L'Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes
Encyclopedia
Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes (literal translation: Analysis of the infinitely small to understand curves) (1696), is the first textbook published on the infinitesimal calculus
of Leibniz. It was written by the French mathematician Guillaume de l'Hôpital
, and treated only the subject of differential calculus
. Two volumes treating the differential and integral calculus, respectively, had been authored by Johann Bernoulli
in 1691–1692, and the latter was published in 1724 to become the first published textbook on the integral calculus.
In this book is the first appearance of L'Hôpital's rule
. The rule is believed to be the work of Johann Bernoulli
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, and until recently, it was believed to be so. Nevertheless, the rule was named for l'Hôpital, who never claimed to have invented it in the first place.
Infinitesimal calculus
Infinitesimal calculus is the part of mathematics concerned with finding slope of curves, areas under curves, minima and maxima, and other geometric and analytic problems. It was independently developed by Gottfried Leibniz and Isaac Newton starting in the 1660s...
of Leibniz. It was written by the French mathematician Guillaume de l'Hôpital
Guillaume de l'Hôpital
Guillaume François Antoine, Marquis de l'Hôpital was a French mathematician. His name is firmly associated with l'Hôpital's rule for calculating limits involving indeterminate forms 0/0 and ∞/∞...
, and treated only the subject of differential calculus
Differential calculus
In mathematics, differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus....
. Two volumes treating the differential and integral calculus, respectively, had been authored by Johann Bernoulli
Johann Bernoulli
Johann Bernoulli was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family...
in 1691–1692, and the latter was published in 1724 to become the first published textbook on the integral calculus.
In this book is the first appearance of L'Hôpital's rule
L'Hôpital's rule
In calculus, l'Hôpital's rule uses derivatives to help evaluate limits involving indeterminate forms. Application of the rule often converts an indeterminate form to a determinate form, allowing easy evaluation of the limit...
. The rule is believed to be the work of Johann Bernoulli
Johann Bernoulli
Johann Bernoulli was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family...
since l'Hôpital, a nobleman, paid Bernoulli a retainer of 300₣
French franc
The franc was a currency of France. Along with the Spanish peseta, it was also a de facto currency used in Andorra . Between 1360 and 1641, it was the name of coins worth 1 livre tournois and it remained in common parlance as a term for this amount of money...
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, and until recently, it was believed to be so. Nevertheless, the rule was named for l'Hôpital, who never claimed to have invented it in the first place.
External links
- Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes in various formats (djvuDjVuDjVu is a computer file format designed primarily to store scanned documents, especially those containing a combination of text, line drawings, and photographs. It uses technologies such as image layer separation of text and background/images, progressive loading, arithmetic coding, and lossy...
, pdf, etc.) at the Wayback machine
- 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