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“diverge” in Latin

The English word diverge itself goes back to Latin vergō, through dīvergō.

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

diverge
abire in diversas partes: abire in contrarias partes: divaricare (used intransitively, Varr.): refringi (of rays that fall on a reflecting surface, and thence diverge or are reflected): lines that diverge from the centre, lineae, quae ex centro emittuntur (Plin.; where the divergency is only implied). A genealogical tree rises with a single stem, and then branches out into two diverging lines, στέμματα cognationum diverso limite in duas lineas separantur.

Quick answer

What is the Latin word for diverge?
The usual Latin words for “diverge” are dīvāricō, refringō, linō; also līnea. 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.