what languages were spoken here?
Latin and koine Greek
Roman Empire
The language of the Romans was Latin, which Virgil emphasizes as a source of Roman unity and tradition. Until the time of Alexander Severus (reigned 222–235), the birth certificates and wills of Roman citizens had to be written in Latin. Latin was the language of the law courts in the West and of the military throughout the Empire, but was not imposed officially on peoples brought under Roman rule. This policy contrasts with that of Alexander the Great, who aimed to impose Greek throughout his empire as the official language. As a consequence of Alexander's conquests, koine Greek had become the shared language around the eastern Mediterranean and into Asia Minor. 
the roman empire reached its greatest extent during the During the reign of Trajan what is this empire? It was the post-Republican period of ancient Rome. who was the first ruler of this empire? Caesar Augustus
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Roman Empire [SEP] Languages
Suetonius quotes him as referring to "our two languages". In the Eastern empire, laws and official documents were regularly translated into Greek from Latin. The everyday interpenetration of the two languages is indicated by bilingual inscriptions, which sometimes even switch back and forth between Greek and Latin. After all freeborn inhabitants of the empire were universally enfranchised in 212 AD, a great number of Roman citizens would have lacked Latin, though Latin remained a marker of "Romanness." Among other reforms, the emperor Diocletian (reigned 284–305) sought to renew the authority of Latin, and the Greek expression "hē kratousa dialektos" attests to the continuing status of Latin as "the language of power." In the early 6th century, the emperor Justinian engaged in a quixotic effort to reassert the status of Latin as the language of law, even though in his time Latin no longer held any currency as a living language in the East.