a. Also Euclidian. [f. L. Euclīdē-us, Gr. Εὐκλείδειος (f.Euclīd-ēs, Εὐκλείδης Euclid) + -AN.] Of or pertaining to Euclid; that is according to the principles of Euclid.
By recent writers Euclidean geometry has been used as the distinctive name of the geometry based on an acceptance of the axioms laid down by Euclid, as distinguished from the systems (constructed e.g. by Lobatchewsky, Grassmann, Riemann) which develop the consequences that would follow from the rejection of some of these. So also Euclidean space: the kind of space actually known to us, for which these axioms are valid, as opposed to hypothetical kinds of space for which one or more of the axioms would be false.
1660. Barrow, Euclid, To Rdr. (1714), 2. The whole Euclidean work.
c. 1865. in Wylde’s Circ. Sc., I. 551/2. Pure Euclidean geometry tolerates no such imperfections.
1883. Standard, No. 18464. 5. This abstruse discourse on Euclidian space and magnitudes of four dimensions must have been barely intelligible.
1883. Cayley, in American, VII. 75/2. This would be their Euclidian geometry.
