Crossword Genius

Isti movebantur; ____ peribant they were dying of thirst (4)

Ross

I believe the answer is:

siti

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'movebantur peribant they were dying of thirst' is the definition.
I don't know anything about this answer so I can't tell whether this works.

'isti' is the wordplay.
I cannot quite understand how this works, but
an anagram of 'isti' is 'siti' which is present in the answer.
No letters remain.
This explanation may well be incorrect...

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I've seen this clue in The Times.
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