α = cos ½θ exp ½ (φ + ψ) i,
(12)
β = i sin ½θ exp ½ (−φ + ψ) i,
(13)
γ = i sin ½θ exp ½ (φ − ψ) i,
(14)
δ = cos ½θ exp ½ (−φ − ψ) i.
(15)
Next Klein takes two functions or co-ordinates λ and Λ, defined by
| λ = | x + yi | = | r + z | , |
| r − z | x − yi |
α = cos ½θ exp ½ (φ + ψ) i,
(12)
β = i sin ½θ exp ½ (−φ + ψ) i,
(13)
γ = i sin ½θ exp ½ (φ − ψ) i,
(14)
δ = cos ½θ exp ½ (−φ − ψ) i.
(15)
Next Klein takes two functions or co-ordinates λ and Λ, defined by
| λ = | x + yi | = | r + z | , |
| r − z | x − yi |