I've tried to explain things in terms of what he says directly after this sentence. He's interested in Rome. The narration for the Greek republics is easy because their constitutional histories are clear and the effects of those constitutions, the now infamous rises and falls, are clear. For Rome, the constitution is more complex and historical record is far murkier. Collective fate? Far from it. Perhaps in some of my earlier rejected interpretations, I was saddled with that. But not with my latest proposal. What they share is they provide clear data, more a historiographical matter than a historical one. How many does Aristotle survey? About 150 city-states. And remember Polybius is writing for the folks back home who know quite about the rises and falls of those 150 having had 200 years more than Aristotle to observe and ponder.
And he's going to drop the term politeuma and take up the division into democracy, oligarchy and kingship and even expand it. So he certainly doesn't think they have collective fates. I'm still somewhat confused as to how he can talk about them having any independent futures at all given that I think it is post 146. But that is a topic for another thread.
Having taking time to ponder (time I should have taken before making the last couple of posts
-sorry), your adverbial interpretation does now seem to be correct even to me.
The one thing that bothered me about your translation was that ηὔξηται is singular which
didn't seem to fit your interpretation but actually it fits rather well.
Making the rising and falling singular in your translation gives
Of the Greek republics, so far as on the one hand (a city) has often risen to greatness and on the other hand often fallen into insignificance, it happens that the narration concerning what has come to pass and the prediction concerning what will come to pass is easy.
With often being there it implies that most of the cities have at one time or another gone through
rising and falling but there is no implication they did it on the same trajectory.
Does that sound like it is on the right track?