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
His younger contemporary, Titus Maccius Plautus (500?-570), appears to have been far inferior to him both in outward position and in the conception of his poetic calling. A native of the little town of Sassina, which was originally Umbrian but was perhaps by this time Latinized, he earned his livelihood in Rome at first as an actor, and then--after he had lost in mercantile speculations what he had gained by his acting--as a theatrical composer reproducing Greek comedies, without occupying himself with any other department of literature and probably without laying claim to authorship properly so called.
There seems to have been at that time a considerable number of persons who made a trade of thus editing comedies in Rome; but their names, especially as they did not perhaps in general publish their works,(32) were virtually forgotten, and the pieces belonging to this stock of plays, which were preserved, passed in after times under the name of the most popular of them, Plautus.
32. This hypothesis appears necessary, because otherwise the ancients could not have hesitated in the way they did as to the genuineness or spuriousness of the pieces of Plautus: in the case of no author, properly so called, of Roman antiquity, do we find anything like a similar uncertainty as to his literary property. In this respect, as in so many other external points, there exists the most remarkable analogy between Plautus and Shakespeare.
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Reference address : https://www.ellopos.net/elpenor/rome/3-14-literature-art.asp?pg=50