This appears to be a variant or Latin form that is not standard in English; it may be a historical or technical variant of extirpation.
Likely a Latinized or archaic form related to extirpate, possibly from scholarly or scientific Latin usage in early modern texts where Latin endings were sometimes applied to borrowed words.
This word illustrates how scientific and scholarly writing once freely mixed Latin and English—early naturalists and philosophers would invent forms like this to sound more authoritative and learned, a practice that gradually fell away as English standardized.
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