what was the function of the Roman cavalry?

[Tarbicus]

Just to add that a way he believed cavalry could defeat infantry was by scaring them off before they even engaged:

There never was an encounter between cavalry and infantry. The cavalry harassed with its arrows, with the lance perhaps, while passing rapidly, but it never attacked.

Man always has had the greatest fear of being trampled upon by horses. That fear has certainly routed a hundred thousand times more men than the real encounter. This was always more or less avoided by the horse, and no one was knocked down. When two ancient cavalry forces wanted really to fight, were forced to it, they fought on foot (Note the Tecinus, Cannae, examples of Livy). I find but little real fighting on horseback in all antiquity like that of Alexander the Great at the passage of the Granicus. Was even that fighting? His cavalry which traversed a river with steep banks defended by the enemy, lost eighty-five men; the Persian cavalry one thousand; and both were equally well armed!

The fighting of the Middle Ages revived the ancient battles except in science. Cavalrymen attacked each other perhaps more than the ancient cavalry did, for the reason that they were invulnerable: it was not sufficient to throw them down; it was necessary to kill when once they were on the ground. They knew, however, that their fighting on horseback was not important so far as results were concerned, for when they wished really to battle, they fought on foot. (Note the combat of the Thirty, Bayard, etc.)

http://www.bellum.nu/literature/ardantdupicq003.html

(Added: we were posting at the same time :wink: )