Ancient Greece was the direct democracy. Rome was a Republic but not a democracy. It was an oligarchy. The people didn't elect representatives to the Senate, it was comprised of the powerful and wealthy elite.
Robert W , there is nothing wrong with America being both a Republic and a democracy. These terms aren't at odds with one another, they describe different aspects of government. We could be a Republic and an oligarchy like the Roman Republic but instead every citizen at the age of 18 gets to vote for representatives in local, State, and federal government. This makes us a Republic and a
representative democracy.