Overengineering. Brute force. There are just a few basic principles to follow, such as arches being stable, and then they just threw a lot of materials and labor at it. The trick with modern engineering/architecture is doing more with less, making the building safe in case of fire or earthquakes, keeping moisture out, keeping it warm/cool, etc, etc.
The really old impressive structures like pyramids are kind of a no-brainer in terms of engineering. The challenge there is just getting the materials to the site.
And don’t underestimate the knowledge ancient people had. It just wasn’t usually written down. They passed the knowledge along directly from teachers to students.
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