- A special application of his theory of continuous groups was to the general problem of
**non-Euclidean**geometry. - 0) 2 = i suitable for
**non-Euclidean**space, and w 2 = o suitable for Euclidean space; we confine ourselves to the second, and will call the indicated bi-quaternion p+wq an octonion. - He was much interested, too, in universal algebra,
**non-Euclidean**geometry and elliptic functions, his papers "Preliminary Sketch of Bi-quaternions" (1873) and "On the Canonical Form and Dissection of a Riemann's Surface" (1877) ranking as classics.