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
It was one of those moments when calculation ceases, and when faith in men's own and in their country's destiny alone gives them courage to grasp the hand which beckons to them out of the darkness of the future, and to follow it no one knows whither.
Long and seriously the senate deliberated on the proposal of the consuls to lead the legions to the help of the Mamertines; it came to no decisive resolution. But the burgesses, to whom the matter was referred, were animated by a lively sense of the greatness of the power which their own energy had established.
The conquest of Italy encouraged the Romans, as that of Greece encouraged the Macedonians and that of Silesia the Prussians, to enter upon a new political career. A formal pretext for supporting the Mamertines was found in the protectorate which Rome claimed the right to exercise over all Italians. The transmarine Italians were received into the Italian confederacy;(3) and on the proposal of the consuls the citizens resolved to send them aid (489).
3. The Mamertines entered quite into the same position towards Rome as the Italian communities, bound themselves to furnish ships (Cic. Verr. v. 19, 50), and, as the coins show, did not possess the right of coining silver.
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Reference address : https://www.ellopos.net/elpenor/rome/3-02-war-rome-carthage-sicily.asp?pg=10