Final answer:
Polybius' statement implies that Rome sought to establish a universal empire, with their victory over Carthage prompting further expansion into Greece and Asia to extend their dominance.
Step-by-step explanation:
In Polybius' statement, a crucial assumption implicit is that Rome sought to establish a universal empire. This assumption can be inferred from the mention of Rome's victory over the Carthaginians in the Hannibalic War, and their conviction that it marked a significant step towards a universal empire. The statement suggests that Rome saw this victory as a turning point that encouraged them to extend their influence beyond Italy and into Greece and Asia.
The crucial assumption implicit in Polybius' statement is that Rome sought to establish a universal empire. After their victory over Carthage in the Hannibalic War, the Romans were emboldened and viewed the defeat of their strongest rival as a pivotal moment in their expansion.
This belief led them to intervene in Greece and Asia to further extend their power and influence. Their success in the Punic Wars and their subsequent actions against Philip V of Macedon and Antiochus III of the Seleucid Empire illustrate Rome's ambitions towards establishing a dominant empire that would reign supreme over the Mediterranean and beyond.