Poncelet's discovery of homology (Q6174615)

Based on various problems which were solved by Poncelet from 1809 onwards, including the problem of Apollonius of finding tangent circles to three given circles, the article describes the path of this mathematician to his concept of \textit{homologie}, as finally expounded and applied in his \textit{Traité des propriétés projectives des figures} (1822). According to Poncelet, a homology is a collineation in the projective plane, where each point on a given line is a fixed point. Poncelet developed this concept mainly through investigations on points, chords, and secants attributed to a pair of circles which he treated as figures that can be transformed into each other by a homothety. The article supplements the author's work [in: Research in history and philosophy of mathematics. The CSHPM 2019--2020 volume. Cham: Birkhäuser. 45--58 (2022; Zbl 1526.01014)].