L’Hôpital ka mara bɔyɔrɔ

Guillaume-François-Antoine Marquis de l’Hôpital, Marquis de Sainte-Mesme, Comte d’Entremont et Seigneur d’Ouques-la-Chaise, min tun bɛ wele kosɛbɛ ko Guillaume L’Hôpital, bangera san 1661 Pari denbaya dɔ kɔnɔ min tun ye sɔrɔdasi ciyɛn barikama ye. Nka, a ka denbaya sago n’a ka faamako faamuyali min tun bɛ Faransi, a tun bɛ jatebɔ diyabɔ kabini a denmisɛnman. A ka sɔrɔdasi baara senfɛ, a y’a kɛ i n’a fɔ a bɛ lafiɲɛ a ka fanibugu kɔnɔ, wa o nɔ na, ​​a ye jateminɛ kɛ. Bernard de Fontenelle y’a sɛbɛn a ko la a ka L’Hôpital tanuli kɔnɔ:

Sabula a ka kan ka Sɔn a ma ko Faransi jamana, hali n’a kɛcogo ka ɲi i n’a fɔ jamana tɔw bɛɛ, a bɛ o barbari sugu la hali bi, n’a b’a yɛrɛ ɲininka n’a y’a sɔrɔ dɔnniyaw, n’u taara yɔrɔ dɔ la, n’u tɛ bɛn ni bonya ye, wa n’a tɛ bonya ye ka tɛmɛ o kan ka foyi dɔn. ... Ne yɛrɛ ye mɔgɔ dɔw ye minnu ye baara kɛ waati kelen na, u kabakoyara kosɛbɛ ko cɛ min tun bɛ balo i n’a fɔ olu, o tun ye jatebɔla ŋana dɔ ye Erɔpu jamanaw na.

L’Hôpital bɔra Faransi sɔrɔdasikulu la k’a sababu kɛ yelibaliya ye, hali n’a tun bɛ fɔ ko a b’a fɛ dɔrɔn ka jatebɔ kɛ waati dafalen na. Sisan, a si bɛ san mugan ni naani na, a taara Oratori jɛkulu la Nicolas Malebranche ka sɛrɛkili la (jɛkulu min bɛ ɲɔgɔn lajɛ baro ni jɛɲɔgɔnya kama,) min tun falen bɛ Pari jatebɔla ni dɔnnikɛla ŋana caman fɛ. O yɔrɔ la, a ye Johann Bernoulli sɔrɔ, Jakob Bernoulli dɔgɔkɛ min tun ye petulant ye, min tun ye Leibniz kalan a ka kamalenninya waati la, wa a tun jatera jatebɔla ŋana ye kaban. L’Hôpital tun ye Bernoulli ka kalanden timinandiyalenba ye, wa a ma mɛn, a y’a sara walasa a k’a kalan a kelen na, o nɔ na.

L’Hôpital ye gɛlɛya ɲɛnabɔcogo dɔ di ka bɔ kalan na, Bernoulli tun ye min di a ma, ka di Christiaan Huygens ma, k’a sɔrɔ a m’a fɔ ko o tɛ ale yɛrɛ ta ye. A faamuyalen don ko dalilu si tun tɛ yen min b’a jira ko Huygens y’a miiri ko L’Hôpital de y’o kɛ. Bernoulli dimina, wa a y’a ka batakiw cilenw tiɲɛ tuma caman na ni L’Hôpital ye kalo wɔɔrɔ kɔnɔ–nka a y’a ka makun tiɲɛ siɲɛ kelen L’Hôpital y’a ɲini a fɛ a ka “sɔrɔli” wɛrɛw kɛ kilo kɛmɛ saba (ani min bɛ ka caya) minɛfɛn dɔ kan. A y’a ɲini a ka kalanfa fɛ fana a ka josariyaw danma di a ma a ka bεnkanw n’a ka jɛmukanw na. Bernoulli y’a jaabi joona ko ale tɛna foyi bɔ tugun a ka ɲɛnamaya kɔnɔ ni L’Hôpital b’a fɛ.

L’Hôpital ye Bernoulli ka sɔrɔw n’a ka sɛbɛnniw bɔ a ka jɛmukanw na, a ye min bɔ min bɛna kɛ jatebɔ gafe fɔlɔ ye: Analyse de infiniment petits pour l’intelligence des lignes courbes (Analyse of Infinitely Small Quantities for the Understanding of Curves.) O kɔnɔ, a bɛ dan minnu tɛ dantigɛ, n’o tɛ, olu jateminɛcogo jira:

1. A’ y’a to hakɛ fila, minnu danfara ye hakɛ fitinin danma ye, olu bɛ se ka ta (walima ka baara kɛ ni u ye) k’a sɔrɔ u ma u janto ɲɔgɔn na; walima (o ye fɛn kelen ye) ko hakɛ min bɛ caya walima ka dɔgɔya ni hakɛ fitinin danma dɔrɔn ye, o bɛ se ka jate ko a tora a cogo la.

