Final answer:
Machiavelli's secondary purpose is to persuade readers of the necessity for a conqueror to destroy a republic to ensure control, utilizing historical instances to argue liberty's enduring influence on a city's resistance. The correct option is O to persuade readers that a conquering prince must destroy a former republic if he hopes to hold it.
Step-by-step explanation:
Machiavelli's secondary purpose in writing the passage from chapter 5 of The Prince is to persuade readers that a conquering prince must destroy a former republic if he hopes to hold it. By examining historical examples like the Spartans' failure to retain control of Athens and Thebes, compared to the Romans' successful dismantling of Capua, Carthage, and Numantia, Machiavelli argues that cities accustomed to freedom pose a persistent threat unless completely brought to ruin.
These insights are part of Machiavelli's broader discussion on power, control, and political strategy, emphasizing that liberty and ancient privileges are powerful motifs that conquered republics will continually seek to reclaim.