Roman swords vs Greek swords

[Macedon]

Wouldn't this involve the cavalrymen (provided again Livy knows what he is talking about, but in order to have any discussion at all, we will have to trust him that far) to be dismounted? I can only with difficulty see infantry reaching shoulders of mounted men with their comparatively short gladii, even from the elevated position of fortifications; if those cavalrymen have already dismounted, the situation would be different.

My comment was about other theoretical instances, not this specific one. Just wanted to say that such action would probably produce such results too.