Def. 5. And that straight line is said to be at a greater distance on which the greater perpendicular falls.
These definitions could have been broadened to distances from a line to a point, but Euclid's needs are for this situation.
| 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. |
Book III Introduction - Definitions III.2 and III.3. Definitions III.6 through III.9.