The History of Science Centre’s blog at the Royal Society has an article on what is perhaps the first attempt to estimate the human population of the world:
Leeuwenhoek wrote: “If we assume that the inhabited part of the earth is as densely populated as Holland [which then had a population of perhaps one million people]… the inhabited earth being 13,385 times larger than Holland yields . . . 13,385,000,000 human beings on the earth” In the 20th century much larger and much smaller estimates of how many people the Earth can support were offered, Cohen remarked – all of them based, like Leeuwenhoek’s, on incomplete data and questionable assumptions.
Read the complete article at The twelve billion lives of Antoni van Leeuwenhoek