Acies quadrata

[Cesco]

To be honest, I can't see Vegetius mentioning a quadratum unless it was specifically different in formation from the formations preceding and following it - the line, the doubled line (and all its multiplications), the square and the circle or orbis. The square is a specifically tactical formation different from the orbis or circle in that it is an offensive mobile posture used against larger forces which have encircled you (as above) whereas the orbis is a static one used once the acies is broken or disordered in battle - or at least, that is my reading of it via Vegetius and Ammianus!

I get what you mean, and this is a good point: substantially doubling a simple line or cubing a doubled line was the same thing...Anyway, as I said before, there is a passage in Maurice's Stratecikon in which is described a pretty similar manouvre.