The ancient world was never a technologically based society as is the case today. Wealth was primarily generated and maintained through agriculture and to a lesser extent through mining and inter-regional trade.
A Practical Technology based on Observation and Applied Mathematics
However technological skills were certainly not neglected and were well advanced by the time of the main expansion of the Roman Empire. This was notably so in medicine, concrete technology and agriculture, but even more so in fields requiring hard science and applied mathematics, such as engineering, architecture, land surveying, hydrology, ship building and various branches of military science, such as ballistics and siege warfare.
Ancient technology was based not only upon practical experience and careful observation of physical phenomena, but was also backed up by the highly developed theoretical principles of pure mathematics and scientific logic, that had been discovered by several generations of early Greek innovative thinkers, such as Pythagoras, Euclid and Aristotle. Moreove, although, at first glance seemingly unsuited for sophisticated calculations, the Roman and Greek numeral systems, when backed up by the use of the abacus could support surprisingly accurate solutions, even by modern standards.