Anchiton as a transcription from Greek

[Koen G]

This is probably a huge stretch, but for what it's worth:

I was thinking, if "anchiton" is a Latinized Greek name or noun, which case could it be? 

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Apart from the obvious nominative (e.g. phaenomenon), it could also be an accusative. In that case, it is in our interest to know what the corresponding nominative would be. (I only know about this from the wiki so take this with some care).

"A few Greek nouns in -os, mostly geographical, belong to the second declension, and sometimes make Accusative in -on as Dēlos, Acc. Dēlon (but Dēlum in prose)."

--> in this case, our nominative would be "anchitos" or "anchitus". 

There are also words in -es with accusative -on. Socrates --> Socraton. 

Googling "anchites" gives some proper names, like the father of Pausanias. Also, an alternative for "anachites" You are not allowed to view links. Register or Login to view.

which, according to Pliny, is a diamond against sadness

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But he used the form "ananciten", which is probably quite far off. Greek nominative ἀναγκίτης