Lemoine's problem

In geometry, Lemoine's problem is a straightedge and compass construction problem posed by French mathematician Émile Lemoine in 1868:
The problem was published as Question 864 in Nouvelles [Annales de Mathématiques]. The chief interest in the problem is that a discussion of the solution of the problem by Ludwig Kiepert published in Nouvelles Annales de Mathématiques contained a description of a hyperbola which is now known as the Kiepert hyperbola.

Ludwig Kiepert's solution

Kiepert establishes the validity of his construction by proving a few lemmas.

Other solutions

Several other people in addition to Kiepert submitted their solutions during 1868–9, including Messrs Williere, Brocard, Claverie, Joffre, Racine, Augier, V. Niebylowski, and L. Henri Lorrez.
Kiepert's solution was more complete than the others.