According to the modern military historian Jonathan Roth, the ancient Roman military historian Vegetius says that in the antiqua legio (ancient legion), by which he means from the Republican period, "nine of its cohorts contain 555 infantry and 66 cavalry divided into five centuries, while the first cohort comprises 1,105 infantry and 132 cavalry, also divided into ten centuries, totaling 6,100 infantry and 730 cavalry in fifty centuries." [Veg. Epitoma Rei Militaris 111.5.].
There is a problem with this, since it appears that the doubled first cohort came in the early Principate, not the republic, also according to Roth:
"The question of the size of the legion is complicated by the indications that, at some point subsequent to the Augustan reform, the organization of the legion was altered by the introduction of a doubled first cohort. The doubled first cohort was introduced at some time in the first century, but it is not known when or how long it remained in use. The principal evidence for this reform comes from Pseudo- Hyginus and Vegetius.... The archaeological evidence is ambiguous: space for a double-size first cohort has been uncovered only at two legionary camps, Caerleon and Inchtuthil...."
Source:
"The Size and Organization of the Roman Imperial Legion," by Jonathan Roth; Historia: Zeitschrift für Alte Geschichte, Vol. 43, No. 3 (3rd Qtr., 1994), pp. 346-362.
