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Born 1661 Paris, France Died 2 February 1704 Paris, France Summary**De L"Hôpital**was a French mathematician who wrote the first textbook on calculus, which consisted of the lectures of his teacher Johann Bernoulli.

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### Biography

khổng lồ give**Guillaume de l"Hôpital**"s full name would take a whole paragraph so we give just a much shortened version:

**Guillaume-François-Antoine Marquis de l"Hôpital, Marquis de Sainte-Mesme, Comte d"Entremont and Seigneur d"Ouques-la-Chaise**. The family had been a prominent one in France over many generations going back to around the 12th century. There are various spellings of the name Hôpital, the earlier versions being l"Hospital or Lhospital with l"Hôpital being a relatively modern form of the name. His father was Anne-Alexandre de l"Hôpital, a Lieutenant-general in the King"s Army; he was Comte de Sainte-Mesme and Duc d"Orléans. Guillaume"s mother was Elisabeth Gobelin, the daughter of Claude Gobelin who was an Intendant in the King"s Army và a Councillor of State. Sturdy writes

**Histoires Paris Academy of Sciences (1704), 125." href="../../Biographies/De_LHopital/#reference-7">7>, recounts that when l"Hôpital was fifteen years old he was, on one occasion, discussing mathematics with the Duke of Roannès & a Mr Arnaud. They told him about a very difficult problem on the cycloid that Blaise Pascal had proposed. A few days later l"Hôpital had solved the problem. Given his family background it is not surprising that Guillaume de l"Hôpital followed a military career & served as a captain in a cavalry regiment. He certainly did not give up his interest in mathematics, as Fontenelle explains**

**Histoires Paris Academy of Sciences (1704), 125." href="../../Biographies/De_LHopital/#reference-7">7>:-He entered into the service, but without giving up his dearest passion. He studied geometry even in his tent. It is not just that he retired there khổng lồ study, it was also to hide his application to study. For it must be admitted that the French nation, although as well mannered as any other, is still in that sort of barbarism by which it wonders whether the sciences, taken to a certain point, are incompatible with nobility, và whether it is not more noble to know nothing. ... I have personally seen some of those who served at the same time, greatly astonished that a man who lived lượt thích them was one of the leading mathematicians in Europe.However he resigned from the army because of nearsightedness being unable khổng lồ see beyond ten paces. Julian Coolidge writes**The Mathematics of Great Amateurs (Oxford University Press, 1990)." href="../../Biographies/De_LHopital/#reference-3">3>:-One is inclined to lớn believe that it was l"Hôpital"s love of mathematics rather than the imperfection of his vision that led him to lớn abandon a military career in favour of a scientific one.Certainly from that time on he directed his attention to lớn mathematics. It is almost certain that l"Hôpital would be totally unknown in the world of mathematics today but for a chance meeting between him và Johann Bernoulli towards the end of 1691. Bernoulli at this time was 24 years old và he had just arrived in Paris after giving lectures on the latest development in mathematics, namely Leibniz"s differential calculus. L"Hôpital was at the time a thành viên of Nicolas Malebranche"s circle at the Congregation of the Oratory which contained the leading mathematicians and scientists of Paris. It was an obvious place for Bernoulli khổng lồ go to lớn meet the leading French mathematicians and he soon discovered that l"Hôpital was the most enthusiastic. L"Hôpital, for his part, was intrigued to meet Bernoulli, for it quickly became clear lớn him that he was much more knowledgeable about the new developments in infinitesimal methods than anyone else in Paris. Bernoulli told l"Hôpital, and others in Malebranche"s circle, that he knew the general formula for the radius of curvature of a curve. Although others such as Huygens, Leibniz and Newton knew this, it was thought in Paris khổng lồ be an important xuất hiện question so l"Hôpital, although probably one of the best mathematicians in France, realised he could learn much from Bernoulli. Bernoulli agreed khổng lồ give four lectures a week khổng lồ Malebranche"s circle và he did so for the next six months. L"Hôpital attended these lectures but then moved from Paris lớn his estate at Ouques where he employed Bernoulli khổng lồ give him private lessons. By November 1692 Bernoulli had left Ouques & returned to lớn Basel from where he carried out a correspondence with l"Hôpital.L"Hôpital had published a few brief mathematical notes, but in 1692, while Bernoulli was giving him lessons at Ouques, l"Hôpital sent a solution of de Beaune"s problem lớn Huygens. Florimond de Beaune had asked for a curve for which the subtangent had a fixed length & Bernoulli had included the solution in the course he had given l"Hôpital. L"Hôpital did not claim that the solution he sent Huygens was his own but Huygens made the reasonable assumption that it was. Shortly after this l"Hôpital published the solution under a pseudonym. By the time Bernoulli saw the published solution he was back in Basel and, naturally enough, he was highly displeased. For about six months the correspondence between l"Hôpital and Bernoulli ceased then, on 17 March 1694, l"Hôpital sent a letter lớn Bernoulli with a remarkable proposition Isis Isis

