Etymology
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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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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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psycho- 

word-forming element meaning "mind, mental; spirit, unconscious," from Greek combining form of psykhē "the soul, mind, spirit; life, one's life, the invisible animating principle or entity which occupies and directs the physical body; understanding, the mind (as the seat of thought), faculty of reason" (see psyche). It also was used to form compounds in Greek, such as psychapates "soul-beguiling" (with apate "deceit").

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phreno- 

before vowels phren-, word-forming element meaning "mind," also, in medical use, "diaphragm, muscle which parts the abdomen from the thorax;" from Greek phrēn, phrenos "the mind, spirit," also "the midriff, diaphragm," also (in plural, phrenes) "the parts around the heart, the breast," and hence "wits, sense, sanity, mind" on the notion of the breast or heart as the seat of thoughts and passions.

The word is of uncertain origin; Watkins has it under a proposed PIE root ‌‌*gwhren- "to think." Beekes finds the connection with phrassein "to fence or hedge in" "semantically attractive," but there are phonetic difficulties, and he finds "quite feasible" a relationship with phrazomai "to think, consider" (later phrazein; see phrase (n.)), itself an isolated word.

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pt- 

An initial consonant combination common in Greek; the p- typically is silent in English words that have it but pronounced in French, German, etc.

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di- (2)

word-forming element of Latin origin meaning "apart, asunder," the form of dis- before certain voiced consonants. As des- was a form of dis- in Old French, some Middle English words have forms in both de- and di-; compare devise, which really belongs to di- and is related to divide.

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be- 

word-forming element of verbs and nouns from verbs, with a wide range of meaning: "about, around; thoroughly, completely; to make, cause, seem; to provide with; at, on, to, for;" from Old English be- "about, around, on all sides" (the unstressed form of bi "by;" see by (prep.)). The form has remained by- in stressed positions and in some more modern formations (bylaw, bygones, bystander).

The Old English prefix also was used to make transitive verbs and as a privative prefix (as in behead). The sense "on all sides, all about" naturally grew to include intensive uses (as in bespatter "spatter about," therefore "spatter very much," besprinkle, etc.). Be- also can be causative, or have just about any sense required. The prefix was productive 16c.-17c. in forming useful words, many of which have not survived, such as bethwack "to thrash soundly" (1550s) and betongue "to assail in speech, to scold" (1630s).

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hetero- 

before vowels heter-, word-forming element meaning "other, different," from Greek heteros "the other (of two), another, different; second; other than usual." It is a compound; the first element means "one, at one, together," from PIE root *sem- (1) "one; as one, together with;" the second is cognate with the second element in Latin al-ter, Gothic an-þar, Old English o-ðer "other."

Compounds in classical Greek show the range of the word there: Heterokretes "true Cretan," (that is, of the old stock); heteroglossos "of foreign language;" heterozelos "zealous for one side;" heterotropos "of a different sort or fashion," literally "turning the other way;" heterophron "raving," literally "of other mind."

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super- 

word-forming element meaning "above, over, beyond," from Latin super (adverb and preposition) "above, over, on the top (of), beyond, besides, in addition to," from *(s)uper-, variant form of PIE root *uper "over." In English words from Old French, it appears as sur-. The primary sense seems to have shifted over time from usually meaning "beyond" to usually meaning "very much," which can be contradictory. E.g. supersexual, which is attested from 1895 as "transcending sexuality," from 1968 as "very sexual."

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cero- 

word-forming element meaning "wax, waxy," from Latinized form of Greek kēros "beeswax," a word of unknown origin with no obvious ulterior connections. "As there is no evidence for Indo-European apiculture, we have to reckon with foreign origin for κηρός" [Beekes].

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