designating or of a geometry that rejects any of the postulates of Euclidean geometry, esp. the postulate that through a given point only one line can be drawn parallel to another line that does not contain the given point
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.