Thébault's theorem, discovered in 1938 (see [5]), has the remarkable property that it required three decades to obtain a first proof, which then took 24 pages of calculations. Subsequent shorter proofs, but not easy ones, were published mainly in Elemente der Mathematik ([4] and [6]) and in Dutch language. We refer to [1], [2], and [7] for complete accounts of all these and recent proofs. In this note we want to emphasize the role of a certain parabola which comes out of a dynamic machine, and which allows an easy understanding.