The ultimate reference for this is the Foundations of Mechanical Accuracy, which is available as a PDF[1], the print versions aren't cheap.

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 main way is by averaging error terms toward zero.

For example, Da Vinci's machine cuts the new screw blank in the centre of the carriage, which is driven by leadscrews on either side. The nuts would have likely been something like a wide strip of leather clamped over the screw thread, so there's enough compliance to average over a few pitches of thread, and the position of the cutter would be close to the average of the position set by each leadscrew thread.

Imagine the rough-cut screw threads have a pitch vs rotation angle described by p1(θ) and p2(θ). Running the machine then creates a new screw which is nearly a duplicate of the drive-screws in the machine but with pitch p3(θ) = (p1(θ) + p2(θ))/2. You can make two of these screws and swap them for the two leadscrews in the machine (it's built to be easy to do this). The random errors from a rough-cut screw gradually average out. But the cleverness doesn't end there. You then flip one of the screws backward end-to-end, so now you're averaging p3(θ) with p4(L-θ). You can also offset θ by any amount for either screw by offsetting the change-gear and re-clamping the carriage nut. Repeating these actions, you gradually can eliminate all systematic thread errors from the initial rough-cut screws and converge towards cutting a screw with nearly-constant pitch.

(It doesn't end there either; there's really a lot of flexibility with Da Vinci's design. Changing the gear ratio lets you create a fine-pitch thread from a coarse-pitch thread, or vise-versa, or cut a multi-start screw by rotating the blank 180 degrees or end-over-end).

Just some examples: take a string, don't bother to measure it, just any length between 1 and two meters or so would do. Take a pencil (or a piece of charcoal if you really want to go native) and a smooth branch. Stick the branch in the ground, tie the string around it so that it can slide with little friction and put the pencil in a loop of string on the other side. Now use this to create a circle. You started off with very rough elements not specifically sized for any purpose and ended up with a high precision representation of a mathematical concept.

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.