Iwdi Laamu L’Hôpital

Gillaume-François-Antoine Marquis de l’Hôpital, Marquis de Sainte-Mesme, Konte d’Entremont e Seigneur d’Ouques-la-Chaise, ganndiraaɗo e nder yimɓe heewɓe Gilaum L’Hôpital, jibinaa ko e hitaande 1661 to Pari, e nder galle militeeruuji lega doole. Kono, e dow yiɗde ɓesngu makko e yiɗde jaajde teddungal e nder Farayse, o woni ko e yiɗde hiisa gila e cukaagu makko. E nder golle makko konu, o waɗiri no fooftorde e nder laylaytol makko, o janngi joometiri. Bernard de Fontenelle winndii e makko e nder deftere makko mawnde wiyeteende L’Hôpital:

Sibu ina haani jaɓeede wonde leñol Farayse ngol, hay so tawii noon ina jogii nehdi no feewi, ina woni e oon sifaa barbarism mo nganndu-ɗaa ina haawnii so tawii gannde ɗee, ƴettaaɗe e nokku gooto, ina njahdi e teddungal, tawa kadi ko ɓuri teddungal ko anndude hay huunde. ... Miin e hoore am mi yiyii won e gollotooɓe e oon sahaa, ina kaawaa no feewi wonde gorko guurɗo no maɓɓe nii ina jeyaa e annduɓe hiisaaji ɓurɓe mawnude e nder Orop.

L’Hôpital yalti konu Farayse sabu ŋakkeende yiytere, hay so tawii noon ina wiyee o yiɗi tan ko jokkude jaŋde hiisawal haa timma. Jooni ko duuɓi capanɗe jeegom e nay, o tawtoraama Congregation de l’Oratoire e nder dingiral Nicolas Malebranche (fedde nde mooɓotoo ngam yeewtidde e jokkondirde,) nde heewɓe e annduɓe hiisiwal e annduɓe mawɓe Pari ngoni heen. Ko ɗoon o hawri e Johann Bernoulli, miñiiko Jakob Bernoulli ɓurɗo famɗude e pettuɗo, jannginoowo Leibniz e cukaagu mum, mo nganndu-ɗaa ko ganndo hiisa. L’Hôpital ko almuudo ɓurɗo waawde Bernoulli, ɓooyaani ko o yoɓi mo ngam jannginde mo e nder suudu, e nokku makko.

L’Hôpital rokkii Christiaan Huygens feere caɗeele ummoraade e kursus mo Bernoulli rokki mo oo, tawi o wiyi wonaa mo. Faamde noon, tawi alaa ko holliti ɗum, Huygens miijii ko L’Hôpital waɗi ɗum. Bernoulli tikkani, o taƴi ɓataake makko keewɗo jokkondirde e L’Hôpital fotde lebbi jeegom–kono o taƴi silki makko nde L’Hôpital naamndii mo yo o ɓeydu “yiytude” e dow reenoowo teemedde tati kiloo (e ɓeydagol). O ñaagii kadi jannginoowo makko yo rokku mo hakkeeji keewɗi e ƴellitgol makko e lectures makko. Bernoulli jaabtii ko yaawi wonde o yaltintaa hay huunde kadi e nguurndam makko so L’Hôpital yiɗii.

E tuugnaade e jiytugol Bernoulli e binndanɗe makko e nder yeewtere makko, L’Hôpital yaltinii ko wonata deftere janngirnde hiisawal adannde : Analyse de infinite petits pour l’intelligence des lignes courbes (Anndude limtooji goɗɗi ɗi ngalaa keerol ngam faamde limtooji ɗii, no limtooji ɗii mbaɗirtee nii keeri ɗi nganndaaka:

1. Hokkude wonde limtooji ɗiɗi, ɗi ceergal mum en ko limtooji tokoosi ɗi ngalaa keerol, ina mbaawi ƴetteede (walla huutoreede) tawa ko e mbaydiiji ɗiɗi ; walla (ko huunde wootere) wonde keewal ɓeydaande walla ustaade tan ko e keewal tokosal ngal alaa keerol ina waawi siforeede ko heddii koo.

