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1810

Gergonne publishes the first volume of his new mathematics journal

1811

Poisson publishes *Traité de mécanique* (*Treatise on Mechanics*). It includes Poisson's work on the applications of mathematics to topics such as electricity, magnetism and mechanics.

1812

Laplace publishes the two volumes of *Théorie Analytique des probabilités* (*Analytical Theory of Probabilities*). The first book studies generating functions and also approximations to various expressions occurring in probability theory. The second book contains Laplace's definition of probability, Bayes's rule, and mathematical expectation.

1814

Argand gives a beautiful proof (with some gaps) of the fundamental theorem of algebra. (See this History Topic.)

1814

Barlow produces Barlow's Tables which give factors, squares, cubes, square roots, reciprocals and hyperbolic logs of all numbers from 1 to 10000.

1815

Peter Roget (the author of Roget's Thesaurus) invents the "log-log" slide rule.

1815

Pfaff publishes important work on what are now called "Pfaffian forms".

1816

Peacock, Herschel and Babbage are the leaders of the Analytical Society at Cambridge which publishes an English translation of Lacroix's textbook *Traité de Calcul differéntiel et intégral*.

1817

Bessel discovers a class of integral functions, now called "Bessel functions", in his study of a problem of Kepler to determine the motion of three bodies moving under mutual gravitation.

1817

Bolzano publishes *Rein analytischer Beweis* (*Pure Analytical Proof*) which contain an attempt to free calculus from the concept of the infinitesimal. He defines continuous functions without the use of infinitesimals. The work contains the Bolzano-Weierstrass theorem.

1818

Inspired by the work of Laplace, Adrain publishes Investigation of the figure of the Earth and of the gravity in different latitudes.

1819

Horner submits a paper giving "Horner's method" for solving algebraic equations to the Royal Society and was published in the same year in the Philosophical Transactions of the Royal Society.

1820

Brianchon publishes *Recherches sur la determination d'une hyperbole equilatère, au moyen de quatres conditions données* which contains a statement and proof of the nine point circle theorem.

List of mathematicians alive in 1810.

List of mathematicians alive in 1820.

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