Etymology
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Words related to expedite

ex- 
word-forming element, in English meaning usually "out of, from," but also "upwards, completely, deprive of, without," and "former;" from Latin ex "out of, from within; from which time, since; according to; in regard to," from PIE *eghs "out" (source also of Gaulish ex-, Old Irish ess-, Old Church Slavonic izu, Russian iz). In some cases also from Greek cognate ex, ek. PIE *eghs had comparative form *eks-tero and superlative *eks-t(e)r-emo-. Often reduced to e- before -b-, -d-, -g-, consonantal -i-, -l-, -m-, -n-, -v- (as in elude, emerge, evaporate, etc.).
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*ped- 

Proto-Indo-European root meaning "foot."

It forms all or part of: antipodes; apodal; Arthropoda; babouche; biped; brachiopod; cap-a-pie; centipede; cephalopod; cheliped; chiropodist; expedite; expedition; foot; foosball; fetch (v.); fetter; fetlock; gastropod; hexapod; impair; impede; impediment; impeach; impeccable; isopod; millipede; octopus; Oedipus; ornithopod; pajamas; pawn (n.2) "lowly chess piece;" peccadillo; peccant; peccavi; pedal; pedestrian; pedicel; pedicle; pedicure; pedigree; pedology; pedometer; peduncle; pejoration; pejorative; peon; pessimism; petiole; pew; Piedmont; piepowder; pilot; pinniped; pioneer; platypus; podiatry; podium; polyp; pseudopod; quadruped; sesquipedalian; stapes; talipes; tetrapod; Theropoda; trapezium; trapezoid; tripod; trivet; vamp (n.1) "upper part of a shoe or boot;" velocipede.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit pad-, accusative padam "foot;" Avestan pad-; Greek pos, Attic pous, genitive podos; Latin pes, genitive pedis "foot;" Lithuanian padas "sole," pėda "footstep;" Old English fot, German Fuß, Gothic fotus "foot."

expediate (v.)
a 17c. error for expedite that has gotten into the dictionaries.
expedient (adj.)

late 14c., "advantageous, fit, proper to a purpose," from Old French expedient "useful, beneficial" (14c.) or directly from Latin expedientem (nominative expediens) "beneficial," present participle of expedire "make fit or ready, prepare" (see expedite). The noun meaning "a device adopted in an exigency, that which serves to advance a desired result" is from 1650s. Related: Expediential; expedientially (both 19c.).

Expedient, contrivance, and device indicate artificial means of escape from difficulty or embarrassment; resource indicates natural means or something possessed; resort and shift may indicate either. [Century Dictionary]
expedition (n.)

early 15c., expedicioun, "military campaign; the act of rapidly setting forth," from Old French expedicion "an expediting, implementation; expedition, mission" (13c.) and directly from Latin expeditionem (nominative expeditio) "an enterprise against an enemy, a military campaign," noun of action from past-participle stem of expedire "make ready, prepare" (see expedite). Meaning "journey for some purpose" is from 1590s. Sense by 1690s also included the body of persons on such a journey.

expeditious (adj.)
late 15c., expedycius "useful, fitting," from Latin expeditus "disengaged, ready, convenient, prompt; unfettered, unencumbered," past participle of expedire (see expedite). Meaning "speedy, speedily accomplished" is from 1590s. Related: Expeditiously; expeditiousness.