This isn’t a straightforward question, because the ancient Mediterranean world covers a very wide range of time and geography. Maps were drawn in many different ways for different purposes. Also we just don’t have maps for a large range of that time. Often the maps you see are actually based on textual descriptions. Do you have any specific maps you’re thinking of?
Drawing maps on a relatively small scale can be done by eye, without any special technology. The scales and distances might be off, but a map of, say, a coastline will be broadly recognisable. It *is* time consuming but it’s perfectly doable.
I’m not sure about the Romans, but I don’t think the Greeks used geometry systematically at this scale. They definitely didn’t use compasses, because they weren’t aware of them.
It’s when the scale gets bigger that things get more complicated. Geographers often used descriptions “two days sail past the river is a wide and smooth peninsula with a town on it…” Then you draw an idea of what that looks like.
When it comes to distance, a common way to measure it was by using travel times. Most of the time, maps are used for travel, so the main thing you need to know is what direction to go in and how long it’ll take. Maps showing the towns along a road and the travel time between them are pretty common.
If you know roughly how far you travel in a day, you can estimate the distance. But only estimate… Wiggly roads, hills, wind, currents, etc. will all make this more complicated.
So while maps drawn this way usually have recognisable geography, the distances are often way off, and often places aren’t lined up in terms of longitude and latitude. This was made worse by a tendency to consider the world as fitting into a circle, which dictated a certain scale.
Things improved around the 4th century BC, with geographers travelling around the Mediterranean world and using the angle of the sun to calculate latitude. However estimates of longitude remained very rough.
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