**Émile Lemoine** was a French civil engineer, mathematician and geometer.

- In this paper, Lemoine describes himself as a pupil in the Spéciales of the Prytanee impérial of La Flèche.
- Graduating from the Prytanée Militaire in 1860, Lemoine entered the École Polytechnique in Paris.
- Lemoine was very musical and while at the École Polytechnique he founded an amateur musical group named "La Trompette" which, several years later, was good enough to have Saint-Saëns write music especially for it.
- Saint-Saëns composed Septet in E flat major Op 65, at Lemoine's request.
- Saint-Saëns composed other works for Lemoine.
- For example he gave Lemoine the work Préambule as a present for Christmas 1879.
- It was played at a concert in January 1880 and Saint-Saëns was so pleased with the result that he promised Lemoine that he would write a complete work with Préambule as its first movement, which he had done by the end of 1880.
- Let us return to Lemoine's university career which he completed when he graduated from the École Polytechnique in 1866.
- However, Lemoine's life was not simply one of enjoying the social life of Paris.
- Because of the war, Lemoine served for a while in the army.
- After peace was restored, Lemoine returned to Paris in the summer of 1871 and, changing career, he became a civil engineer.
- This is such a nice little question that the reader will almost certainly like to know what answer Lemoine came up with.
- Lemoine's contribution to mathematics was mainly on geometry and he published Note sur un point remarquable du plan d'un triangle in 1873.
- He proved that the symmedians are concurrent, the point where they meet now being called the Lemoine point.
- Among other results on symmedians in Lemoine's 1873 paper is the result that the symmedian from the vertex AAA cuts the side BCBCBC of the triangle in the ratio of the squares of the sides ACACAC and ABABAB.
- He also proved that if parallels are drawn through the Lemoine point parallel to the three sides of the triangle then the six points lie on a circle, now called the Lemoine circle.
- Its centre is at the mid-point of the line joining the Lemoine point to the circumcentre of the triangle.
- These results are interesting but Lemoine's next venture failed to interest many mathematicians.
- Lemoine then classified the "simplicity" of a construction according to how many times these five operations had to be used.
- The usual construction required over 400 of Lemoine's operations but he was able to reduce the number to 199.
- Why are these results of Lemoine not found interesting?
- Lemoine gave up active mathematical research in 1895 but continued to support the subject.
- Let us end by quoting David E Smith's personal comments about Lemoine and his music.
- To this justly celebrated mathematician, M Laurent, is due the name of M Lemoine's soirées, "La Trompette".
- Long ago he one day remarked to M Lemoine in a jesting way, as the latter was excusing himself to attend one of his musical reunions, "Stay here with me, let the trumpet alone." Struck by the name, Lemoine adopted it, and La Trompette has ever since designated the delightful soirées with which the Paris cultured world is familiar.
- A final word concerning the modesty of M Lemoine.

Born 22 November 1840, Quimper, Finistère, France. Died 21 February 1912, Paris, France.

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**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive