My opinion is supported by what one historian calls the “fossilization” of Roman design, meaning that the Romans changed the purpose or behavior of a structure but always stuck to its traditional design. Examples: the Hastati were probably named for the “hasta” thrusting spear but in the imperial period they carried a pilum and gladius. The principes where probably the “prime” force originally but in historical times they are in the second position.
The drawing above lists the names of the six centurions assigned to the cohort. The “prior” centurion is on the right and the “posterior” on the left facing the enemy – each leading his century. I have not shown the first cohort which had a unique structure of five double centuries for a total of 800 men. The senior centurion, in command of the first cohort, was called the Primus Pilus.