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 existing provisions were still,
when the Roman circumvallation was closed, sufficient for a month
and perhaps something more; at the last moment, when there was still
free passage at least for horsemen, Vercingetorix dismissed
his whole cavalry, and sent at the same time to the heads
of the nation instructions to call out all their forces and lead them
to the relief of Alesia. He himself, resolved to bear in person
the responsibility for the plan of war which he had projected
and which had miscarried, remained in the fortress, to share in good
or evil the fate of his followers.
But Caesar made up his mind
at once to besiege and to be besieged. He prepared his line
of circumvallation for defence also on its outer side, and furnished
himself with provisions for a longer period. The days passed;
they had no longer a boll of grain in the fortress, and they
were obliged to drive out the unhappy inhabitants of the town
to perish miserably between the entrenchments of the Celts
and of the Romans, pitilessly rejected by both.