Polybius on the Battle of Cannae
Section from Polybius on how the Romans were outmaneuvered by the Carthaginians:
115. The battle was begun by an engagement between the advanced guard of the two armies; and at first the affair between these light-armed troops was indecisive. But as soon as the Iberian and Celtic cavalry got at the Romans, the battle began in earnest, and in the true barbaric fashion: for there was none of the usual formal advance and retreat; but when they once got to close quarters, they grappled man to man, and, dismounting from their horses, fought on foot. But when the Carthaginians had got the upper hand in this encounter and killed most of their opponents on the ground---because the Romans all maintained the fight with spirit and determination---and began chasing the remainder along the river, slaying as they went along and giving no quarter; then the legionaries took the place of the light-armed and closed with the enemy. For a short time the Iberian and Celtic lines stood their ground and fought gallantly; but, presently overpowered by the weight of the heavy-armed lines, they gave way and retired to the rear, thus breaking up the crescent. The Roman maniples followed with spirit, and easily cut their way through the enemy's line; since the Celts had been drawn up in a thin line, while the Romans had closed up from the wings towards the center and the point of danger. For the two wings did not come into action at the same time as the center: but the center was first engaged, because the Gauls, having been stationed on the arc of the crescent, had come into contact with the enemy long before the wings, the convex of the crescent being towards the enemy.
The Romans, however, going in pursuit of these troops, and hastily closing in towards the center and the part of the enemy which was giving ground, advanced so far that the Libyan heavy-armed troops on either wing got on their flanks. Those on the right, facing to the left, charged from the right upon the Roman flank; while those who were on the left wing faced to the right, and, dressing by the left, charged their right flank, the exigency of the moment suggesting to them what they ought to do. Thus it came about, as Hannibal had planned, that the Romans were caught between two hostile lines of Libyans---thanks to their impetuous pursuit of the Celts. Still they fought, though no longer in line, yet singly, or in maniples, which faced to meet those who charged them on the flanks."