We shall speak of lines and circles as generalized circles. A line is a generalized circle that passes through the point at infinity. Under the inversion 𝜁=1/z the generalized circle (53.3) goes into

(53-4) 𝛽|𝜁|²-p𝜁-◌̅p◌̅𝜁+𝛼=0,

which is a generalized circle in the ζ-plane.