Etymology
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in- (2)
Origin and meaning of in-

element meaning "into, in, on, upon" (also im-, il-, ir- by assimilation of -n- with following consonant), from Latin in- "in," from PIE root *en "in."

In Old French (and hence in Middle English) this often became en-, which in English had a strong tendency to revert to Latin in-, but not always, which accounts for pairs such as enquire/inquire. There was a native form, which in West Saxon usually appeared as on- (as in Old English onliehtan "to enlighten"), and some of those verbs survived into Middle English (such as inwrite "to inscribe"), but all now seem to be extinct.

Not related to in- (1) "not," which also was a common prefix in Latin, causing confusion: to the Romans impressus could mean "pressed" or "unpressed;" inaudire meant "to hear," but inauditus meant "unheard of;" in Late Latin investigabilis could mean "that may be searched into" or "that cannot be searched into." Latin invocatus was "uncalled, uninvited," but invocare was "to call, appeal to."

The trouble has continued in English; the hesitation over what is meant by inflammable being a commonly cited example. Implume (1610s) meant "to feather," but implumed (c. 1600) meant "unfeathered." Impliable can mean "capable of being implied" (1865) or "inflexible" (1734). Impartible in 17c. could mean "incapable of being divided" or "capable of being imparted." Impassionate can be "free from passion" or it can mean "strongly stirred by passion." Inanimate (adj.) is "lifeless," but Donne uses inanimate (v.) to mean "infuse with life or vigor." Irruption is "a breaking in," but irruptible is "unbreakable."

In addition to improve "use to one's profit," Middle English also had a verb improve meaning "to disprove" (15c.). To inculpate is "to accuse," but inculpable means "not culpable, free from blame." Infestive has meant "troublesome, annoying" (1560s, from infest) and "not festive" (1620s). In Middle English inflexible could mean "incapable of being bent" or "capable of being swayed or moved." In 17c., informed could mean "current in information," formed, animated," or "unformed, formless" ("This was an awkward use" [OED]). Inhabited has meant "dwelt in" (1560s) and "uninhabited" (1610s); inhabitable likewise has been used on opposite senses, a confusion that goes back to Late Latin.

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in- (1)
Origin and meaning of in-
word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."

In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.
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im- 
variant of in- before -b-, -m-, -p- in the sense of "not, opposite of" (immobile, impersonal; see in- (2)) as well as "in, into" (implant, impoverish; see in- (1)). In some English words it alternates with em- (1).
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il- 
assimilated form of Latin prefix in- used with words beginning in l-; see in-.
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ir- 
assimilated form of the two Latin prefixes in- "not," or "in" (see in-) before -r-.
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intra- 
word-forming element meaning "within, inside, on the inside," from Latin preposition intra "on the inside, within, in, into;" of time, "during, in the course of," related to inter "between," from PIE *en-t(e)ro-, from root *en "in." Commonly opposed to extra-, and compare inter-. The use of intra as a prefix was rare in classical Latin.
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inter- 
word-forming element used freely in English, "between, among, during," from Latin inter (prep., adv.) "among, between, betwixt, in the midst of" (also used extensively as a prefix), from PIE *enter "between, among" (source also of Sanskrit antar, Old Persian antar "among, between," Greek entera (plural) "intestines," Old Irish eter, Old Welsh ithr "among, between," Gothic undar, Old English under "under"), a comparative of root *en "in."

A living prefix in English from 15c. and used with Germanic as well as Latinate words. Spelled entre- in French; most words borrowed into English in that form were re-spelled 16c. to conform with Latin except entertain, enterprise. In Latin, spelling shifted to intel- before -l-, hence intelligence, etc.
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intro- 
word-forming element, from Latin intro (adv.) "in, on the inside, within, to the inside," from PIE *en-t(e)ro-, suffixed form of root *en "in."
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infra- 
word-forming element meaning "below, beneath," from Latin infra (adverb and preposition) "below, underneath, on the under side, beneath," also "later than; smaller than; inferior to," related to infernus "low, below," from PIE *ndher "under" (source also of Sanskrit adnah "below," Old English under "under, among;" see under). Modern popular use of it dates from the 1920s, as an opposite to super-, often in science fiction. "This use of infra- is scarcely a Latin one" [OED].
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Indo- 
word-forming element meaning "of or pertaining to India" (and some other place), from Greek Indo-, from Indos "India" (see India).
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