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“industrious” in Latin

The English word industrious itself goes back to Latin industrius, through industriosus.

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

industrious
industrius (of a restless activity, laborious, fond of labor; opposed to iners, segnis): navus (quick, active, that goes quickly to work without loss of time; opposed to ignavus). (The words are found in this connection and order.) navus et industrius; industrius et acer: assiduus (constant, assiduous; keeping up one’s activity to the end): sedulus (busy, active, that employs every moment considerately to some useful purpose; opposed to piger; often = “bustling;” of a housewife, etc.): diligens (one who with care and accuracy attends to the object he is pursuing; opposed to negligens): studiosus alicujus rei (of him who pursues a task, especially a menial one, with zeal, predilection, often even with passion; always with genitive of the object; hence, “a very industrious scholar,” not discipulus studiosissimus, without adding litterarum, bonarum artium, etc.): curiosus (that bestows a care bordering on anxiety on even the most trivial things): impiger (that feels no weariness or disgust even in a long, oppressive labor): Very industrious, qui singulari est industria: to be industrious in anything, diligentem esse in re (rarely diligentem esse alicujus rei, which occurs more frequently in the meaning, to love or value anything): in an industrious manner; [Vid: INDUSTRIOUSLY]. The Latins also frequently express “industrious” by frequentative verbs; as, “to be industrious in writing,” scriptitare.

Quick answer

What is the Latin word for industrious?
The usual Latin words for “industrious” are industrius, nāvus, assiduus; also sēdulus, dīligō, cūriōsus. 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.