Earlier quoted context omitted.
Interesting. On that note, Da Vinci's design (which I was fortunate enough to see a replica of at a local museum) was also very clever, being suited not only for screw cutting but also screw origination, as it could make new screws more accurately than the two leadscrews in the machine itself, and swap them out to improve its own accuracy. But I suppose it doesn't extend that date even further back because it wasn't…
having no experience in precision manufacturing and metrology... how does one become more precise than input tools?
Another: take a bunch of roughly cast metal balls. Put them on a sieve and let it vibrate until the balls have all passed through the holes in the sieve. Behold: metal spheres, so precise that you probably can't really measure the degree to which they are not spherical without resorting to instruments that you're not supposed to have in this scenario. Then sort by weight (which is a proxy for size). Now you can make ball bearings.
Yet another example: you can cut a lens for a telescope to within ridiculous precision using very primitive methods (https://www.instructables.com/Grind-and-Polish-a-DobsonianNe... ).
Put another way: it is always possible to increase your precision as long as you don't particularly care about absolutes or temperature effects.