Jed, because I'm not smart, and am basically an alcoholic redneck that holds sparklers for a living
Cory, the building and rebuilding of machining tools uses hand scraping, which is using a single edged tool and by hand shaving down high spots. They mark the high points using marking dye and a known flat (or curved) surface, and then carefully scrape them. This process has been around since at least the beginning of the industrial revolution, but i could easily see ancient people coming to the same process, especially considering their very high understanding of math and geometry. This is the exact process that granite surface plates are made and adjusted as well.
en.m.wikipedia.org
What's also pretty cool, if you actually look into machine technology history, you notice that every step usually builds upon another step. First the lathes came, then the shapers and planers, then milling, then grinding, e.t.c. As the industry advanced, the average machinist was able to be less and less trained, but production and precision increased exponentially. This was due to the highly skilled machinists setting everything up, which had a traditional apprenticeship. In their apprenticeship they were first taught hand techniques; filing, scraping, lapping e.t.c. By the time they were halfway thorough their apprenticeship (meaning they had much much more to learn) they could build just about anything, by hand and to greater accuracy.
It used to be commonplace for your regular shade tree mechanic to be able to do this too, obviously to a certain degree. Your head gaskets, engine and other bearings, cylinder walls, e.t.c could all resurfaced by hand. All a machine tool does is make it an easier and quicker process, although if utmost care is taken, hand work is still always more accurate.