There’s a lot of talk about protractors and string here … that’s only partly right. Traditional survey instruments (same principles often used today) measured angles, horizontally and vertically, extremely precisely. Quick precise distance measurement came later, but one carefully measured baseline and a series of intersecting angles can coordinate points better than you’d expect.
GPS isn’t as useful as you’d think for surveying in closed-in or covered areas, so we still use similar instruments almost every day. Behind all the software, modern terrestrial survey instruments still just measure horizontal angles, vertical angles, and slope distances.
Leveling is even easier! In fact, if you want to be really basic, you can even do it with water.
Source: professional land surveyor.
Today we seem puzzled that people could have built anything without digital technology and other gizmos.
But, we tend to forget that great builders, like the Romans for example, constructed roads, sewers, aqueducts, bridges, structures, without lasers and computers. Their works have stood for centuries. And, imagine doing math with Roman numerals! They even had rudimentary cranes and understood gearing. They could do a lot of things we do now, but just didn’t have power machinery to do it.
For a great look at ancient building techniques, read the Roman author and architect, Vitruvius, who wrote [De architectura](https://en.wikipedia.org/wiki/De_architectura).
Modern measuring tools are more practical and resistant to human error, but precision isn’t necessarily a modern thing. The [theodolite](https://en.m.wikipedia.org/wiki/Theodolite) has been around since 1600 and along with other precise distance measuring tools it allowed for incredible precision in building.
Antique topography instruments were much more mechanical and human dependent, but topography isn’t a new science and the old instruments weren’t necessarily much less precise than modern instruments.
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