The origin of the ring was to prevent interference from outsiders! In the 1800's fans would punch fighters, see the movie far and away with tom cruise and nicole kidman for a portayal of this.
The square ring allowed for better viewing and safe distances.
According to The Encyclopedia of Boxing, by Gilbert Odd, the term "boxing ring" goes back to bare-knuckle days.
Spectators held a circle of ropes around the fighters, but they were always crowding in on the action. Eventually, they used stakes to hold the ropes, forming a square.