This is from Kiselev's Geometry: Planimetry, page 2:
For every two points in space there is a straight line passing through them, and such a line is unique.
So I have two fixed points, and I draw a line through them. Now I make an exact copy of the line, and the copy coincides with the original. It seems like I should be allowed to say: "I have two lines passing through the same points". But the book says that a line passing through two fixed points is unique, so there seems to be a contradiction here.
If I move the copy and the original so they no longer coincide, are they still just one line, or are they two lines now?