2. A di a ma ko kurukuru bɛ ​​se ka jate i n’a fɔ tigɛli misɛnnin dan tɛ minnu na, olu lajɛlen ye; walima (o ye fɛn kelen ye) i n’a fɔ kɛrɛ hakɛ danmadɔ camanba, minnu kelen-kelen bɛɛ ka dɔgɔ dan tɛ minnu na, minnu bɛ kurukuruni kurulen dantigɛ u bɛ kɛrɛ minnu kɛ ni ɲɔgɔn ye.

Hali n’a ma jira cogo la min bɛ kɛ cogo la i n’a fɔ bi jatebɔ gafew kɔnɔ, i n’a fɔ Stewart’s Calculus: Early Transcendentals sigida 4.4 kɔnɔ, min b’a ɲɛfɔ:

i n’a fɔ L’Hôpital ka sariya (a fɔra gafe kɔnɔ ko L’Hospital,) a ka kuma fɔlɔ ni bi segin-ka-bɔnyew ye kelen ye hakilina ta fan fɛ. Ni L’Hôpital bɛ kuma danfara misɛnnin danmadɔw kan, o bɛ tali kɛ danyɔrɔw jiracogo la. «Jɛkulu tilennen misɛnnin dan tɛ minnu na» hakilina bɛ danfara faamuyali jateminɛ jateminɛ, wa a ye an ka sisan hakilina kɔrɔba ye min ye fɛn bɔlen ye. Kuma bɛɛ la, i n’a fɔ a kɛra cogo min na sigida 4.4., L’Hôpital ka hakilina fɔlɔ b’a fɔ ko cogoya dantigɛbaliw bɛ se ka ɲɛnabɔ ni baarakɛcogo caman yeli hakɛ sɔrɔli ye.

Johann Bernoulli hinɛbagaw b’a fɔ ko a wajibiyara ka a yɛrɛ bila mɔgɔba sago kɔrɔ. Hali ni Bernoulli ye bɛnkan fɔlɔ kɛ wariko gɛlɛya kosɔn, o labɛn tora senna kabini waati jan fo ka se a ka karamɔgɔya ɲɛtaa ma Groningen. Bernoulli y’a fɔ ko L’Hôpital ka gafe in tun ye “a yɛrɛ ta ye” a ka kalanden kɔrɔ salen kɔfɛ dɔrɔn. O waati la, Bernoulli tɔgɔ tun bɛ dibi la, a kɛlen kɔ ka ɲɔgɔn sɔsɔ siɲɛ caman n’a kɔrɔkɛ ye. O waati la, a tun ye sariya ye faamaw bolo ka baara sara ka bɔ baarakɛlaw yɔrɔ minnu fanga ka bon i n’a fɔ politikikɛlaw ni sariyatigiw, wa mɔgɔ caman tun bɛ L’Hôpital jate jatebɔla ŋana ye a yɛrɛ la.

Siga fɔlɔ dɔ min kɛra L’Hôpital ka baara dafalen na, o kɛra a ka brachistochrone gɛlɛya ɲɛnabɔcogo ye (Johann Bernoulli ye min bila sen kan san 1696, gɛlɛya min bɛ jigin teliya kurulen kan):

Gɛlɛya kura min Jateblaw bɛ Weele ka ɲɛnabɔ: Ni yɔrɔ fla A ni B Dira 'yɔrɔ jɔlen na, ka sira AMB Di fɛnɲɛnɛma-yɔrɔ M dɔ ma, n'a Jiginna a yɛrɛ girinya 'kɔnɔ, a bɛ Tɛmɛ yɔrɔ A la ka Taa yɔrɔ B la waati kunkurunnin kɔnɔ.

A jirala ko L’Hôpital ka ɲininkali jaabi tɛ a yɛrɛ ta ye, n’a sɔrɔla a karamɔgɔ Bernoulli yɛrɛ ta tɛ.

A laban na, L’Hôpital tun bɛ se Johann Bernoulli ka kalansiraw faralen ɲɔgɔn kan, wa a ye opus nafama dɔ bɔ jatebɔyɔrɔ la min bɛ yiriwa joona, o min ye yiriwaliw kɛ jamaba ye. Nka, a ka baara tun tɛna se ka se sisan kalanko dafalen sariyaw ma, wa a bɛ se k’a fɔ ko a ye a ka wariko jɔyɔrɔ tiɲɛ walasa ka kɛ kalanko tɔgɔba ye san kɛmɛ tan ni wolonwulanan na Faransi k’a sɔrɔ a tɔɲɔgɔnw ma kokura lakika kɛ.

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.