These definitions could have been broadened to distances from a line to an arbitrary point, but Euclid’s needs only distances from a line to the center of a circle.

The perpendiculars AE and AH drawn from the center A to the lines CD and FG respectively are equal, so the lines CD and FG are equally distant from the center.

As the perpendicular AM is greater, the line KL is at a greater distance from the center. java applet or image