https://archive.org/details/Foundations_of_Mechanical_Accura...
Manufacturing got down to nanometer precision starting with macroscopic precision visible to the naked eyeball.
BTW, in later parts of the book, Michelson appears as interferometry is used to check the accuracy of parts.
One example of precision is the Whitworth 3 plate method (invented in the 1830s), with this method, you can make surfaces that approach precision in the micron range, if necessary.
Leonardo Da Vinici's screw cutting lathe sketches show a machine that uses 2 lead screws to generate another, which averages the values of the other two screws, using careful rotations of threads, etc, it should be possible to use this method to work your way up to a uniform precise screw where each new generation is better than the ones before it.
[1] https://pearl-hifi.com/06_Lit_Archive/15_Mfrs_Publications/M...
_The Perfectionists: How Precision Engineers Created the Modern World_
(alternately title _Exactly_)
https://www.goodreads.com/work/editions/56364115-the-perfect...
and for further technical details see:
_Foundations of Mechanical Accuracy_ by Wayne R. Moore
https://mitpress.mit.edu/9780262130806/foundations-of-mechan...
[1]: https://www.nist.gov/news-events/news/2016/09/meet-bob-pmls-...
"When two plates are not flat but still match, one will not match the third. By continually lapping or scraping the high points of their contact until all three show perfect bearing when intercompared, three flat planes are created" [1]
[1] Foundations of Mechanical Accuracy by Wayne R. Moore c. 1970
(An absolutely fantastic read)