Why is L'hospital law pronounced Lopita? ==

L'Hospital, Guillaume Francis Antoine de (1661-1704) "The first calculus textbook was published in 1696, and it was written by Lopidus."　--Ives "The 'Lobida's Law' for finding the limit of a partition whose numerator and denominator converge to zero was told to Lobida by John Bernoulli in 1694."　─ ─ from Liang Zongju edited by the World Mathematical History Compendium Lopida was a French mathematician.Born in Paris in 1661; died on February 2, 1704 in Paris. Born in Paris in 1661; died in Paris on February 2, 1704. Born into a French noble family, Lobeda held the title of Count of Entremont, Marquis of Saimte Mesme. As a young man he served as an officer in the cavalry, but retired because of his nearsightedness and turned to scholarship.　Lobeda showed his mathematical talent at an early age, solving at the age of fifteen a problem of the pendulum posed by Pascal. He was a great believer in Leibniz's calculus and was a pupil of Johann Bernoulli, whose "fastest descending line" problem he successfully solved. He was a member of the French Academy of Sciences.　Loppitta's greatest achievement was to write the world's first systematic calculus tutorial - "Infinitesimal Analysis for the Understanding of Curves", so that the American historian Eves (Eves) said: "The first calculus textbook was published in 1696, which was written by Loppitta." It was later revised and reprinted several times and played an important role in popularizing calculus on the European continent, especially in France.　The book follows the classical paradigm of Euclid and Archimedes and takes definitions and axioms as its starting point. In this book, the following definitions and axioms are given first: "Definition 1, call those quantities that are continuously increasing or decreasing variables, ......" "Definition 2, an infinitesimal portion of a variable that is continuously increasing or decreasing in its neighborhood is called a difference (differential), ......" Two axioms are then given, the first stating that several quantities differing only by infinitesimal amounts can be substituted for each other, and the second stating that a curve is considered as a collection of infinitely many infinitesimal straight lines... ...After these two axioms, the fundamental laws and examples of differential operations are given. Chapter II applies these laws to determine the slope of a curve at a given point, and gives many examples, using a more general approach. Chapter 3 discusses the great and small problems, including some examples drawn from mechanics and geography, and goes on to discuss inflection and cusp problems, and introduces higher-order differentiation. Later chapters discuss problems such as asymptotes and divergence curves.　Much of Lopidar's book is taken from the early writings of his teacher, John Bernoulli.　The story goes like this: John Bernoulli wrote two short treatises on the calculus between 1691 and 1692, but they were not published. Shortly afterward, he agreed to teach calculus to the young Marquis de Lobeda in return for a regular salary. He passed on his mathematical discoveries to Lopidus and allowed him to use them whenever he wanted. Lopidar then wrote "The Analysis of Infinitesimals for the Understanding of Curves", based on John Bernoulli's teachings and unpublished treatises, as well as on his own studies. This work not only popularized calculus, but also helped John Bernoulli to complete and disseminate the theory of plane curves.　It is worth noting in particular that in the ninth chapter of this work there is a law for finding the limit of a fraction whose numerator and denominator converge to zero, the so-called "Lobida's law": if it is a differentiable function and the limit at the right-hand end exists or is infinite. But at that time, Lopida's argument did not use the function's notation, but was narrated in words, equivalent to the assertion , his conclusion is: if the vertical coordinate of a given curve "is expressed as a fraction, and x taken to the limit of the numerator and denominator are equal to zero", then "if the numerator of the differential, and then divided by the the differential of the denominator, and finally make , in it, the value (of the longitudinal coordinate when ) is obtained". This law was actually told to him by John Bernoulli in a letter dated July 22, 1694. The laws that are now used in general calculus textbooks for solving the limits of other undetermined equations are later extensions of Lopidar's law (e.g., the law for undetermined equations was later given by Euler), but they are now called "Lopidar's law" in general.　Lobeda had planned to publish a book on integration, but abandoned his plans when he learned that Leibniz also intended to write such a book. He also wrote a book on conic curves, Analytics of Conic Curves, which was published 16 years after his death.　Lopidar was a generous man with a great sense of humor. Because of his association with the leading mathematicians of Europe at the time, he became a prominent figure in the spread of calculus throughout Europe.