He played against Martin Kližan, but his opponent retired due to left foot injury, when the result was 6-1, 3-0.
The second day saw both Nadal and Murray win when their opponents retired.
He won his next three matches, one in straight sets and the other two when his opponent retired.
This was the third match Mauresmo played during the tournament where her opponent retired.
Cosgrave's erstwhile opponent, Declan Costello, had retired in 1969.
In each case, the opponents must retire to a distance 10 m from the point at which the penalty is awarded.
Andy Roddick was leading when a second opponent, Tomáš Berdych, retired on him in a week.
If a contestant is down, his opponent shall retire to the farthest corner and remain there until the count is completed.
Nunn won when his opponent, Darnell Knox, retired after four rounds of a scheduled 12-round bout.
In the first round of the main draw, she was leading when her opponent, Ayumi Morita, retired from the match.