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
Popular amusements increased to an alarming extent. For five hundred years the community had been content with one festival in the year, and with one circus. The first Roman demagogue by profession, Gaius Flaminius, added a second festival and a second circus (534);(45) and by these institutions--the tendency of which is sufficiently indicated by the very name of the new festival, "the plebeian games"--he probably purchased the permission to give battle at the Trasimene lake. When the path was once opened, the evil made rapid progress. The festival in honour of Ceres, the goddess who protected the plebeian order,(46) must have been but little, if at all, later than the plebeian games.
45. The laying out of the circus is attested. Respecting the origin of the plebeian games there is no ancient tradition (for what is said by the Pseudo-Asconius, p. 143, Orell. is not such); but seeing that they were celebrated in the Flaminian circus (Val. Max. i, 7, 4), and first certainly occur in 538, four years after it was built (Liv. xxiii. 30), what we have stated above is sufficiently proved.
46. Cf. II. II. Political Value of the Tribunate
On the suggestion of the Sibylline and Marcian prophecies, moreover, a fourth festival was added in 542 in honour of Apollo, and a fifth in 550 in honour of the "Great Mother" recently transplanted from Phrygia to Rome.
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Reference address : https://www.ellopos.net/elpenor/rome/3-11-government-governed.asp?pg=54