This is an offshoot from a twtter conversation in which the general 140char limit got out of hand.
The question began with "How did Whitworth generate fine accurate threads from hand made screws."
The answer, of course, once you think about it is by using a screw cutting lathe.
The lead screw on a lathe has a very coarse thread, only 3 or 4 turns per inch (this is Whitworth we are talking about). That shaft is then geared to the main shaft so that it turns at the speed required to create the fine thread you are trying to cut.
Early, coarse threads were, I think made by positioning cutters in sets of 3 or more positioned in a spiral pattern in a tube. So the initial precision is not in shaping the faces of the thread but "merely" in positioning the cutters. They, in turn could be positioned using coarser hand made screws tweaked to get measurably good positioning.
So you make a coarse thread, made in the same way as (for example) the thread in a printing press was made. And then use gears to turn that precisely to use it as a micrometer to make finer threads.