With a bit of rooting around in Perseus I found the story of Theseus and Ariadne as told by Apollodorus. The Greek word used was linon, the most relevant dictionary definition of which is cord or fishing-line (http://perseus.csad.ox.ac.uk/cgi-bin/ptext?doc=Perseus:text:1999.04.0058:entry=#19760). In Ovid's poem "Letter from Ariadne to Theseus", he uses the Latin word filum, which means thread or string (http://perseus.csad.ox.ac.uk/cgi-bin/ptext?doc=Perseus:text:1999.04.0058:entry=#19760. If you're carrying a thread or cord long enough to trace your path through a labyrinth, I suppose the obvious way to carry it is wound up into a ball.

Bingley

Bingley