| 释义 |
non-Euclidean geometry After unsuccessful attempts had been made at proving that the parallel postulate could be deduced from the other postulates of Euclid's, the matter was settled by the discovery of non-Euclidean geometries by Lobachevsky and Bolyai. In these, all Euclid's postulates hold except the parallel postulate. In hyperbolic geometry, given a point not on a given line, there are at least two lines through the point parallel to the line (i.e. these parallel lines do not intersect the given line). In elliptic geometry, given a point not on a given line, there are no parallels through the point. See elliptic plane, hyperbolic plane, neutral geometry.
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