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
He subdued the Daunians around Sipontum, and the Messapians in the south-eastern peninsula; he already commanded from sea to sea, and was on the point of arranging with the Romans a joint attack on the Samnites in their native abodes. But successes so unexpected went beyond the desires of the Tarentine merchants, and filled them with alarm. War broke out between them and their captain, who had come amongst them a hired mercenary and now appeared desirous to found a Greek empire in the west like his nephew in the east.
Alexander had at first the advantage; he wrested Heraclea from the Tarentines, restored Thurii, and seems to have called upon the other Italian Greeks to unite under his protection against the Tarentines, while he at the same time tried to bring about a peace between them and the Sabellian tribes. But his grand projects found only feeble support among the degenerate and desponding Greeks, and the forced change of sides alienated from him his former Lucanian adherents: he fell at Pandosia by the hand of a Lucanian emigrant (422).(1)
1. It may not be superfluous to mention that our knowledge Archidamus and Alexander is derived from Greek annals, and that the synchronism between these and the Roman is in reference to the present epoch only approximately established. We must beware, therefore, of pursuing too far into detail the unmistakable general connection between the events in the west and those in the east of Italy.
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Reference address : https://www.ellopos.net/elpenor/rome/2-06-italians-rome.asp?pg=2