Etymology
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Words related to reinforce

re- 

word-forming element meaning "back, back from, back to the original place;" also "again, anew, once more," also conveying the notion of "undoing" or "backward," etc. (see sense evolution below), c. 1200, from Old French re- and directly from Latin re- an inseparable prefix meaning "again; back; anew, against."

Watkins (2000) describes this as a "Latin combining form conceivably from Indo-European *wret-, metathetical variant of *wert- "to turn." De Vaan says the "only acceptable etymology" for it is a 2004 explanation which reconstructs a root in PIE *ure "back."

In earliest Latin the prefix became red- before vowels and h-, a form preserved in redact, redeem, redolent, redundant, redintegrate, and, in disguise, render (v.). In some English words from French and Italian re- appears as ra- and the  following consonant is often doubled (see rally (v.1)).

The many meanings in the notion of "back" give re- its broad sense-range: "a turning back; opposition; restoration to a former state; "transition to an opposite state." From the extended senses in "again," re- becomes "repetition of an action," and in this sense it is extremely common as a formative element in English, applicable to any verb. OED writes that it is "impossible to attempt a complete record of all the forms resulting from its use," and adds that "The number of these is practically infinite ...."   

Often merely intensive, and in many of the older borrowings from French and Latin the precise sense of re- is forgotten, lost in secondary senses, or weakened beyond recognition, so that it has no apparent semantic content (receive, recommend, recover, reduce, recreate, refer, religion, remain, request, require). There seem to have been more such words in Middle English than after, e.g. recomfort (v.) "to comfort, console; encourage;" recourse (n.) "a process, way, course." Recover in Middle English also could mean "obtain, win" (happiness, a kingdom, etc.) with no notion of getting something back, also "gain the upper hand, overcome; arrive at;" also consider the legal sense of recovery as "obtain (property) by judgment or legal proceedings." 

And, due to sound changes and accent shifts, re- sometimes entirely loses its identity as a prefix (rebel, relic, remnant, restive, rest (n.2) "remainder," rally (v.1) "bring together"). In a few words it is reduced to r-, as in ransom (a doublet of redemption), rampart, etc.

It was used from Middle English in forming words from Germanic as well as Latin elements (rebuild, refill, reset, rewrite), and was used so even in Old French (regret, regard, reward, etc.).

Prefixed to a word beginning with e, re- is separated by a hyphen, as re-establish, re-estate, re-edify, etc. ; or else the second e has a dieresis over it: as, reëstablish, reëmbark, etc. The hyphen is also sometimes used to bring out emphatically the sense of repetition or iteration : as, sung and re-sung. The dieresis is not used over other vowels than e when re is prefixed : thus, reinforce, reunite, reabolish. [Century Dictionary, 1895]
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enforce (v.)

mid-14c., "to drive by physical force; to try, attempt, strive; to fortify, strengthen a place;" late 14c. as "exert force, compel; make stronger, reinforce; strengthen an argument; grow stronger, become violent," from Old French enforcier "strengthen, reinforce; use force (on), offer violence (to); oppress; violate, rape" (12c.) or a native formation from en- (1) "make, put in" + force (n.). Meaning "compel obedience to" (a law, etc.) is from 1640s. Related: Enforced; enforcing.

re-enforce (v.)

also reenforce, 1580s, "to give fresh strength to," from re- "back, again" + enforce (v.). Originally of persons or military units; of buildings, structures, etc., "to strengthen by additional support," from 1883. Compare reinforce. Related: Re-enforced; re-enforcing.

en- (1)
word-forming element meaning "in; into," from French and Old French en-, from Latin in- "in, into" (from PIE root *en "in"). Typically assimilated before -p-, -b-, -m-, -l-, and -r-. Latin in- became en- in French, Spanish, Portuguese, but remained in- in Italian.

Also used with native and imported elements to form verbs from nouns and adjectives, with a sense "put in or on" (encircle), also "cause to be, make into" (endear), and used as an intensive (enclose). Spelling variants in French that were brought over into Middle English account for parallels such as ensure/insure, and most en- words in English had at one time or another a variant in in-, and vice versa.
reinforcement (n.)

c. 1600, "act of reinforcing," from reinforce + -ment. Meaning "an augmentation, an additional force, that which reinforces" is from 1650s. In psychology by 1876. Related: Reinforcements.