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
Caesar in Front of Alesia - Siege of Alesia
Vercingetorix hastened the more to shut himself up in Alesia; and if Caesar was not disposed altogether to renounce the offensive, no course was left to him but for the third time in this campaign to proceed by way of attack with a far weaker force against an army encamped under a well-garrisoned and well-provisioned fortress and supplied with immense masses of cavalry. But, while the Celts had hitherto been opposed by only a part of the Roman legions, the whole forces of Caesar were united in the lines round Alesia, and Vercingetorix did not succeed, as he had succeeded at Avaricum and Gergovia, in placing his infantry under the protection of the walls of the fortress and keeping his external communications open for his own benefit by his cavalry, while he interrupted those of the enemy.
The Celtic cavalry, already discouraged by that defeat inflicted on them by their lightly esteemed opponents, was beaten by Caesar's German horse in every encounter. The line of circumvallation of the besiegers extending about nine miles invested the whole town, including the camp attached to it. Vercingetorix had been prepared for a struggle under the walls, but not for being besieged in Alesia; in that point of view the accumulated stores, considerable as they were, were yet far from sufficient for his army--which was said to amount to 80,000 infantry and 15,000 cavalry--and for the numerous inhabitants of the town. Vercingetorix could not but perceive that his plan of warfare had on this occasion turned to his own destruction, and that he was lost unless the whole nation hastened up to the rescue of its blockaded general.
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Reference address : https://www.ellopos.net/elpenor/rome/5-07-subjugation-west.asp?pg=126