How was such fine, geometric engraving achieved with the technology of 1863?

In this thread about updating currency, Lord Feldon posted a link to this lovely high-res image of a US 20$ banknote from ca.1863. If you examine it carefully at the highest resolution, there are all type of exquisite sinusoidal patterns (and more).

How were such ‘perfect’ patterns etched onto the printing plates using the technology of the times? How could the drill head or etching head (or whatever it’s called) be controlled and guided with such precision?

I’d guess that they were done by hand. If you take the image into an image editor like photoshop and flip some pieces around you can see that there are many imperfections in the symmetry. I’m sure the united states government searched far and wide for the artist who designed it but humans aren’t perfect and neither is that bill.

They had to be very difficult to do, because those patterns were the anti-counterfeiting technology of their day.

It’s unfortunate that the anti-counterfeiting measures used in US currency nowadays tend to make the bills ugly, rather than beautiful.

Look at the ‘sine curve’ around the center part of the back of the bill (where it is says 'this note is legal tender . . . '). You really think that was etched onto a printing plate by hand? The precision is pretty impressive; beyond that, it would take years to do, no? That’s why I assume it was done, at least in large part, using some sort of machine, or gear set-up, or …?

Geometric lathe.

Ah! Thanks.