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 nation was thus obliged to resign itself to the fate appointed for it. The Romans demanded the cession of half the territory (563); the demand could not be refused, and even within the diminished district which was left to the Boii, they soon disappeared, and amalgamated with their conquerors.(1)
1. According to the account of Strabo these Italian Boii were driven by the Romans over the Alps, and from them proceeded that Boian settlement in what is now Hungary about Stein am Anger and Oedenburg, which was attacked and annihilated in the time of Augustus by the Getae who crossed the Danube, but which bequeathed to this district the name of the Boian desert.
This account is far from agreeing with the well-attested representation of the Roman annals, according to which the Romans were content with the cession of half the territory; and, in order to explain the disappearance of the Italian Boii, we have really no need to assume a violent expulsion--the other Celtic peoples, although visited to a far less extent by war and colonization, disappeared not much less rapidly and totally from the ranks of the Italian nations.
On the other hand, other accounts suggest the derivation of those Boii on the Neusiedler See from the main stock of the nation, which formerly had its seat in Bavaria and Bohemia before Germanic tribes pushed it towards the south. But it is altogether very doubtful whether the Boii, whom we find near Bordeaux, on the Po, and in Bohemia, were really scattered branches of one stock, or whether this is not an instance of mere similarity of name. The hypothesis of Strabo may have rested on nothing else than an inference from the similarity of name--an inference such as the ancients drew, often without due reason, in the case of the Cimbri, Veneti, and others.
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Reference address : https://www.ellopos.net/elpenor/rome/3-07-peace-hannibal-third-period.asp?pg=7