Analyse Des Infiniment Petits Pour L'Intelligence Des Lignes Courbes
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''Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes'' (literal translation: ''Analysis of the infinitely small to understand curves'') of 1696, is the first
textbook A textbook is a book containing a comprehensive compilation of content in a branch of study with the intention of explaining it. Textbooks are produced to meet the needs of educators, usually at educational institutions, but also of learners ( ...
published on the
infinitesimal calculus Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the calculus of ...
of
Gottfried Wilhelm Leibniz Gottfried Wilhelm Leibniz (or Leibnitz; – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Sir Isaac Newton, with the creation of calculus in addition to ...
. It was written by the French mathematician Guillaume de l'Hôpital, and treated only the subject of
differential calculus In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus—the study of the area beneath a curve. ...
. Two volumes treating the differential and
integral calculus In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus,Int ...
, respectively, had been authored by
Johann Bernoulli Johann Bernoulli (also known as Jean in French or John in English; – 1 January 1748) was a Swiss people, Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is known for his contributions to infin ...
in 1691–1692, and the latter was published in 1724 to become the first published textbook on the integral calculus.


L'Hôpital's rule

The book includes the first appearance of L'Hôpital's rule. The rule is believed to be the work of
Johann Bernoulli Johann Bernoulli (also known as Jean in French or John in English; – 1 January 1748) was a Swiss people, Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is known for his contributions to infin ...
, since l'Hôpital, a nobleman, paid Bernoulli a retainer of 300 per year to keep him updated on developments in calculus and to solve problems he had. Moreover, the two signed a contract allowing l'Hôpital to use Bernoulli's discoveries in any way he wished. Among these problems was that of limits of indeterminate forms. When l'Hôpital published his book, he gave due credit to Bernoulli and, not wishing to take credit for any of the mathematics in the book, he published the work anonymously. Bernoulli, who was known for being extremely jealous, claimed to be the author of the entire work. Nevertheless, the rule was named for l'Hôpital, who never claimed to have invented it in the first place.


See also

* l'Hôpital controversy


References


External links

*
Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes
' in various formats ( djvu,
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, etc.) at the
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. *
Calculi infinitesimalis Pars I
seu calculus differentialis, expositus analysi infinite parvorum'' : a 1764 edition (Trattner) of Analyse des infiniment petits'', at the université de Strasbourg. 1696 in science 1696 non-fiction books History of calculus Mathematics textbooks Works published anonymously {{Math-hist-stub