Umsuka Womthetho we-L'Hôpital

UGuillaume-François-Antoine Marquis de l'Hôpital, uMarquis de Sainte-Mesme, uComte d'Entremont et Seigneur d'Ouques-la-Chaise, owaziwa kakhulu ngokuthi uGuillaume L'Hôpital, wazalwa ngo-1661 eParis emndenini onefa elinamandla lezempi. Kodwa-ke, ngokumelene nezifiso zomndeni wakhe kanye nombono owandile wokuhlonishwa eFrance, wayenentshisekelo ngezibalo kusukela esemncane. Phakathi nenkonzo yakhe yezempi, wenza sengathi uphumule etendeni lakhe futhi esikhundleni salokho wafunda i-geometry. UBernard de Fontenelle wabhala ngaye encwadini yakhe ethi L'Hôpital:

Ngoba kufanele kuvunywe ukuthi isizwe samaFulentshi, nakuba siziphatha kahle njengazo zonke ezinye, sisekulolo hlobo lobuqaba esizibuza ngalo ukuthi ngabe isayensi, ezithathwe endaweni ethile, azihambisani nezicukuthwane, nokuthi ayiyona yini into enhle kakhulu ukungazi lutho. … Ngizibonele mathupha abanye balabo ababesebenza ngesikhathi esifanayo, bemangele kakhulu ukuthi indoda eyayiphila njengabo yayingomunye wochwepheshe bezibalo abahamba phambili eYurophu.

UL’Hôpital washiya ebuthweni laseFrance ngenxa yokukhubazeka kwamehlo, nakuba kwakunamahemuhemu ukuthi wayefuna ukwenza izibalo ngokugcwele. Manje amashumi amabili nane, wayethamele iBandla Le-Oratory embuthanweni kaNicolas Malebranche (iqembu elihlangana ukuze lixoxisane futhi libe nobudlelwane,) elaligcwele ongoti bezibalo nososayensi abaningi baseParis. Lapho, wahlangana no-Johann Bernoulli, umfowabo omncane kaJakob Bernoulli, owayefundise uLeibniz ebusheni bakhe futhi wayesebhekwa njengongqondongqondo wezibalo. U-L'Hôpital wayengumfundi oshiseka kakhulu kaBernoulli futhi ngokushesha wamkhokhela ukuze amfundise ngasese, kunalokho.

I-L'Hôpital ithumele isixazululo senkinga esifundweni uBernoulli ayemnike sona kuChristiaan Huygens ngaphandle kokuthi kwakungesona esakhe. Ngokuqondakalayo, ngaphandle kobufakazi obuphambene nalokho, u-Huygens wacabanga ukuthi uL'Hôpital ukwenzile. U-Bernoulli wayethukuthele futhi wephula izincwadi zakhe ezivame ukubhalelana ne-L'Hôpital izinyanga eziyisithupha-kodwa wephula ukuthula lapho u-L'Hôpital emcela "okutholakele" okwengeziwe ngomshini ogcina imali ongamakhulu amathathu (kanye nokwandayo). Ucele umfundisi wakhe ukuthi amnikeze namalungelo akhethekile okuphumelela kwakhe nezifundo zakhe. UBernoulli waphendula ngokushesha ukuthi wayengeke aphinde ashicilele lutho empilweni yakhe uma u-L'Hôpital efisa.

Ithathela kulokho okwatholwa uBernoulli namanothi avela ezifundweni zakhe, i-L’Hôpital yashicilela lokho okwakuzoba incwadi yokuqala yokubala: Analyse de infiniment petits pour l’intelligence des lignes courbes (Ukuhlaziywa Kwamanani Amancane Ngokungenakulinganiswa Ukuze Kuqondwe Ama-Curves.) Kuyo, ubeka umkhawulo wokuthi unganquma kanjani:

1. Nikeza ukuthi amanani amabili, umehluko wawo oyinani elincane ngokungenamkhawulo, angase athathwe (noma asetshenziswe) ngokunganaki komunye nomunye; noma (okuyinto efanayo) ukuthi inani elenyuka noma lehliswa kuphela ngenani elincane elingenakulinganiswa lingabhekwa njengelihlala lifana.

2. Nikeza ukuthi ijika lingabhekwa njengokuhlanganiswa kwenombolo engapheli yemigqa eqondile emincane ngokungenamkhawulo; noma (okuyinto efanayo) njengepholigoni yenombolo engapheli yezinhlangothi, ngayinye incane ngokungenakulinganiswa, enquma ukugoba kwejika ngama-engeli awenzayo namanye.

Nakuba kungethulwanga ngokusemthethweni njengasezincwadini zezibalo zesimanje, njengakuSigaba 4.4 se-Stewart's Calculus: Early Transcendentals, esichazayo:

njengomthetho we-L'Hôpital (ocashunwe encwadini njenge-L'Hospital,) isitatimende sakhe sokuqala kanye nokuphindaphinda kwesimanje kuyefana ngokomqondo. Lapho i-L’Hôpital ikhuluma ngomehluko omncane kakhulu, lokhu kufana nokumelwa kwemikhawulo. Umqondo "wemigqa emincane eqondile ngokungenamkhawulo" umelela ukuqonda kwejiyomethri kokuhlukanisa futhi ungukhokho womqondo wethu wamanje wokuphuma kokunye. Sekukonke, njengaseSigabeni 4.4., ithiyori yokuqala ye-L’Hôpital ithi amafomu angapheli angaxazululwa ngokuthola izinga loshintsho lwemisebenzi.

Abazwelana no-Johann Bernoulli bathi waphoqwa ukuba athobele intando yezikhulu. Naphezu kwesivumelwano sokuqala sikaBernoulli ngenxa yokuphelelwa yithemba kwezezimali, ukuhlelwa kwaqhubeka isikhathi eside kuprofesa wakhe ophumelelayo eGroningen. UBernoulli uthe incwadi ka-L'Hôpital "eyakhe empeleni" ngemuva kokushona komfundi wakhe wangaphambili. Ngaleso sikhathi, idumela likaBernoulli lalifiphele ngemva kwemigqa eminingi nomfowabo omdala. Ngaleso sikhathi, kwakujwayelekile ukuthi izicukuthwane zikhokhele izinsizakalo ezivela kochwepheshe abanamandla aphezulu njengosopolitiki nabameli, futhi abaningi babebheka u-L’Hôpital njengesazi sezibalo esinekhono ngokwaso.

Iphuzu lokuqala lokungabaza ngobuqotho bomsebenzi ka-L'Hôpital kwakuyisixazululo sakhe senkinga ye-brachistochrone (eyadalwa u-Johann Bernoulli ngo-1696, inkinga mayelana nejika lokwehla okusheshayo):

Inkinga Entsha Izazi Zezibalo Ezimenywa Ukuba Ziyixazulule: Uma amaphuzu amabili u-A no-B enikezwa endizeni eqondile, ukunikeza inhlayiya engu-M ehamba umzila u-AMB lapho, yehla ngaphansi kwesisindo sayo, idlule isuka endaweni A iye endaweni B ngesikhathi esifushane.

Kwaphakanyiswa ukuthi impendulo kaL'Hôpital kulo mbuzo kwakungeyona eyakhe, mhlawumbe ekathisha wakhe uBernoulli ngokwakhe.

Ekugcineni, i-L'Hôpital yayinekhono ekuhlanganiseni izimfundiso zika-Johann Bernoulli futhi yanyathelisa i-opus ebalulekile emkhakheni wokubala othuthukayo, okwenza intuthuko ifinyeleleke kubabukeli abaningi. Kodwa-ke, umsebenzi wakhe ubungeke ubambelele ezindinganisweni zamanje zobuqotho bezemfundo, futhi kungathiwa wasebenzisa kabi isikhundla sakhe sezezimali ukuze abe usaziwayo wezemfundo eFrance ekhulwini leshumi nesikhombisa ngaphandle kokuqamba okusha kwangempela kontanga yakhe.

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.