Relating to or characteristic of astrology or astrologers; involving the study or interpretation of celestial bodies for divination.
From 'astrolog-' + '-ic' (adjective suffix). This form competes with 'astrological' as the adjectival form, appearing in older texts and specialized contexts.
This is a perfect example of English's redundancy—we have both 'astrologic' and 'astrological' meaning the same thing, but only 'astrological' survived in modern usage, showing how language naturally prunes unused variants!
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