Émile Michel Hyacinthe Lemoine (; 22 November 1840 – 21 February 1912) was a French civil engineer and a mathematician, a geometer in particular. He was educated at a variety of institutions, including the Prytanée National Militaire and, most notably, the École Polytechnique. Lemoine taught as a private tutor for a short period after his graduation from the latter school. Lemoine is best known for his proof of the existence of the Lemoine point (or the symmedian point) of a triangle. Other mathematical work includes a system he called Géométrographie and a method which related algebraic expressions to geometric objects. He has been called a co-founder of modern triangle geometry, as many of its characteristics are present in his work. For most of his life, Lemoine was a professor of mathematics at the École Polytechnique. In later years, he worked as a civil engineer in Paris, and he also took an amateur's interest in music. During his tenure at the École Polytechnique and as a civil engineer, Lemoine published several papers on mathematics, most of which are included in a fourteen-page section in Nathan Altshiller Court's College Geometry. Additionally, he founded a mathematical journal titled, L'Intermédiaire des Mathématiciens. Biography Early years (1840–1869) Lemoine was born in Quimper, Finistère, on 22 November 1840, the son of a retired military captain who had participated in the campaigns of the First French Empire occurring after 1807. As a child, he attended the military Prytanée of La Flèche on a scholarship granted because his father had helped found the school. During this early period, he published a journal article in Nouvelles annales de mathématiques, discussing properties of the triangle. Lemoine was accepted into the École Polytechnique in Paris at the age of twenty, the same year as his father's death. As a student there, Lemoine, a presumed trumpet player, helped to found an influential chamber music society called La Trompette, for which Camille Saint-Saëns composed several pieces, including the Septet for trumpet, string quintet and piano. After graduation in 1866, he considered a career in law, but was discouraged by the fact that his advocacy for republican ideology and liberal religious views clashed with the ideals of the incumbent government, the Second French Empire. Instead, he studied and taught at various institutions during this period, studying under J. Kiœs at the École d'Architecture and the École des Mines, teaching Uwe Jannsen at the same