LATIN DICTIONARYLexicon Latīnum
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“prevailing, prevalent” in Latin

Riddle & Arnold A Copious and Critical English–Latin Lexicon, 1864

prevailing, prevalent
That is in force, etc., quod viget, increbruit, etc. To be prevalent, vigere, etc.: to become prevalent, increbrescere, percrebrescere (Cic.); invalescere (Suet., Quint.); (longius) serpere (Cic.).
Common, general, vulgatus, pervagatus (spread abroad among the common people): communis (common, or belonging to all). (The words are found in this connection and order.) communis et pervagatus. Also by the genitives vulgi (= vulgatus) or omnium (= communis); e.g., the prevalent opinion, vulgi, or vulgata, or omnium opinio: a prevalent fault, vitium commune et pervagatum.

Quick answer

What is the Latin word for prevailing, prevalent?
The usual Latin words for “prevailing, prevalent” are incrēbrēscō, et cētera, vigeō; also vulgō, pervagor, commūnis. The right choice depends on the sense; see the distinctions below.

Entry from J. E. Riddle & T. K. Arnold, A Copious and Critical English–Latin Lexicon (rev. C. Anthon, New York: Harper, 1864), digitised by Fergus J. P. Walsh, CC BY-SA 4.0; Latin markup adapted by latindictionary.co.