Real Roman engineering theory came from Marcus Vitruviouss Pollio's De Archetectura. Considered to be the ultimate reference text for building and engineering projects in Rome in 32bce, It's ten volumes cover how to build everything from temples, to aqueducts, to water mills to machines used for construction. A fascinating read, if you're curious how Romans built things.
De Architectura provides the sort of long-term perspective required to build and engineer projects that were meant to last for centuries, based on experience gathered from centuries of recorded experience.
I'm not sure if De Architectura is the only book that Roman Architects used. But it was certainly the most important.
Hundreds of pages of De Architectura list dimensions of older ancient buildings, the dimension and spacing of pillars, and failures encountered during or after construction. Something along the following lines (not actual text):
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The second Temple at Delos was built in 432bce. It consisted of 13 x 29 doric columns, 6' in diameter, 22' high, spaced on 12' intervals, with two rows in the pro-cella. The cella measured ..... The entrance to the cella was 16' high and 12' wide with a granite lintel measuring 16' x 3' x 2'.
The lintel above the entrance cracked and had to be replaced after an earthquake in 430bce. The front-right architrave cracked in 329bce, but was not repaired. The temple was subsequently abandoned and collapsed completely after an earthquake in 327bce.
The temple of Apollo at Thebes ....
The main architrave cracked while it was being mounted, and further construction was abandoned.
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Given a hundred or so such examples, a Roman architect of a new temple could make somewhat informed decisions about how high, how wide, and how thick he would need to build a new temple, and how afraid he should be when he was commissioned to build a new temple that was higher, wider, or taller.