Regarding architectural engineering specifically, the most important text remaining from Roman times is De Architectura by Vitruvius. In this treatise, he uses long verbal descriptions and geometry (Euclidean geometry, constructions, ratios, etc.) to explain how to construct things like columns and aqueducts. Arithmetic was known to the Greeks and Romans, though their positional numeral systems made them unwieldy for complex calculations. If they needed to be done, as was possibly needed for Roman engineering, counting boards and Roman abaci could have been used as well.

Hi, Roman mathematics and engineering are a fairly popular subjects in this sub, so while you're waiting for direct responses, you may find these earlier threads interesting:

• What was math/physics before calculus? Finishing 2nd year college physics, and its in pretty much everything featuring /u/ManicMarine

• How did the Romans do engineering? featuring /u/Tiako

• Were architectural innovations such as arches, columns, and bridges understood by the Romans on a mathematical level? Or was trial and error the central driver?

• I am a young man in the Roman Empire with a profound interest in engineering. I want to build aquaducts and bridges when I grow up. How do I receive the training/education to do this? featuring /u/Alkibiades415

Mathematics

• What mathematical symbols (ie + and -) were used in the Roman Republic and Empire? Did they change? featuring /u/kohatsootsich

• FAQ section Using Roman numerals to do mathematics