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I have made free use of their discoveries, as well as those of Mr Leibniz, so that I frankly return to them whatever they please to lớn claim as their own.He was also aware of Newton"s contributions, writing:-I must here in justice own (as Mr Leibniz himself has done in "Journal des Sçavans" for August 1694) that the learned Sir Isaac Newton likewise discovered something lượt thích the Calculus Differentialis ... Bit the method of Mr Leibniz is much more easy and expeditious, on tài khoản of the notation he uses, not to lớn mention the wonderful assistance it affords on many occasions.The book begins with two definitions:

**49**(1) (1958), 54-62." href="../../Biographies/De_LHopital/#reference-11">11>:-I will be happy to lớn give you a retainer of 300 pounds, beginning with the first of January of this year. ... I promise shortly khổng lồ increase this retainer, which I know is very modest, as soon as my affairs are somewhat straightened out. ... I am not so unreasonable as khổng lồ demand in return all of your time, but I will ask you lớn give me at intervals some hours of your time khổng lồ work on what I request & also to lớn communicate lớn me your discoveries, at the same time asking you not khổng lồ disclose any of them to lớn others. I ask you even not to send here lớn Mr Varignon or khổng lồ others any copies of the writings you have left with me; if they are published, I will not be at all pleased. Answer me regarding all this ...Although no copy of Johann Bernoulli"s reply has been found, we know from l"Hôpital"s next letter that Bernoulli rapidly accepted the proposition. The correspondence continued and in one of the letters Bernoulli sent to lớn l"Hôpital in 1695 he made the following remarkable promise

**49**(1) (1958), 54-62." href="../../Biographies/De_LHopital/#reference-11">11>:-You have only khổng lồ let me know your definite wishes, if I am to lớn publish nothing more in my life, for I will follow them precisely & nothing more by me will be seen.On 1 September 1695 Johann Bernoulli left Basel khổng lồ take up a new appointment as professor of mathematics at Groningen. In 1696 L"Hôpital"s famous book

*Analyse des infiniment petits pour l"intelligence des lignes courbes*Infinitesimal analysis lớn understand curved lines">Ⓣ(Infinitesimal analysis lớn understand curved lines) was published; it was the first text-book khổng lồ be written on the differential calculus. In the introduction l"Hôpital acknowledges his indebtedness khổng lồ Leibniz, Jacob Bernoulli and Johann Bernoulli but l"Hôpital regarded the foundations provided by him as his own ideas. He wrote:-I must own myself very much obliged khổng lồ the labours of Messieurs Bernoulli, but particularly to lớn those of the present Professor at Groningen.

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I have made free use of their discoveries, as well as those of Mr Leibniz, so that I frankly return to them whatever they please to lớn claim as their own.He was also aware of Newton"s contributions, writing:-I must here in justice own (as Mr Leibniz himself has done in "Journal des Sçavans" for August 1694) that the learned Sir Isaac Newton likewise discovered something lượt thích the Calculus Differentialis ... Bit the method of Mr Leibniz is much more easy and expeditious, on tài khoản of the notation he uses, not to lớn mention the wonderful assistance it affords on many occasions.The book begins with two definitions: