"engineering before physics" is exactly wrong. No one did Engineering before a sophisticated understanding of Physics was achieved. They built bridges and towers, Engineering enables statements to be made about the performance of machines and buildings; it will survive a wind like x, you can do n cycles, do not load the wings in this way.
Translate a first year engineering paper on structures into Latin.
Ask Roman to sit said paper.
What will happen and why? The Roman chap will look very confused and will make statements (in Latin) about how stupid this stuff is and how it has nothing to do with proper engineering. The Roman will score 0. The why is that the understanding of structures and materials in the ancient world was artizanal, based on trade knowledge (often secret and hard to reproduce) and not systematic, based on the scientific method and inspectable or testable.
Currently we accept that knives, cabinets and sheds may be built or made using artisanal knowledge, we do not accept that apartment blocks, aircraft or automobiles are built this way. Society insists that these are built using systematic knowledge because otherwise they sometimes fall down or crash.
The systematic approach to aircraft is the best example - think how much civil air traffic there is now, and how rare air crashes are. The issues of subsonic flight have been systematically accounted for, right up to the point where we now see 1:2,000,000 crashes per flight.
Mechanical, aeronautical and civil engineering proceed in this way. Issues are discovered with mechanisms or structures or materials, these are characterized with scientific investigation, the characterizations lead to constraints and parameters that are required to be accounted for in future designs and old designs are re-evaluated in the light of the new knowledge.
Stating that you will build a new building in a certain way because domes are strong and concrete is strong would not cut the mustard in the modern world... The parthenon has stood for 2000 years, but how many similar structures collapsed after a few months?
I think you underestimate how smart your ancestors were to bring you to the point in time that you now exist. No offense, but the "best" Roman engineer was probably smarter than the vast majority of us.
