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 head of the Roman column, formed of 6000 infantry, cut their way through the infantry of the enemy, and proved once more the irresistible might of the legions; but, cut off from the rest of the army and without knowledge of its fate, they marched on at random, were surrounded on the following day, on a hill which they had occupied, by a corps of Carthaginian cavalry, and--as the capitulation, which promised them a free retreat, was rejected by Hannibal--were all treated as prisoners of war. 15,000 Romans had fallen, and as many were captured; in other words, the army was annihilated. The slight Carthaginian loss--1500 men--again fell mainly upon the Gauls.(3)
3. The date of the battle, 23rd June according to the uncorrected calendar, must, according to the rectified calendar, fall somewhere in April, since Quintus Fabius resigned his dictatorship, after six months, in the middle of autumn (Lav. xxii. 31, 7; 32, i), and must therefore have entered upon it about the beginning of May. The confusion of the calendar (p. 117) in Rome was even at this period very great.
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Reference address : https://www.ellopos.net/elpenor/rome/3-05-war-hannibal-cannae.asp?pg=18