I can see how παριόντες is a participle for "come by" but not for "be by", yet Perseus dishes up both. Wouldn't the participle for "be by" be παρόντες sans ι?
http://www.perseus.tufts.edu/hopper/mor ... s&la=greek
I thought about contractions and the possibility of α+o > αι. But my table of contractions has α+o >ω. So, I dunno.