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 improved scenic arrangements and the reintroduction of masks about the time of Terence are doubtless connected with the fact, that the erection and maintenance of the stage and stage-apparatus were charged in 580 on the public chest.(16)
16. Hitherto the person providing the play had been obliged to fit up the stage and scenic apparatus out of the round sum assigned to him or at his own expense, and probably much money would not often be expended on these. But in 580 the censors made the erection of the stage for the games of the praetors and aediles a matter of special contract (Liv. xli. 27); the circumstance that the stage- apparatus was now no longer erected merely for a single performance must have led to a perceptible improvement of it.
The plays which Lucius Mummius produced after the capture of Corinth (609) formed an epoch in the history of the theatre. It was probably then that a theatre acoustically constructed after the Greek fashion and provided with seats was first erected, and more care generally was expended on the exhibitions.(17)
17. The attention given to the acoustic arrangements of the Greeks may be inferred from Vitruv. v. 5, 8. Ritschl (Parerg. i. 227, xx.) has discussed the question of the seats; but it is probable (according to Plautus, Capt. prol. 11) that those only who were not -capite censi- had a claim to a seat. It is probable, moreover, that the words of Horace that "captive Greece led captive her conqueror" primarily refer to these epoch-making theatrical games of Mummius (Tac. Ann. xiv. 21).
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Reference address : https://www.ellopos.net/elpenor/rome/4-13-literature-art.asp?pg=27