Louis Benjamin Francoeur

Born: 16 August 1773 in Paris, France
Died: 15 December 1849 in Fontainbleau, Paris, France

Louis Benjamin Francoeur was born into a famous Paris family of musicians. His father, Louis-Joseph Francoeur (1738-1804), was the son of Louis Francoeur (1692-1745), who was the leader of the Vingt-Quatre Violons du Roi, and the nephew of François Francoeur who also played in the Vingt-Quatre Violons. Louis-Joseph, Louis and François all also played in the Opéra orchestra. At the time Louis Benjamin was born, his father was maître of the Opéra orchestra and he became its director in 1779. Louis Benjamin was brought up in Saint Cloud, a wealthy commune to the west of Paris, and educated at the College d'Harcourt. This ancient educational establishment was founded in 1280 but was renamed the Lycée Saint-Louis in 1820; it is today known for its exceptional teaching. He became a clerk to a notary in 1790 but, by this time, Paris was in turmoil as the Revolution took its course. The Opera had been the Royal Opera until 1792 when it became a public utility independent of the king. Louis Francoeur resigned as director of the Opera and tried to set up a new company with the King's support. He founded the Francoeur-Cellerier company in 1792 and Louis Benjamin he took a position as deputy cashier in his father's opera company. Like other members of his family he was exceptionally talented musically, so working for an opera company was a pleasant task.

The execution of Louis XVI on 21 January 1793 meant that the Francoeur-Cellerier company was short-lived and a financial disaster. Louis Benjamin lost his position and, in September 1793, his father was imprisoned because of his royal connections; Louis-Joseph Francoeur spent nearly a year in prison and when he was released he had no pension and was heavily in debt. Now, as well as internal strife, France was faced with attacks from the Austrians and Prussians and, from 1793, Louis Benjamin was required to serve in the French Revolutionary army. At first he was sent as a sergeant major to a regiment of the French Guard stationed at Péronne in northern France. Following this he served in the Auvergne Regiment which was at Maubeuge trying to defend against the Austrian army under the command of Prince Josias of Coburg. Francoeur, however, became involved in a musical role at Maubeuge. He had risen to 'Chef de brigade', a rank equivalent to colonel, but on hearing that technicians for the arms factories were being recruited in Paris, he quickly returned there. Having failed to get such a position, he sadly set off for Maubeuge in August 1794 but when he heard that students were being sought for the new École Centrale des Travaux Publics (soon to be renamed the École Polytechnique) he returned again to Paris.

Passing the entrance examination, he studied mathematics with Gaspard Monge at the École Centrale des Travaux Publics, beginning in November 1794. He was a brilliant pupil, completing his studies in 1797. Then he was appointed to the School of Geographical Engineers, which allowed him to remain in Paris to give private lessons to favoured students, such as Jérôme Bonaparte, the youngest brother of Napoleon Bonaparte. He also studied botany under the direction of René Louiche Desfontaines and Jean-Louis Thuillier while he waited to continue an army career as a geographer. However, Gaspard de Prony had realised that Francoeur was a talented mathematician and lecturer so, in 1798, he appointed him as répétiteur d'analyse to teach an analysis course for Sylvestre Lacroix. De Prony was the first teacher of mechanics at the École Polytechnique and Francoeur, as his teaching assistant, quickly produced the substantial Traité de méchanique élémentaire (1801) to serve as an introduction to the subject for students at the École. His academic position saved Francoeur from the dangers and discomforts of army life but he carried on with both a military and an academic career. He was theoretically made a sub-lieutenant in the artillery in 1802 although by this time he was taking no active part in the military. In 1804 he was appointed professor of mathematics at the École Polytechnique, then in 1805 he became professor of mathematics at the Lycée Charlemagne. In 1808 he was made professor of mathematics at the Faculté des Sciences in Paris, a post he was to hold in addition to others until 1845.

Francoeur had many duties in his capacity as an examiner for the École Polytechnique and he often travelled in France and Italy carrying out these duties. The French, under Napoleon, fought inconclusive battles and campaigns in various parts of Spain and Portugal during 1809-10. Francoeur was sent on this Peninsular Campaign but he broke a leg in an accident with a carriage. During 1810 he spent four months in bed as a result of this accident. In 1811 a comet appeared causing great interest with the public. It was first observed in March of that year, but it was not until September that it was a bright object in the evening sky, reaching its maximum brightness in October. Francoeur became interested in astronomy as a result of this comet and was appointed professor of astronomy at the Athénée in Paris. However, in 1814 Napoleon Bonaparte was defeated and the Bourbon Restoration government was set up. In 1815 over 50,000 civil servants were sacked, and 15,000 army officers dismissed. Francoeur lost his chair at the Lycée Charlemagne and also his position at the École Polytechnique. In 1816 he became a founding member of the Société pour l'enseignement élémentaire, a society whose aim was to promote elementary instruction in schools. He later became secretary of the Society. Francoeur encouraged learning in schools and he did his part writing books, particularly Le dessin linéaire d'après la méthode de l'enseignement mutuel (1819) which popularised line drawing in French schools.

