LATIN DICTIONARYLexicon Latīnum
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“run on” in Latin

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

run on
procurrere (to run further): profluere (to flow further; of water): decurrere (e.g., manus in scribendo, Quint., 10, 7, 11): the pay runs on, procedunt alicui aera (Liv., 5, 7, 12). The interest runs on (i. e., at compound interest), centesimae fenore perpetuo ducuntur (Cic., Att., 5, 21, extr.). Interest that runs on, centesimae perpetuae (opposed to quotannis renovatae, ibid., 6, 2, extr.). RUN OUT,
As liquids from a vessel, effluere: emanare: stillare: exstillare (by drops): clepsydra extremum stillicidium exhausit (has run out, Sen.).
To project, excurrere: procurrere: prominere (in architecture). A promontory that runs out into the sea, promontorium in mare procurrens.

Quick answer

What is the Latin word for run on?
The usual Latin words for “run on” are prōcurrō, prōfluō, dēcurrō; also effluō, ēmānō, stīllō. 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.