Bret, Jean Jacques

(b. Mercuriol, Drôme, France, 25 September 1781; d. Grenoble, France, 29 January 1819)

mathematics.

He was the son of Jacques Bret, a notary. After passing the entrance examinations given at Lyons, Bret entered the École Polytechnique on 22 November 1800 and was admitted to the course of preparation for civil engineering (Service des Ponts et Chaussées). Unfortunately, because of poor health, he did not complete his studies, but was forced to take a leave of absence from October 1802 to November 1803. The school administration offered to let him stay a fourth year on condition that he take the examinations. He was definitely removed from the rolls in December 1803.

In 1804 Bret became professor of transcendental mathematics at the lycée in Grenoble, and from 8 October 1811 until his death, he was professor at the Faculté des Sciences in the same city, having became docteur ès sciences on 10 March 1812.

There are some twenty publications by Bret in the Annales de mathématiques de Gergonne, a note in the Correspondance of the École Polytechnique, and a memoir in the latter’s journal. Most of his articles deal with analytical geometry on plane surfaces and in space, notably with the ory of conics and quadrics. He sets forth, for example, the third–degree equation that determines the length of the axes of a central quadric.

In this research the cumbersome techniques of the time are unpleasantly obvious. By way of exception, a study on the squares of the distance between a point in space and fixed points is remarkable for its simplicity, elegance, and generality.

Other works have a bearing on the ory of algebraic equations, particularly upon the limitation of real roots, a subject in style at the time. Bret also worked on the ory of elimination, where he used the greatest common divisor of polynomials in order to establish Bézout’s theorem on the degree of the polynomial resultant.

Bret became involved in a long polemic with J.B.E. Dubourguet in the Annales de Gergonne. This had to do with the demonstration of the fundamental theorem that an algebraic equation admits a number of roots equal to its degree.

BIBLIOGRAPHY

Among Bret’s works are “Sur la méthode du plus grand commun diviseur appliquée à l’élimination,” in Journal de l’ècole polytechnique, 15 (1809), 162–197; and “Sur les équations du quatrième degré,” in Correspondance de l’École polytechnique, 2 (1811), 217–219.

Of particular note, all in Annales de mathématiques, are “Recherche des longueurs des axes principaux dans les surfaces du second ordre qui ont un centre,” 2 (1812), 33–38; “Recherche de la position des axes principaux dans les surfaces du second ordre,” ibid., 144–152; “Discussion de l’èquation de second degrè entre deux variables,” ibid., 218–223; “Dèmonstration de quelques théorëmes relatifs au quadrilatère,” ibid., 310–318; “Théorie de l’élimination entre deux équations de degrés quelconques, fondée sur la théorie du plus grand commun diviseue,” 3 (1812), 13–18; “Démonstration du principe qui sert de fondement au calcul des fonctions symétriques et de la formule binomiale de Newton,” 4 (1813), 25–28; “Théorèmes nouveaux sur les limites des racines des équations numériques,” 6 (1815), 112–122; and “Théorie générale des fractions continues,” 11 (1818), 37–51.

An article on Bret is Niels Nielsen, “Bret,” in Géomètres français sous la Révolution (Copenhagen, 1929), pp. 31–37.

Jean Itard