All these are correct really. They're interchangeable.
My understanding has always been that à terre describes a position and par terre describes an action. Is this correct?
You know how it is with your language as mother tongue, you just use it as you think fits best. In this case, I don't think there's a relevant explanation (there are exceptions to every rule in French as well, which doesn't help!)
Personally, I prefer 'à terre' for anything. 'Par terre' actually works too, but to me, it just sounds better with 'à'.
'Battement frappé à terre' or 'rond de jambe à terre' for eg, just sounds better than par terre.
From 'gut feeling' and instinct of my language, I feel that 'à' has got a meaning of direction (towards the ground -which is very true in anything you do on the ground as for rond de jambe for eg; you press against the floor), whereas par terre is an inactive position (so the contrary to what you explained, but in a way, 'par terre' is ON the ground). So, he's sitting on the ground, would be 'il est assis par terre' and there, you would not have 'à' at all.
Whereas 'à' is a little posher maybe. For eg, you could say 'il est tombé par terre' (everyone would say it this way nowadays: he fell on the ground). Somehow, the description of ballet movements work better with 'à' though. Possibly because you have 'à 90 degrés' and so, everyone gets it easily (not 'par 90 degrés')
Jambe à la hauteur, à 90 degrés, à mi-hauteur, rond de jambe à terre, etc... Yes, it does work better! You would certainly hear it that way in France (I believe 'par' is a Russian interpretation of the French terminology and is now accepted as correct, but you would not hear it as often in France)
So, a non answer really... Both are fine.
<small>[ 24 June 2004, 11:01 AM: Message edited by: balletowoman ]</small>