Limiting parallel

In neutral or absolute geometry, and in hyperbolic geometry, there may be many lines parallel to a given line ${\displaystyle l}$ through a point ${\displaystyle P}$ not on line ${\displaystyle R}$; however, in the plane, two parallels may be closer to ${\displaystyle l}$ than all others (one in each direction of ${\displaystyle R}$).

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