Etymology
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Words related to achieve

ad- 

word-forming element expressing direction toward or in addition to, from Latin ad "to, toward" in space or time; "with regard to, in relation to," as a prefix, sometimes merely emphatic, from PIE root *ad- "to, near, at."

Simplified to a- before sc-, sp- and st-; modified to ac- before many consonants and then re-spelled af-, ag-, al-, etc., in conformity with the following consonant (as in affection, aggression). Also compare ap- (1).

In Old French, reduced to a- in all cases (an evolution already underway in Merovingian Latin), but written forms in French were refashioned after Latin in 14c. and English did likewise 15c. in words it had picked up from Old French. In many cases pronunciation followed the shift. Over-correction at the end of the Middle Ages in French and then English "restored" the -d- or a doubled consonant to some words that never had it (accursed, afford). The process went further in England than in France, where the vernacular sometimes resisted the pedantic, resulting in English adjourn, advance, address, advertisement (Modern French ajourner, avancer, adresser, avertissement). In modern word-formation sometimes ad- and ab- are regarded as opposites, but this was not in classical Latin.

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*kaput- 
Proto-Indo-European root meaning "head."

It forms all or part of: achieve; behead; biceps; cabbage; cabochon; caddie; cadet; cap; cap-a-pie; cape (n.1) "garment;" cape (n.2) "promontory;" capital (adj.); capital (n.3) "head of a column or pillar;" capitate; capitation; capitulate; capitulation; capitulum; capo (n.1) "leader of a Mafia family;" capo (n.2) "pitch-altering device for a stringed instrument;" caprice; capsize; captain; cattle; caudillo; chapter; chef; chief; chieftain; corporal (n.); decapitate; decapitation; forehead; head; hetman; kaput; kerchief; mischief; occipital; precipice; precipitate; precipitation; recapitulate; recapitulation; sinciput; triceps.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit kaput-; Latin caput "head;" Old English heafod, German Haupt, Gothic haubiþ "head."
achievable (adj.)
1620s; see achieve (v.) + -able. Related: Achievably; achievability.
achievement (n.)

late 15c., "act of completing" (something), from French achèvement "a finishing," noun of action from Old French achever "to finish, accomplish" (see achieve). Meaning "thing achieved" is recorded from 1590s.

overachiever (n.)

also over-achiever, "one who achieves more than is expected,"  by 1946 in education publications, from over- + agent noun of achieve (v.). Related: Overachieve; overachieving; overachievement.

reprieve (v.)

1570s, reprive, "take back to prison," alteration (perhaps by influence of reprove) of Middle English repryen "to remand, detain" (late 15c.), probably from French repris, past participle of reprendre "take back" (see reprise). Meaning "to suspend an impending execution" is recorded from 1590s; this sense evolved probably because being sent back to prison was the alternative to execution. Spelling with -ie- is from 1640s, perhaps by analogy of achieve, etc. Related: Reprieved; reprieving.

under-achiever (n.)
also underachiever, 1953, from under + agent noun from achieve (v.). Under-achievement is recorded from 1951.