I made an allusion to this in my reply to the Machiavelli guy, so here's a little fuller treatment.

Rome was seen as remarkable in the ancient world. That in itself isn't unusual; every people thinks they are remarkable and have stories justifying that to themselves. For instance, Thucydides has a comparison of Athens and Sparta that (I think? this might be a matter of interpretation) favorably compares Athens.

For they love innovation and are swift to devise and also to execute what they resolve on. But you on the contrary are only apt to save your own, not devise anything new, nor scarce to attain what is necessary. [3] They again are bold beyond their strength, adventurous above their own reason, and in danger hope still the best. Whereas your actions are ever beneath your power, and you distrust even what your judgment assures, and being in a danger never think to be delivered. They are stirrers, you studies; they love to be abroad, and you at home the most of any.

"They" are Athenians and "You" are Spartans here. There's a lot more of that stuff if you want to read it around the location I linked. But this is the stuff of any state looking to define its own characteristics.

Rome caused a problem for Greek intellectuals - how did a barbarian, and not even the Mede, manage to conquer Greeks? Dionysius, and he claims others, solved this by trying to show Romans were really Greek.

Polybius is a better thinker for us. While Dionysius was writing during Augustus' reign and so well after the Roman conquest, Polybius lived through that conquest, and he was trying to explain to Greeks dealing with it as a new reality. Polybius' explanation took up much of his sixth book, which you can get here.

Polybius drew on Plato and Aristotle, who had classified potential government into three good and three bad forms (I might be fudging the philosophy of it; I'm an historian! Forgive me!). Here is a Stanford.edu page outlining what Aristotle was on about. Short version, Aristotle distinguished between monarchy, aristocracy, and democracy, and noted advantages to each - they also have evil twins, tyranny, plutocracy, and mob rule - and other people might have different translations for the Greek terms.

Polybius looking at the Rome of the middle 2nd century saw Rome, in its consuls, its senate, and its people as one that incorporated all the advantages of the several modes of government, and provided counters for the accompanying weaknesses, so long as the three elements remained in competition.

Here is some Polybius on the Roman Constitution:

For if one fixed one's eyes on the power of the consuls, the constitution seemed completely monarchical and royal; if on that of the senate it seemed again to be aristocratic; and when one looked at the power of the masses, it seemed clearly to be a democracy.

Having stated how political power is distributed among the different parts of the state, I will now explain how each of the three parts is enabled, if they wish, to counteract or co-operate with the others.

This is followed by specifics for each "branch of government," from the link I provided earlier. I'll finish with one long quote:

Such being the power that each part has of hampering the others or co-operating with them, their union is adequate to all emergencies, so that it is impossible to find a better political system than this. 2 For whenever the menace of some common danger from abroad compels them to act in concord and support each other, so great does the strength of the state become, that nothing which is requisite can be neglected, as all are zealously competing in devising means of meeting the need of the hour, 3 nor can any decision arrived at fail to be executed promptly, as all are co-operating both in public and in private to the accomplishment of the task which they have set themselves; 4 and consequently this peculiar form of constitution possesses an irresistible power p311of attaining every object upon which it is resolved. 5 When again they are freed from external menace, and reap the harvest of good fortune and affluence which is the result of their success, and in the enjoyment of this prosperity are corrupted by flattery and idleness and wax insolent and overbearing, as indeed happens often enough, 6 it is then especially that we see the state providing itself a remedy for the evil from which it suffers. 7 For when one part having grown out of proportion to the others aims at supremacy and tends to become too predominant, it is evident that, as for the reasons above given none of the three is absolute, but the purpose of the one can be counterworked and thwarted by the others, none of them will excessively outgrow the others or treat them with contempt. 8 All in fact remains in statu quo....

So, here we have a bunch of Greeks seeing Rome dominate the Mediterranean, saying to each other, "How the fuck did this happen?" and our buddy Polybius is there on the ground, saying "Guys, they solved the Constitution problem! They don't have revolutions, and they can fight wars, because they know how to build a government!"

Unfortunately for Polybius, he was both unconvincing and wrong. Greeks were not satisfied with his explanation, as evidenced by Dionysius, whom I already mentioned a hundred years or so later was trying to make Roman domination OK because they're really Greeks, and Polybius was wrong because, in the end, the Roman constitution wasn't stable.