From this site, one of Parmenides' fragments is translated:
Since, then, it has a furthest limit, it is complete on every side, like the mass of a rounded sphere, equally poised from the centre in every direction; for it cannot be greater or smaller in one place than in another. For there is no nothing that could keep it from reaching out equally, nor can aught that is be more here and less there than what is, since it is all inviolable. For the point from which it is equal in every direction tends equally to the limits.
I think Parmenides is arguing that the object on enquiry (i.e. what exists) has to necessarily be uniform and perfect, but I don't see how he reaches this conclusion. It seems like he's using his previous argument that the object of enquiry must be bounded (by bonds and limits), but I can't see the reasoning behind this argument?