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mid-14c., amonesten "remind, urge, exhort, warn, give warning," from Old French amonester (12c.) "urge, encourage, warn," from Vulgar Latin *admonestare, from Latin admonere "bring to mind, remind, suggest;" also "warn, advise, urge," from ad- "to" (see ad-) + monere "advise, warn" (see monitor (n.)).
The -d- was restored on Latin model. The ending was influenced by words in -ish (e.g. astonish, abolish). Related: Admonished; admonishing.