How did the ancient Romans incorporate science into the formation of their legions?

Answer 1

The Roman legion was built upon a battle formation that was successful and it became improved over time. Romans discovered that an infantryman could fight at his peak on the front lines for approximately 15 to 20 minutes before he became exhausted. The Romans devised a system whereby the first line of battle would then fall back to a protected resting area as a new line of troops took their place on the front lines. Rest time was measured at 75 minutes. Then the soldier would return to the battle formation and be able to move up in rank as the front line troops had done their 15 minutes of fighting. The fighting time for a Roman "division" meaning a "cohort" was estimated to be 10 hours. At that point the soldiers would be totally exhausted. This system was not always perfect of course, however, for its time it was an innovation in battle tactics unmatched by its rivals.
This was a break through of sorts for ancient times. The enemy army had no such system. Their front line soldiers would fight until they were killed or fell down from exhaustion.
Roman legions dominated the ancient world for centuries based on a systematic approach to warfare.