rediscover v.

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]

c. 1300, discoveren, "divulge, reveal, disclose, expose, lay open to view, betray (someone's secrets)," senses now obsolete, from stem of Old French descovrir "uncover, unroof, unveil, reveal, betray," from Medieval Latin discooperire, from Latin dis- "opposite of" (see dis-) + cooperire "to cover up, cover over, overwhelm, bury" (see cover (v.)).

At first with a sense of betrayal or malicious exposure (discoverer originally meant "informant"). Also in Middle English used in literal senses, such as "to remove" (one's hat, the roof from a building). The meaning "to obtain the first knowledge or sight of what was before not known," the main modern sense, is by 1550s.

Discover, Invent, agree in signifying to find out; but we discover what already exists, though to us unknown; we invent what did not before exist: as, to discover the applicability of steam to the purposes of locomotion, and to invent the machinery necessary to use steam for these ends. ... Some things are of so mixed a character that either word may be applied to them. [Century Dictionary]

Sense of "make famous or fashionable" is by 1908. Related: Discovered; discovering.

That man is not the discoverer of any art who first says the thing; but he who says it so long, and so loud, and so clearly, that he compels mankind to hear him—the man who is so deeply impressed with the importance of the discovery that he will take no denial, but at the risk of fortune and fame, pushes through all opposition, and is determined that what he thinks he has discovered shall not perish for want of a fair trial. [Sydney Smith, in Edinburgh Review, June 1826]