Trial and error, mostly, at first. However, once they had a good base of construction knowledge, rules of thumb were able to be passed down to the next generation of architects and builders. They obviously did not have some of the advanced mathematical or computing tools that we have, but it turns out that you can make do with basic tools and techniques.
For example, when building something like arches, there would be specific ratios to follow for the height, radius, and thickness of the material used. Once a bunch of these basic techniques are established, you can start building more complex buildings.
For more information, the Engineer Guy on youtube has a great video on [construction techniques without the use of mathematics.](https://www.youtube.com/watch?v=_ivqWN4L3zU)
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