Let's say we have an Earth-sized planet and the same general solar activity and climatology. However, the continents are much smaller, and it's effectively impossible to accomplish travel between them (due to distance, inability to navigate, lethal oceanic weather, or something). That is, any island continent is effectively cut off and isolated. What is the smallest land-mass that would be required to support a human civilization with cities and technology to the level of an ancient culture (e.g., Sumeria, Egypt, Rome)? And what is the optimal terrain and natural resources to achieve that minimum?
Note this is different from this question which asks for the smallest planet that could support a civilization, in which the answers focus largely on issues of gravity difference. In my question I'm stipulating Earth-like size and gravity, but wondering what the minimal dry land mass would be required to support an organized human civilization approximately similar to something in our history.
Edit: As a point of clarification, assume that this question is about only the support of a human civilization with ancient-city-level technology. That is: Possibly the human civilization has been set down fully-formed by magic or advanced technology. The question subsumes the requirement that the population be large enough to maintain a healthy genetic pool over a long period of time.
A separate question has been made on the topic of the smallest land area to develop (evolve) such a human civilization.