Please give it the necessary close look, this snapshot of the TLG text of Euthydemus. In particular please look closely at that dialogue’s cluster of the key term aei/aiei,
Now in Chapt. 22, which runs to only 32 lines, it is given a striking emphasis by being put inside quotation marks by the always-careful Oxford editor John Burnet.
Such ‘encrustation’ is of course open to a reasonable reader’s scepticism. John Cooper inaugurated this point of criticism in his Complete Plato, (Hackett, Indianapolis 1997). On the other hand this is Plato’s way of writing our ‘eternal’ or ‘always’.
This is clearly a term Plato puts much emphasis on. Further, it is a concept close to the heart of Amphinomus, who is well known to Proclus and other commentators on Euclid. It is likely he to whom we owe Scholion #18 to Euclid I, which complains about the opening proposition. What complaint, exactly ? Well it is not a Theorem proper, but rather a construction. Thus its product appears to be one of those hitherto-non-existent items, just ‘at this moment’ built by our geometer. He is scornful toward the ‘tote=trigwnon’, i.e. the ‘then-triangle’. It is as if Triangle weren’t an eternal object !
Plato had used the term in many of the centrally platonic contexts — well over 700 specimens of this occur corpus-wide — either in its 3-letter or its 4-letter variant.
This seemingly small variation of spelling has a very direct bearing on the report in Dionysius of Halicarnassus — the remark that Plato was fond of and preferential towards a diphthongal pair of letters, ahead of using the simpler monophongal variant. This latter variant, == which I have echoed here just a dozen or so lines below this — harks back to an earlier, Pre-Plato Attic.
Quite possibly young Theaetetus grew up writing this older style of Attic in Sunium, as witness the 70% preference shown at the beginning of Euclid X, where it very likely to be his authorship. This is exactly where potentially infinite ongoing processes come over the mathematical horizon in early Greek mathematics. the Theaetetus
On the literary side a chief model of that centenary=earlier writing is Thucydides, who favors it by a 128:0 ratio over the simpler form ἀεὶ .
Here is the snapshot of our ‘flock’ of αἰεὶ