David Galbraith graphs the population of Rome from 300 BC to the present.
The population [of Rome] during the Renaissance was miniscule (yet it was still a global center), when Michelangelo was painting the Sistine Chapel it was considerably smaller than a town like Palo Alto is today (60K); Rome at its nadir was about the size of Google (20K employees); the growth of Rome during the Industrial era is much greater than the rise of Ancient Rome.
David, you should check out The Inheritance of Rome; I'm about 100 pages in and pretty interesting so far. Also, it would be instructive to do the same graph but Rome's population as a percentage of world population.