The line is named after Nobel laureate Frederick Soddy, who published a proof of a special case of Descartes' theorem about tangent circles as a poem in Nature in 1936.
Zuming Feng: Why Are the Gergonne and Soddy Lines Perpendicular? A Synthetic Approach. In: Mathematics Magazin, Band 81, Nr. 3, Juni 2008, S. 211-214 (JSTOR)
Roger Alperin: The Gergonne and Soddy lines. In: Elemente der Mathematik,. Band 70, Nr. 1, 2015, S. 1-6 (online)