Shame - one of the Latin words is very, very well known in English.... How's your hunt for a question coming on?
Haven't had a proper chance to think yet, been stupidly busy with work. Things should get quieter later on, will see if I can come up with anything interesting...
I love the way you think it is slightly cryptic. The only thing my old brain cells remember from Latin is that a river horse is a hippopotamus! I'll leave that here in the hope it may help someone else!
I couldn't include the 4th quarter of the word as it's Greek not Latin - and it would have given the answer away too quickly....
The name was used for many different theatres and music halls..... hippodrome was derived from animal acts forming a significant part of the entertainment ??