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
The state-
envoys sent to Syracuse in the year 262 transact business with
Dionysius the elder, who ascended the throne eighty-six years
afterwards (348). This naive uncritical spirit is especially apparent
in the treatment of Roman chronology. Since according to the Roman
reckoning--the outlines of which were probably fixed in the previous
epoch--the foundation of Rome took place 240 years before the
consecration of the Capitoline temple(63) and 360 years before the
burning of the city by the Gauls,(64) and the latter event, which
is mentioned also in Greek historical works, fell according to these
in the year of the Athenian archon Pyrgion 388 B. C. Ol. 98, i, the
building of Rome accordingly fell on Ol. 8, i.
This was, according
to the chronology of Eratosthenes which was already recognized as
canonical, the year 436 after the fall of Troy; nevertheless the
common story retained as the founder of Rome the grandson of the
Trojan Aeneas.