LATIN DICTIONARYLexicon Latīnum
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“commission” in Latin

The English word commission itself goes back to Latin mittō, through commissiō.

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

commission
appointment of an officer in the army, *prasfectura militum.
A trust or warrant, mandatum (commission or order to deliver any message; either verbally or by writing): negotium (commission to perform anything; instead of which provincia is sometimes used): to give a commission to anybody, alicui negotium dare or mandare; mandare alicui aliquid: to receive a commission mandatum datur mini a aliquo: to execute a commission mandatum exsequi, persequi, conficere, perficere, peragere: execute a commission in the most exact manner, exhaurire mandatum: in a careless manner, negligenter rem mandatam gerere.
Act of committing a crime, perhaps patratio: (Velleius, but of concluding a peace: commissio, e.g., piaculi, Arnobius, late: perpetratio, Tert..) better by circumlocution patrare: perpetrare: facere: committere, etc. [Vid: COMMIT]. A sin of commission, peccatum, quod in effectu est (opposed to “sin of omission,” delictum: though Döderlein does not confine delictum to this notion): To issue a commission of bankruptcy against anybody, *recuperatores dare, qui bona alicujus in gratiam creditorum vendant. To have received, or to hold a commission (in the army), perhaps ordines ducere: or praefectura ornari (after Cic., Ep. ad Fam., 7, 5): A ship in commission perhaps *navis omnibus rebus ornata atque instructa: to put a ship in commission navem expedire atque instruere (Vid: Hirt., B. Alex., 25).
A body of persons intrusted with an inquest or the decision of a matter, recuperatores; arbitri: to appoint such a commission recuperatores (arbitros) dare: to reject the commission recuperatores rejicere: the decision of a commission judicium recuperatorium: To send to any place a commission of inquiry, mittere, qui praesentia spectent (Tac.): to order a commission of inquiry to be sent, de re praesenti cognosci jubere. Vid: also, COMMITTEE.
commission v.
mandata alicui dare: mandare alicui, ut; negotium dare alicui, ut (charge with the execution of anything): to be commissioned with anything, jussus sum facere aliquid: by anybody, mandatum habere a aliquo [Vid: also, among COMMISSION, subst.] : alicui alicujus rei faciendae licentiam dare or permittere (cf: Cic., Verr., 3, 94, 220; Sall., Jug., 103, 2): liberum alicujus rei arbitrium alicui permittere (Liv., 32, 37; both = to authorize anybody, to perform anything: alicujus nomine, in anybody’s name: aliquo auctore, under anybody’s authority, e.g., to do anything, facere aliquid): deferre, demandare alicui aliquid (intrust anybody with the execution of anything, e.g., curam alicujus rei): delegare alicui aliquid (Golden Age, to commission anybody with anything that one ought to perform one’s self; in Silver Age, to commission, in a general sense; Vid :, Herzog, Hirt., B.G., 8, 22).

Quick answer

What is the Latin word for commission?
The usual Latin words for “commission” are mandō, negōtium, patrātiō; also patrō, perpetrō, committō. 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.