An archaic or variant form of apoplectic, relating to stroke or extreme anger.
From apoplexy with the suffix -ical (variant of -ic) meaning 'of or relating to.' This is an older, less common form of the same word that was used more frequently in earlier English medical writing.
You'll mostly find 'apoplectical' in old medical texts and Victorian literature—it's basically the fancy version of 'apoplectic' that doctors and authors used when they wanted to sound extra learned about someone's extreme rage or stroke symptoms.
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