Hannibal offered a release of captives at the expense of the Roman treasury; it was declined, and the Carthaginian envoy who had arrived with the deputation of captives was not admitted into the city: nothing should look as if the senate thought of peace.
Not only were the allies to be prevented from believing that Rome was disposed to enter into negotiations, but even the meanest citizen was to be made to understand that for him as for all there was no peace, and that safety lay only in victory.
Notes for Chapter V 1.

Polybius's account of the battle on the Trebia is quite clear.

If Placentia lay on the right bank of the Trebia where it falls into the Po, and if the battle was fought on the left bank, while the Roman encampment was pitched upon the right--both of which points have been disputed, but are nevertheless indisputable--the Roman soldiers must certainly have passed the Trebia in order to gain Placentia as well as to gain the camp.

But those who crossed to the camp must have made their way through the disorganized portions of their own army and through the corps of the enemy that had gone round to their rear, and must then have crossed the river almost in hand-to-hand combat with the enemy.

On the other hand the passage near Placentia was accomplished after the pursuit had slackened; the corps was several miles distant from the field of battle, and had arrived within reach of a Roman fortress; it may even have been the case, although it cannot be proved, that a bridge led over the Trebia at that point, and that the -tete de pont- on the other bank was occupied by the garrison of Placentia.