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

*Bézout* |
*Trembley* |
*Arbogast* |
*Carnot* |
*Poncelet*

*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.

*Lazare Nicholas Marguerite Carnot*, born at Nolay on May 13,
1753, and died at Magdeburg on Aug. 22, 1823, was educated at
Burgundy, and obtained a commission in the engineer corps of
Condé. Although in the army, he continued his mathematical
studies in which he felt great interest. His first work, published in
1784, was on machines; it contains a statement which foreshadows the
principle of energy as applied to a falling weight, and the earliest
proof of the fact that kinetic energy is lost in the collision of
imperfectly elastic bodies. On the outbreak of the revolution in 1789
he threw himself into politics. In 1793 he was elected on the
committee of public safety, and the victories of the French army were
largely due to his powers of organization and enforcing discipline.
He continued to occupy a prominent place in every successive form of
government till 1796 when, having opposed Napoleon's *coup
d'état*, he had to fly from France. He took refuge in Geneva, and
there in 1797 issued his La métaphysique du calcul
infinitésimal. In 1802 he assisted Napoleon, but his sincere
republican convictions were inconsistent with the retention of office.
In 1803 he produced his Géométrie de position. This
work deals with projective rather than descriptive geometry, it also
contains an elaborate discussion of the geometrical meaning of
negative roots of an algebraical equation. In 1814 he offered his
services to fight for France, though not for the empire; and on the
restoration he was exiled.

*Jean Victor Poncelet*, born at Metz on July 1, 1788, and died
at Paris on Dec. 1867, held a commission in the French engineers.
Having been made a prisoner in the French retreat from Moscow in 1812
he occupied his enforced leisure by writing the Traité des
propriétés projectives des figures, published in
1822, which was long one of the best known text-books on modern
geometry. By means of projection, reciprocation, and homologous
figures, he established all the chief properties of conics and
quadrics. He also treated the theory of polygons. His treatise on
practical mechanics in 1826, his memoir on water-mills in 1826, and his
report on the English machinery and tools exhibited at the
International Exhibition held in London in 1851 deserve mention. He
contributed numerous articles to Crelle's journal; the most valuable of
these deal with the explanation, by the aid of the doctrine of
continuity, of imaginary solutions in geometrical problems.

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).

Transcribed by

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School of Mathematics

Trinity College, Dublin