By the time Rome started stretching its muscles, Greece had rotted into an empty shell; it was unable to defend itself and was easily overrun. Greek civilization had dominated Italy for centuries, and the Romans held Greek culture in high regard. Educated Romans learned to read and write Greek; wealthy Romans imported Greek teachers for their children. Romans adorned their villas with copies of Greek statuary. Anything Greek was sophisticated, reflecting stylishness and good taste.
Try as they might, the Romans never quite understood Greek thinking. They interpreted Greek rationalism as the suppression of emotions. They saw life as a war between body and soul, with the body always seeking stupid goals, requiring the soul (or the mind, the Romans could never decide which) to have the strength and discipline to overrule bodily desires.
The Romans did make some good efforts in the general direction of rationalism, most notably in law. The Romans were obsessed with order and regularity. They had far and away the best bureaucracy of any ancient civilization. Their laws were written down and actually used in court cases — most of the time. However, while they did a good job of cataloguing their laws, after the Republic, laws were simply dictates of the Emperor. The Roman lawyers were kept busy reconciling the often contradictory mess of laws. But, unlike previous civilizations, the Roman lawyers realized that contradictory laws had to be reconciled. While they didn’t have the power to explicitly change the laws, they worked out interpretations that permitted the system to work.
Nevertheless, the body of Roman law had become such a tangled mess that in 529 CE, the Eastern Emperor Justinian set up a commission of top lawyers with the assignment to clean up the mess. They labored for five years and produced the Corpus Juris Civilis: The Body of Civil Law. This was not actually a set of new laws as a kind of guidebook that organized all the laws into categories and provided the “official interpretation” of those laws. This reflected a growing rationalism in Roman thought.
Ultimately, Roman civilization embodied a faint reflection of Greek rationalism. Sometimes they were rational, sometimes not. Merchants, the social drivers behind rationalism, did not enjoy the same power they had in classical Greece. Tyrants with military power were more successful.
Rome’s greatest contribution to Western civilization was its preservation of the Greek spirit of rationalism, primarily through the Roman Church. The Byzantine Church never hopped on the rationalism bandwagon, but the western church, for various reasons, kept the flame of rationalism alive.
Herewith some examples: