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It is commonly stated in books (including Merriam-Webster's dictionary) that the Augean Stables hadn't been cleaned for 30 years prior to the labor of Heracles, yet none of those books list a source for that detail.

Searching on Topostexts I have been unable to find any:

Diodorus Siculus only says

These stables contained an enormous mass of dung which had accumulated over a great period

A vague "great period", not specifically thirty years.

Pseudo-Apollodorus Bibliotheca makes no mention of how long the stables went uncleaned.

Dio Chrysostom writes

But before that, to avoid creating the opinion that he did only impressive and mighty deeds, he went and removed and cleaned away the dung in the Augean stables, that immense accumulation of many years.

Not specifically thirty years.

Lucian of Samosata writes

I may not cleanse that Augean stable completely, but I will do my best, and fetch you out a few loads as samples of the unspeakable filth that three thousand oxen could produce in many years

Again, only a vague amount of years, no specific mention of thirty years.

Robert Graves, perhaps knowing there was no ancient authority for the figure of thirty years, only said

Now, the dung in Augeias's cattle yard and sheepfolds had not been cleared away for many years

Is there any source that specifically states thirty years, and if not, how did this exact number become so prevalent in books today?

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The oldest reference to the 30 year figure I've been able to find, comes from a 17th century translation of Diodorus Siculus' Bibliotheca historic, translated by H.C. Gent and published in 1653.

That version states:

. . . informed him by way of disgrace that he alone by himself, without the help of any other, should cleanse Augeas his stable, which held three thousand Oxen, and had not in thirty years been purged.

Of course, Siculus' original Greek states only "πολλῶν χρόνων", literally, "many years". The rest of the passage however closely tracks and is obviously a direct translation, as advertised.

So it seems 30 years is merely an artistic choice on the part of the translator, who used a large-ish number of years to mean 'long time'. Similar to how old Chinese commonly uses "nine" as a non-exact imaginary number denoting many.

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