Please don't try to equate the Roman and modern army, it just flat out doesn't work. As you just proved.

A Legion was fixed, numbered unit. In that sense it is equivelant to a regiment on infantry, a cohort to a battallian and a century to a company.

HOWEVER, that only tracks to the modern army, during the Napolionic Wars the paper strength for a battallian was 1,000, in 10 companies.