Francoeur is famed as a writer of excellent texts mostly based on lecture courses he gave. He published his mechanics book Traité de mécanique élémentaire, à l'usage des élèves de l'École Polytechnique, rédigé d'après les méthodes de R Prony in 1800, an elementary course of mathematics in two volumes Cours complet de mathématiques pures in 1809, and two astronomy texts l'Uranographie, ou Traité élémentaire d'astronomie, à l'usage des personnes peu versées dans les mathématiques, accompagné de planisphères (1812) and Astronomie pratique, usage et composition de la Connaissance des temps (1830). His other books include Élémens de statique (1810), La goniométrie (1820), L'enseignment du dessin linéaire (1827), Astronomie practique (1830), Élémens de technologie (1833), Géodésie, ou Traité de la figure de la terre et de ses parties, comprenant la topographie, l'arpentage, le nivellement, la géomorphie terrestre et astronomique, la construction des cartes, la navigation, leçons données à la Faculté des sciences de Paris (1835), Algèbre supérieure (1838), Mémoire sur l'Aréométrie (1842), and Traité d'arithmétique appliquée à la banque, au commerce, à l'industrie, etc., recueil de méthodes propres à résoudre les problèmes et à abréger les calculs numériques (1845). Finally, let us also mention his text Flore parisienne ou Description des caractères de toutes les plantes qui croissent naturellement aux environs de Paris, distribuées suivant la méthode du jardin des plantes (1800-01).

Many of these works were dedicated to famous mathematicians, for example the Élémens de statique was dedicated to Pierre-Simon Laplace, the Géodésie was dedicated to Louis Puissant, and the fifth edition l'Uranographie published in 1837 was dedicated to François Arago, the fourth edition of 1828 having been dedicated to Sadi Carnot who died in 1832.

It was for his work in line drawing that Francoeur became most famous, the method he proposed being known as "Francoeur's method". It was first used in a school in Libourne in Aquitaine in south-western France which had been founded by Élie, duc Decazes. His method was published in 1819 in Le dessin linéaire d'après la méthode de l'enseignement mutuel but, before publication of this book, Francoeur had submitted a report on his method to the Société pour l'enseignement élémentaire on 22 July 1818. Extracts from this report are given in [5]. Francoeur's method was used in countries other than France. For example William B Fowle translated Francoeur's book into English and published it as An Introduction to Linear Drawing: Translated from the French of M. Francoeur, and Adapted to the Use of Public Schools in the United States (1825) [3]:-

Fowle's text, which was used by students attending Cambridge High School as early as 1841, teaches drawing according to the mastery of basic geometric shapes. Fowle was a staunch advocate of mandatory drawing classes in public schools and also served as editor of the 'Common School Journal'.
An anonymous review of a later edition of Fowle's translation of Francoeur's text appeared in 1842 the Common School Journal:-
The little work upon 'Linear Drawing' exhibits a plan of teaching large classes at once, by means of a black-board, all the elements of the art of drawing. The teacher stands at the board, draws and explains every line - linear, oblique, curved - and then proceeds to copy from patterns, or objects - explaining every thing in the process - while the pupils copy each line, [and so on], upon their slates or paper, as she slowly proceeds.
Francoeur, in his report of 1818, describes how the students are divided into four classes [5]:-
The lower [class] traces the lines, parallels, perpendiculars, triangles, etc. In the second class, students make circles, regular polygons and plane figures that depend on them. In the third, they mimic perspective in some three-dimensional bodies, such as pyramids, prisms, cylinders, cones, spheres, etc. In the fourth class, they draw some architectural features, vases and ornaments of their choice.
We explained as the beginning of this biography that Francoeur came from an exceptionally musical family so it will come as no surprise that he also reported to the Société pour l'enseignement élémentaire on the teaching of singing and the Society adopted the method he proposed.

Among the honours Francoeur received was election to the Académie des Sciences in 1842. He was elected to the many other Academies including St Petersburg, Lisbon, Edinburgh, Rouen, Lyon, Cambra, and Toulouse.

From 1840 an illness of the larynx curtailed his activities and he visited many spas looking for a cure by taking the waters. The illness forced him to retire from his chair in the Faculty of Sciences in 1845. He health deteriorated further through a disease of his spinal chord and eventually he went blind forcing him to stop all his activities. He died at Fontainbleau and was buried at Chatillon-la-Borde (Seine-et-Marne).

Finally we note that Francoeur's son, Isidore Francoeur, the author of [1], was himself a professor of mathematics at the Collège Chaptal and at the École des Beaux-Arts. He bequeathed to them his library and that of his father. Isidore Francoeur's widow made a gift to set up the mathematics prize the Prix Francoeur.

Article by: J J O'Connor and E F Robertson

May 2010
MacTutor History of Mathematics