Émile Lemoine (1840–1912)

Émile Michel Hyacinthe Lemoine (22 November 1840, Quimper – 21 February 1912, Paris) was one of the central architects of late nineteenth-century synthetic geometry. Educated at the Prytanée National Militaire of La Flèche and the École Polytechnique (entering in 1860), Lemoine combined a career as a civil and municipal gas engineer in Paris with a lifelong devotion to mathematics, chamber music—founding the legendary musical society La Trompette, for which Camille Saint-Saëns composed his Septet, Op. 65—and collaborative scientific correspondence.

Two Mathematical Revolutions

1. Modern Geometry of the Triangle (Lyon, 1873): At the 1873 Lyon Congress of the Association Française pour l’Avancement des Sciences (AFAS), Lemoine presented Sur quelques propriétés d’un point remarquable du triangle, discovering the concurrency of the three symmedians at the Lemoine point \(K = X(6)\) (minimizing the sum of squared distances to the sides of a triangle) along with the first and second Lemoine circles. Alongside Henri Brocard and Joseph Neuberg, Lemoine launched the international renaissance of triangle geometry catalogued today in geometor/etc ().

2. Géométrographie (Oran 1888, Pau 1892, Scientia 1902): Asking how one can objectively compare two valid constructions for the same geometric locus, Lemoine decomposed ruler-and-compass drafting into five irreducible operations (\(R_1, R_2, C_1, C_2, C_3\)), establishing quantitative measures of simplicity (\(S\)) and exactitude (\(E\)). In 1894, together with Charles-Ange Laisant, he founded L’Intermédiaire des Mathématiciens, and in 1895 the French Academy of Sciences awarded him the Prix Francœur repeatedly until his death.