In a manner that is comprehensive, systematic, and covering many subjects like a cyclopedia.
From 'cyclopedical' plus the adverbial suffix '-ly,' forming an adverb that modifies verbs or adjectives by adding the sense of 'in a cyclopedic way.'
If someone treats a subject 'cyclopedically,' they're being extremely thorough—covering every angle, every related topic, and every detail, like a scholar writing an entry for a comprehensive encyclopedia.
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