How did anyone ever make a precise instrument using only less precise instruments?

The central trick, and it is genuinely beautiful once you see it, is to check things against themselves using symmetry, because that requires no reference more accurate than the thing you are making.

The classic example is the three-plate method for making a flat surface. Rub two plates together and they wear towards matching — but matching could mean one convex and one concave. So use three. Lap A against B, then B against C, then A against C, rotating through the pairs. The only shape all three can share, in every pairing, is flat. No reference plane is needed and none existed before the first one was made this way.

The same idea produces a right angle: a square checked against its own mirror image reveals its error at double magnitude, because the error adds rather than cancelling. Reversal techniques of that kind are the backbone of metrology.

So the answer to "what do you check it against" is: against itself, in a configuration where an error cannot hide.

The second mechanism is error averaging, and it directly addresses your worry that errors must accumulate.

They accumulate only if they are systematic. Random errors do the opposite: measure the same thing many times and the average is more accurate than any single measurement, improving with the square root of the number of measurements. Take a hundred readings and you have roughly ten times the precision of one.

This is why a dividing engine cutting a hundred gear teeth can produce a wheel far more accurate than the mechanism cutting it — errors distributed around the circle partially cancel when the whole wheel is used.

So the discipline of metrology is largely about converting systematic errors into random ones — by reversing, rotating, swapping, and repeating — and then averaging them away. Once you know that, the whole field looks like one idea applied in a hundred forms.

The third mechanism is escaping the ratchet entirely by finding a natural constant to measure against.

Once you can count the oscillations of an atom, you do not need a better clock to make a better clock — you need a better way to count, and the reference is free and identical everywhere. Once you can count wavelengths of light, length stops depending on a metal bar in a vault.

This is why modern units are defined in terms of physical constants rather than artefacts. The definition of the metre is now tied to the speed of light and the second, and the kilogram to a fixed constant rather than a lump of metal. That change removed the entire problem of the reference drifting or being damaged.

So the history has two phases: bootstrapping by symmetry and averaging until you can measure a natural constant well enough, then defining the unit in terms of that constant and never bootstrapping again.

One historical detail that makes the bootstrap feel less abstract: much of it happened in workshops rather than laboratories, driven by needing better machine tools.

A more accurate lathe lets you make a more accurate leadscrew, which lets you make a more accurate lathe. That loop ran for generations, each turn improving the next, with the three-plate method and reversal tricks used at every stage.

It is one of the few technological ratchets you can trace step by step, and the people who turned it mostly did not write papers.