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Rewrote first sentence to make it clear how "ultraparallel" is defined |
→Hilbert's construction: asymptotically -> limiting, since the default choice for Wikipedia is "limiting parallel". (I personally prefer "horoparallel", but all that matters is consistency.) |
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Then D' ≠ D. They are the same distance from r and both lie on s. So the perpendicular bisector of D'D (a segment of s) is also perpendicular to r.<ref>{{cite book|last1=H. S. M. Coxeter|author1-link=H. S. M. Coxeter|title=Non-euclidean Geometry|date=17 September 1998|isbn=978-0-88385-522-5|pages=190–192}}</ref>
(If r and s were asymptotically parallel rather than ultraparallel, this construction would fail because s' would not meet s. Rather s' would be
==Proof in the Poincaré half-plane model ==
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