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In hyperbolic geometry, two lines may intersect, be ultraparallel, or be limiting parallel. The ultraparallel theorem states that every pair of (distinct) ultraparallel lines has a unique common perpendicular (a hyperbolic line which is perpendicular to both lines).

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  • En géométrie hyperbolique, deux droites peuvent être sécantes, parallèles asymptotes (elles ont un point à l'infini commun), ou ultraparallèles. Le théorème des ultraparallèles affirme que tout couple de droites ultraparallèles possède une unique perpendiculaire commune (c'est-à-dire une droite coupant à angle droit les deux autres). (fr)
  • In hyperbolic geometry, two lines may intersect, be ultraparallel, or be limiting parallel. The ultraparallel theorem states that every pair of (distinct) ultraparallel lines has a unique common perpendicular (a hyperbolic line which is perpendicular to both lines). (en)
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  • En géométrie hyperbolique, deux droites peuvent être sécantes, parallèles asymptotes (elles ont un point à l'infini commun), ou ultraparallèles. Le théorème des ultraparallèles affirme que tout couple de droites ultraparallèles possède une unique perpendiculaire commune (c'est-à-dire une droite coupant à angle droit les deux autres). (fr)
  • In hyperbolic geometry, two lines may intersect, be ultraparallel, or be limiting parallel. The ultraparallel theorem states that every pair of (distinct) ultraparallel lines has a unique common perpendicular (a hyperbolic line which is perpendicular to both lines). (en)
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  • Théorème des ultraparallèles (fr)
  • Ultraparallel theorem (en)
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