Etymology
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anti- 

word-forming element of Greek origin meaning "against, opposed to, opposite of, instead," shortened to ant- before vowels and -h-, from Old French anti- and directly from Latin anti-, from Greek anti (prep.) "over, against, opposite; instead, in the place of; as good as; at the price of; for the sake of; compared with; in opposition to; in return; counter-," from PIE *anti "against," also "in front of, before" (from root *ant- "front, forehead," with derivatives meaning "in front of, before"), which became anti- in Italian (hence antipasto) and French.

It is cognate with Sanskrit anti "over, against," and Old English and- (the first element in answer). A common compounding element in Greek, in some combinations it became anth- for euphonic reasons. It appears in some words in Middle English but was not commonly used in English word formations until modern times. In a few English words (anticipate, antique) it represents Latin ante.

In noun compounds where it has the sense of "opposed to, opposite" (Antichrist, anti-communist) the accent remains on the anti-; in adjectives where it retains its old prepositional sense "against, opposed to," the accent remains on the other element (anti-Christian, anti-slavery).

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un- (2)
prefix of reversal, deprivation, or removal (as in unhand, undo, unbutton), Old English on-, un-, from Proto-Germanic *andi- (source also of Old Saxon ant-, Old Norse and-, Dutch ont-, Old High German ant-, German ent-, Gothic and- "against"), from PIE *anti "facing opposite, near, in front of, before, against" (from PIE root *ant- "front, forehead," with derivatives meaning "in front of, before").

More or less confused with un- (1) through similarity in the notions of "negation" and "reversal;" an adjective such as unlocked might represent "not locked" (un- (1)) or the past tense of unlock (un- (2)).
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cata- 

word-forming element meaning "down, downward," but also "through, on, against, concerning," etc., from Latinized form of Greek kata-, before vowels kat-, from kata "down, downward, down from, down to," from PIE *kmt- "down, with, along" (source also of Hittite kattan (adv.) "below, underneath," katta "along with"). Occasionally in Greek it had senses of "against" (catapult) or "wrongly" (catachresis), also "along, through, over, across, concerning." Also sometimes used as an intensive or with a sense of completion of action (catalogue). Very active in ancient Greek, this prefix is found in English mostly in words borrowed through Latin after c. 1500.

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bi- 
word-forming element meaning "two, having two, twice, double, doubly, twofold, once every two," etc., from Latin bi- "twice, double," from Old Latin dvi- (cognate with Sanskrit dvi-, Greek di-, dis-, Old English twi-, German zwei- "twice, double"), from PIE root *dwo- "two."

Nativized from 16c. Occasionally bin- before vowels; this form originated in French, not Latin, and might be partly based on or influenced by Latin bini "twofold" (see binary). In chemical terms, it denotes two parts or equivalents of the substance referred to. Cognate with twi- and di- (1).
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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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a- (1)

prefix or inseparable particle, a relic of various Germanic and Latin elements.

In words derived from Old English, it commonly represents Old English an "on, in, into" (see on (prep.)), as in alive, above, asleep, aback, abroad, afoot, ashore, ahead, abed, aside, obsolete arank "in rank and file," etc., forming adjectives and adverbs from nouns, with the notion "in, at; engaged in." In this use it is identical to a (2).

It also can represent Middle English of (prep.) "off, from," as in anew, afresh, akin, abreast. Or it can be a reduced form of the Old English past participle prefix ge-, as in aware.

Or it can be the Old English intensive a-, originally ar- (cognate with German er- and probably implying originally "motion away from"), as in abide, arise, awake, ashamed, marking a verb as momentary, a single event. Such words sometimes were refashioned in early modern English as though the prefix were Latin (accursed, allay, affright are examples).

In words from Romanic languages, often it represents reduced forms of Latin ad "to, toward; for" (see ad-), or ab "from, away, off" (see ab-); both of which by about 7c. had been reduced to a in the ancestor of Old French. In a few cases it represents Latin ex.

[I]t naturally happened that all these a- prefixes were at length confusedly lumped together in idea, and the resultant a- looked upon as vaguely intensive, rhetorical, euphonic, or even archaic, and wholly otiose. [OED]
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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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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.
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e- 

the later Romans evidently found words beginning in sc-, sp-, st- difficult or unpleasant to pronounce; in Late Latin forms begin to emerge in i- (such as ispatium, ispiritu), and from 5c. this shifted to e-. The development was carried into the Romanic languages, especially Old French, and the French words were modified further after 15c. by natural loss of -s- (the suppression being marked by an acute accent on the e-), while in other cases the word was formally corrected back to the Latin spelling (for example spécial). Hence French état for Old French estat for Latin status, etc. It also affected Romanic borrowings from Germanic (such as espy, eschew).

A different e- is a reduced form of Latin ex- before consonants (see ex-), and the e- in enough is an unfelt survival of an Old English alternative form of ge-.

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grand- 
a special use of grand (adj.) in genealogical compounds, originally with the sense of "a generation older than," first attested c. 1200, in Anglo-French graund dame "grandmother," also grandsire (late 13c.), from such use of Old French grand-, which perhaps is modeled on Latin avunculus magnus "great uncle." The partly-Englished grandmother, grandfather are from 15c. Other such words in European languages are formed with the adjectives for "old" or "best" (Danish bedstefar) or as diminutives or pet names (Greek pappos, Welsh taid). The French formation also is the model for such words in German and Dutch. Spanish abuelo is from Latin avus "grandfather" (from PIE *awo- "adult male relative other than the father;" see uncle), via Vulgar Latin *aviolus, a diminutive or adjective substitution for the noun.

The extension of the sense to corresponding relationships of descent, "a generation younger than" (grandson, granddaughter) is from Elizabethan times. The inherited PIE root, *nepot- "grandchild" (see nephew) has shifted to "nephew; niece" in English and other languages (Spanish nieto, nieta). Old English used suna sunu ("son's son"), dohtor sunu ("son's daughter").
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