The Greek historian Polybius wrote a series of books to catalogue the rise of the Roman Empire (220 to 168 BC). Among this work, was an attempt at a unifying theory of political evolution or social theory cycle. He built on the previous works of philosophers, such as Plato, that identified the three simple forms of governments (kingship, aristocracy, and democracy). Polybius' theory was that all these forms of government would eventually decay and collapse over time into new forms: 

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We ought thus to name six kinds of government: the three commonly spoken of which I have just mentioned, and those which have certain elements in common with these, by which I mean one-man rule, minority rule and mob rule. The first of these to come into being is one-man rule, which arises unaided and in the natural course of events. After one-man rule, and developing from it with the aid of art and through the correct of its defects, comes kingship. This later degenerates into its corrupt but associated form, by which I mean tyranny, and then the abolition of both gives rise to aristocracy. Aristocracy by its very nature degenerates into oligarchy, and when the populace rises in anger to avenge the injustices committed by its rulers, democracy is born; then in due course, out of the licence and lawlessness which are generated by this type of regime, mob rule comes into being and completes the cycle.

-- Polybius, Rise of the Roman Empire, Book VI, pp. 304 (Penguin Classics).

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From this theory, Polybius credits Lycurgus crafting the Spartan constitution to account for the natural cycle of each form of government:

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Lycurgus foresaw this, and accordingly did not make his constitution simple or uniform, but combined in it all the virtue and distinctive features of the best governments, so that no one principle should become preponderant, and thus be perverted into its kindred vice, but that the power of each element should be counterbalanced by the others, so that no one of them inclines or sinks unduly to either side. In other words, the constitution should remain for a long while in a state of equilibrium thanks to the principle of reciprocity or counteraction.

-- Polybius, Rise of the Roman Empire, Book VI, pp. 310-311 (Penguin Classics).

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Of course, historical reality shows that this theory is far from accurate, but that did not prevent his work from influencing the establishment of the American republic from taking these considerations into account. Polybius praised the Roman republic for incorporating the three 'virtuous' forms of government into itself, to create a type of resilience against falling into the old political cycles witnessed by the Greek city-states.

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Thousands of years later, Polybius' writings influenced the American Founders' decision in establishing a constitutional republic.