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
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.
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Reference address : https://www.ellopos.net/elpenor/rome/5-07-subjugation-west.asp?pg=127