Final answer:
Polybius aimed to explain Rome's rise to power and the type of political system it had, focusing on its constitution and governance.
Step-by-step explanation:
Polybius, a Greek historian, aimed to answer significant questions about Rome's rise to power in his work The Histories. The phrase "and under what kind of polity" signifies the type of political system Rome had during its ascent. The accurate option that reflects Polybius' objectives is: Option 1: How did Rome rise to power, and what political system did it have? This encompasses Polybius' exploration of the organizational structure, the mixed constitution of the Roman Republic, and the factors contributing to Rome's expansion and domination over known territories.