Analyse des infiniment petits pour l'intelligence des lignes courbes
Traité analytique
อ้างอิง
↑In the 17th and 18th centuries, the name was commonly spelled "l'Hospital", and he himself spelled his name that way. However, French spellings have been altered: the silent 's' has been removed and replaced with the circumflex over the preceding vowel. The former spelling is still used in English where there is no circumflex.
↑Unbeknownst to him, a solution had already been obtained by James Gregory in letters to Collins (1670–1671), ibid.
↑O'Connor, John J.; Robertson, Edmund F. "De L'Hopital biography". The MacTutor History of Mathematics archive. Scotland: School of Mathematics and Statistics, University of St Andrews. คลังข้อมูลเก่าเก็บจากแหล่งเดิมเมื่อ 2015-05-06. สืบค้นเมื่อ 21 December 2008.
↑L’Hospital, Analyse des infiniment petits... , pages 145–146: "Proposition I. Problême. Soit une ligne courbe AMD (AP = x, PM = y, AB = a [see Figure 130] ) telle que la valeur de l’appliquée y soit exprimée par une fraction, dont le numérateur & le dénominateur deviennent chacun zero lorsque x = a, c’est à dire lorsque le point P tombe sur le point donné B. On demande quelle doit être alors la valeur de l’appliquée BD. [Solution: ]...si l’on prend la difference du numérateur, & qu’on la divise par la difference du denominateur, apres avoir fait x = a = Ab ou AB, l’on aura la valeur cherchée de l’appliquée bd ou BD." Translation : "Let there be a curve AMD (where AP = X, PM = y, AB = a) such that the value of the ordinate y is expressed by a fraction whose numerator and denominator each become zero when x = a; that is, when the point P falls on the given point B. One asks what shall then be the value of the ordinate BD. [Solution: ]... if one takes the differential of the numerator and if one divides it by the differential of the denominator, after having set x = a = Ab or AB, one will have the value [that was] sought of the ordinate bd or BD."
Broadwin, Judy. "The Immortal L'Hospital"(PDF). AP Central – The College Board. คลังข้อมูลเก่าเก็บจากแหล่งเดิม(PDF)เมื่อ 2020-10-28. สืบค้นเมื่อ 2017-10-31.