Having the characteristics of an ague; accompanied by chills, fever, or a shaking sensation.
From ague (a fever with chills) + -ish (resembling). Ague itself comes from Old French ague, possibly from Latin febris acuta (sharp fever).
Ague was a common diagnosis in pre-modern medicine, especially for malaria and other fevers. The word 'aguish' is mostly medical history now, but it shows how specific diseases shaped the vocabulary people needed to describe illness!
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