One form of surgery in ancient Rome was the Caesarean section childbirth procedure. A common misconception is that Gaius Julius Caesar himself was born under this procedure, but that is completely without merit.
A Caesarean Section in the ancient world was a last resort operation to comply with Roman ritual and religious custom and had little to do with saving either mother or child.
Roman, or Caesarean Law, demanded that when a pregnant woman died she could not be buried until the child had been delivered. Thus the procedure was developed to remove the infant prior to the burial. It later became more customary as a last ditch effort to save the child, depending on circumstances.
The law stated that a living, pregnant woman could not give birth under Caesarean section until she was into her 10th month of pregnancy (also indicating a fine knowledge of the reproductive cycle). As the mother assuredly wouldn't survive, the procedure was delayed as long as possible to give her a chance, before the baby might be in trouble. Knowing that Caesar's mother, Aurelia, survived well into Julius' adult life proves that he was not born of this procedure, or she would've died at his birth.