uk/Biographies/De_LHopital/.

Stewart, James. Calculus: Early Transcendentals. Vol. 8.