Webster's 1913: 2. Any sharp terminating border; a margin; a brink; extreme verge; as, the edge of a table, a precipice. 4. The border or part adjacent to the

Webster's 1913: 2. Any sharp terminating border; a margin; a brink; extreme verge; as, the edge of a table, a precipice. 4. The border or part adjacent to the line of division; the beginning or early part; as, in the edge of evening. "On the edge of winter." Milton. Either the literal sense 2 or figurative sense 4 works here. The special mathematical sense is nowhere given in that edition of Webster's. I suppose they expected one would consult Euclid if one wished to know its sense in that jargon.