2. Hokkude wonde kurjuru ina waawi hiiseede ko mooɓondiral limre limre limre limre limre tokosere nde limre mum alaa keerol ; walla (ko ɗum huunde wootere) hono poligon banngeeji ɗi ngalaa keerol, heen gooto fof ina famɗi, ɗi nganndu-ɗaa ko ɗi njuuteendi njuuteendi ɗi mbaɗata e koye mum en.

Hay so tawii noon hollitaaka no fotiri e defte janngirɗe hiisaaji hannde ɗee, hono no hollirtee e Taƴre 4.4 Hiisaaji Stewart: Transcendentals gadani, sifotoonde:

hono kuulal L’Hôpital (hono no limtaa e deftere ndee ko L’Hospital,) haala makko gadana kaa e iteraaji jamaanu ɗii ko gootum e miijooji. So L’Hôpital haali ko fayti e ceertugol tokosol ngol alaa keerol, ɗum ina nanndi e hollirde keeri. Miijo “laabi juɓɓuɗi tokoosi ɗi ngalaa keerol” ina hollita faamde joometiri ceertugol, ko iwdi miijo men hannde ngoo e ƴellitaare. Haa teeŋti noon, hono no Taƴre 4.4., teskuyaaji L’Hôpital’s asliiji ɗii mbiyi wonde mbaadiiji ɗi ngalaa keerol ina mbaawi safreede e yiytude tolno waylo-waylo golle ɗee.

Yurmeende Johann Bernoulli ina wiya wonde o dogniraa ko ɗooftaade yiɗde teddungal. Bernoulli fof e nanondiral gadanal ngal sabu ŋakkeende ngalu, peeje ɗee njokkii haa ɓooyi haa o heɓi jappeere makko to Groningen. Bernoulli wiyi deftere L’Hôpital ndee ko “ko ɓuri teeŋtude” tan ko caggal maayde almuudo makko gonnooɗo. E oon sahaa, innde Bernoulli ina muusi caggal nde o waɗi rowreeji keewɗi e mawniiko. E oon sahaa, ko huunde woowaande wonande tedduɓe yoɓde sarwisaaji ummoraade e annduɓe toowɓe ko wayi no politik e awokaaji, heewɓe ina cikkatnoo L’Hôpital ko ganndo hiisiwal baawɗo e mbaadi mum.

Toɓɓere sikkitaare adannde e nuunɗal golle L’Hôpital ko feere makko e caɗeele brachistochrone (ɗe Johann Bernoulli ƴetti e hitaande 1696, caɗeele jowitiiɗe e kurjuru jippagol ɓurngol yaawde):

Caɗeele kese ɗe hiisiwal noddata ngam safrude : So toɓɓe ɗiɗi A e B ndokkaama e nder weeyo ngo, ngam rokkude tagofeere M laawol AMB ngol, jippaade e les teddeendi mum, ngol rewata ko toɓɓere A haa toɓɓere B e nder waktu ɓurɗo juutde.

Ina sikkaa wonde jaabawol L’Hôpital e naamnal ngal wonaa jaabawol makko, ina gasa tawa ko jannginoowo makko Bernoulli e hoore mum.

E joofnirde, L’Hôpital ina anndi sinndude janngirɗe Johann Bernoulli, yaltinii opus keewɗo faayiida e fannu hiisawal jaawɗo ƴellitaade, baɗnooɗo ƴellitaare heɓtaade yimɓe heewɓe. Kono golle makko njogoraani yahdude e tolnooji hannde ɗii e nder nuunɗal jaŋde, ina waawi wiyeede wonde o huutoriima darnde makko e kaalis ngam wonde ceerno jaŋde e nder leydi Farayse e teeminannde sappo e jeeɗiɗaɓiire tawa o alaa heen newingol goongawol ngol sehilaaɓe makko mbaɗi.

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.