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
By a great victory, after which Hiero was proclaimed king of the Siceliots (484), he succeeded in shutting up the Mamertines within their city, and after the siege had lasted some years, they found themselves reduced to extremity and unable to hold the city longer against Hiero on their own resources. It is evident that a surrender on stipulated conditions was impossible, and that the axe of the executioner, which had fallen upon the Campanians of Rhegium at Rome, as certainly awaited those of Messana at Syracuse.
Their only means of safety lay in delivering up the city either to the Carthaginians or to the Romans, both of whom could not but be so strongly set upon acquiring that important place as to overlook all other scruples. Whether it would be more advantageous to surrender it to the masters of Africa or to the masters of Italy, was doubtful; after long hesitation the majority of the Campanian burgesses at length resolved to offer the possession of their sea-commanding fortress to the Romans.
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Reference address : https://www.ellopos.net/elpenor/rome/3-02-war-rome-carthage-sicily.asp?pg=6