A linear transformation of period two. Since a linear transformation has the form, λ' = (αλ + β)/(γλ + δ), applying the transformation a second time gives λ'' = (αλ' + β)/(γλ' + δ) = ((α^2 + βγ) λ + β(α + δ))/((α + δ) γλ + βγ + δ^2). For an involutory, λ'' = λ, so γ(α + δ) λ^2 + (δ^2 - α^2) λ - (α + δ) β = 0.

cross ratio | line involution