Please note that Mommsen uses the AUC chronology (Ab Urbe Condita), i.e. from the founding of the City of Rome. You can use this reference table to have the B.C. dates
From: The History of Rome, by Theodor Mommsen
Translated with the sanction of the author by William Purdie Dickson
The remaining mass was for the most part slaughtered by the elephants and light troops of the enemy in attempting to cross the river: only part of the cavalry and some divisions of infantry were able, by wading through the river, to gain the camp whither the Carthaginians did not follow them, and thus they too reached Placentia.(1)
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.
It is evident that the first passage was just as difficult as the second was easy, and therefore with good reason Polybius, military judge as he was, merely says of the corps of 10,000, that in close columns it cut its way to Placentia (iii. 74, 6), without mentioning the passage of the river which in this case was unattended with difficulty.
The erroneousness of the view of Livy, which transfers the Phoenician camp to the right, the Roman to the left bank of the Trebia, has lately been repeatedly pointed out. We may only further mention, that the site of Clastidium, near the modern Casteggio, has now been established by inscriptions (Orelli-Henzen, 5117).
Few battles confer more honour on the Roman soldier than this on the Trebia, and few at the same time furnish graver impeachment of the general in command; although the candid judge will not forget that a commandership in chief expiring on a definite day was an unmilitary institution, and that figs cannot be reaped from thistles. The victory came to be costly even to the victors. Although the loss in the battle fell chiefly on the Celtic insurgents, yet a multitude of the veteran soldiers of Hannibal died afterwards from diseases engendered by that raw and wet winter day, and all the elephants perished except one.
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Reference address : https://www.ellopos.net/elpenor/rome/3-05-war-hannibal-cannae.asp?pg=9