Did Euclid's circles have two kinds of radius?
The authors make the important point that Euclid's Elements, in contrast to his Data, deal with mathematics in the world of ideas, not in the material world of reality. Therefore, they (as well as Archimedes and Apollonius) use the instrumental dative of διάστημα ``distance'' as equivalent of what would be a real life opening of a compass for a circle to be drawn but the expression ``the (line) drawn from the center'' as term for the radius of a circle whose existence was already proved.
scientific article; zbMATH DE number 1417500