*From `A Short Account of the History of Mathematics' (4th edition, 1908)
by W. W. Rouse Ball.*

*Bézout* |
*Trembley* |
*Arbogast* |
*Pfaff*

*Étienne Bézout*, born at Nemours on March 31, 1730, and
died on September 27, 1783, besides numerous minor works, wrote a
Théorie générale des
équations algébriques,
published at Paris in 1779, which in particular contained much new and
valuable matter on the theory of elimination and symmetrical functions
of the roots of an equation: he used determinants in a paper in the
Histoire de l'académie royale, 1764, but did not treat of
the general theory. *Jean Trembley*, born at Geneva in 1749, and
died on September 18, 1811, contributed to the development of
differential equations, finite differences, and the calculus of
probabilities. *Louis François Antoine Arbogast*, born in
Alsace on October 4, 1759, and died at Strassburg, where he was
professor, on April 8, 1803, wrote on series and the derivatives known
by his name: he was the first writer to separate the symbols of
operation from those of quantity.

I may here mention another writer who has also made a
special study of the integral calculus. This was *Johann
Friederich Pfaff*, born at Stuttgart on Dec. 22, 1765, and died at
Halle on April 21, 1825, who was described by Laplace as the most
eminent mathematician in Germany at the beginning of this century, a
description which, had it not been for Gauss's existence, would have
been true enough.

Pfaff was the precursor of the German school, which under Gauss and his followers largely determined the lines on which mathematics developed during the nineteenth century. He was an intimate friend of Gauss, and in fact the two mathematicians lived together at Helmstadt during the year 1798, after Gauss had finished his university course. Pfaff's chief work was his (unfinished) Disquisitioned Analyticae on the integral calculus, published in 1797; and his most important memoirs were either on the calculus or on differential equations: on the latter subject his paper read before the Berlin academy in 1814 is noticeable.

This page is included in a collection of mathematical biographies taken from A Short Account of the History of Mathematics by W. W. Rouse Ball (4th Edition, 1908).

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School of Mathematics

Trinity College, Dublin