Page "Line at infinity" Paragraph 3

In the affine plane, a line extends in two opposite directions.

In the projective plane, the two opposite directions of a line meet each other at a point on the line at infinity.

Therefore lines in the projective plane are closed curve, i. e., they are cyclical rather than linear.

This is true of the line at infinity itself ; it meets itself at its two endpoints ( which are therefore not actually endpoints at all ) and so it is actually cyclical.