additive theory of prime numbers. Our conjecture reflects this, dealing with interactions of sums involving primes whereas Goldbach's conjecture and Lemoine's conjecture deal with such sums only individually. This conjecture and the open questions about numbers at levels two and three are of interest in their own right because of the issues they raise within this fascinating and often baffling additive realm of the prime numbers." Role in modern triangle geometry Lemoine has been described by Nathan Altshiller Court as a co-founder (along with Henri Brocard and Joseph Neuberg) of modern triangle geometry, a term used by William Gallatly, among others. In this context, "modern" is used to refer to geometry developed from the late 18th century onward. Such geometry relies on the abstraction of figures in the plane rather than analytic methods used earlier involving specific angle measures and distances. The geometry focuses on topics such as collinearity, concurrency, and concyclicity, as they do not involve the measures listed previously. Lemoine's work defined many of the noted traits of this movement. His Géométrographie and relation of equations to tetrahedrons and triangles, as well as his study of concurrencies and concyclities, contributed to the modern triangle geometry of the time. The definition of points of the triangle such as the Lemoine point was also a staple of the geometry, and other modern triangle geometers such as Brocard and Gaston Tarry wrote about similar points. List of selected works Sur quelques propriétés d'un point remarquable du triangle (1873) Note sur les propriétés du centre des médianes antiparallèles dans un triangle (1874) Sur la mesure de la simplicité dans les tracés géométriques (1889) Sur les transformations systématiques des formules relatives au triangle (1891) Étude sur une nouvelle transformation continue (1891) La Géométrographie ou l'art des constructions géométriques (1892) Une règle d'analogies dans le triangle et la spécification de certaines analogies à une transformation dite transformation continue (1893) Applications au tétraèdre de la transformation continue (1894) See also Brocard circle Brocard points Geometrography Nagel point Tarry point Lemoine's problem Modern triangle geometry Notes External links 1840 births 1912 deaths People from Quimper French civil engineers French geometers 19th-century French mathematicians 20th-century French mathematicians École Polytechnique alumni Members of the Ligue de la patrie française École Spéciale d'Architecture alumni