How do you make more accurate tools from less accurate ones?
More specifically, I was reading about reprap and it said it was possible to make components of itself from other previous repraps. However, the errors in them would compound and make less and less accurate/precise models. Therefore there would be some limit to how many times it could replicate.
But, for instance. A lathe requires an accurate/precise leadscrew to control x axis motion. Using a lathe it is possible to make another leadscrew however this would be less accurate/precise than the one already on the machine.
So for my true question. How do they make more accurate ones than the previous ones. If all the current lathes in the world are +- 1mm then how would you make the next set of lathes that are more accurate/precise than that without a piece of machinery that originally had better accuracy. (sort of a chicken and egg problem) Is there some type of machine or algorithm or something that allows a machine to make something that is more accurate/precise than itself.