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.