Well, not quite. Republic actually denotes a leader who is elected by the citizenry, and not heridiatry......

Britannica Concise Encyclopedia: republic
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Form of government in which a state is ruled by representatives elected by its populace. The term was originally applied to a form of government in which the leader is periodically appointed under a constitution; it was contrasted with governments in which leadership is hereditary. A republic may also be distinguished from direct democracy, though modern representative democracies are by and large republics.