Etymology
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chaeto- 

before vowels chaet-, word-forming element meaning "hair," also, in scientific use, "spine, bristle," from Latinized form of Greek khaitē "long, loose, flowing hair" (of persons, also of horses, lions), from an old PIE word for "hair, mane," source also of Avestan gaesa- "curly hair," gaesu- "'curly haired," Modern Persian ges "hair that hangs down, curls;" Middle Irish gaiset "bristly hair."

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sch 

consonant cluster that can represent five distinct sounds in English; it first was used by Middle English writers to render Old English sc-, a sound now generally pronounced (and spelled) "-sh-." Sometimes it was miswritten for ch. It also was taken in from German (schnapps) and Yiddish (schlemiel). In words derived from classical languages (school (n.1)), it represents Latin sch-, Greek skh-, but in some of these words the spelling is a restoration and the pronunciation does not follow it (as in schism; Middle English sisme, cisme).

The Yiddish words with it, often derisive or dismissive, tended to come into 20c. American English. In addition to those with entries here, Saul Bellow used schmegeggy, "Portnoy's Complaint" has schmatte "a ragged garment;" schmeck "a sniff" figures in heroin jargon, and schmutz "dirt, filth" has been used. Directly to English from German also are some specialized words: Schmelz "enamel," schmerz "grief, pain, sorrow," 

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to- 

particle expressing separation, putting asunder, from West Germanic *ti- (source also of Old Frisian ti-, Old High German zi-, German zer-), from Proto-Germanic *tiz-, cognate with Latin-derived dis-. According to OED, some 125 compound verbs with this element are recorded in Old English; their number declined rapidly in Middle English and disappeared by c. 1500 except as conscious archaisms (such as to-shiver "break to pieces;" all to-brast).

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ap- (1)

form of Latin ad- in compounds with words or stems beginning in -p-; see ad-. In Old French reduced to a-, but scribal re-doubling of ap- to app- in imitation of Latin began 14c. in France, 15c. in England, and was extended to some compounds formed in Old French or Middle English that never had a Latin original (appoint, appall).

In words from Greek, ap- is the form of apo before a vowel (see apo-).

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rh- 

consonantal digraph, an initial sequence used in Latin (and thus in English words from Latin) to represent Greek initial aspirated r-. The medial Greek form of it usually is represented by -rrh-, as in catarrh, diarrhea, hemorrhage, myrrh, Pyrrhic. As it was pronounced as simply "r" in Middle English (as in Old French and Spanish), the -h- tended to be dropped in spelling but was restored in early Modern English with the classical revival.

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over- 

word-forming element meaning variously "above; highest; across; higher in power or authority; too much; above normal; outer; beyond in time, too long," from Old English ofer (from PIE root *uper "over"). Over and its Germanic relations were widely used as prefixes, and sometimes could be used with negative force. This is rare in Modern English, but compare Gothic ufarmunnon "to forget," ufar-swaran "to swear falsely;" Old English ofercræft "fraud."

In some of its uses, moreover, over is a movable element, which can be prefixed at will to almost any verb or adjective of suitable sense, as freely as an adjective can be placed before a substantive or an adverb before an adjective. [OED]

Among the old words not now existing are Old English oferlufu (Middle English oferlufe), literally "over-love," hence "excessive or immoderate love." Over- in Middle English also could carry a sense of "too little, below normal," as in over-lyght "of too little weight" (c. 1400), overlitel "too small" (mid-14c.), overshort, etc.

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mis- (1)

prefix of Germanic origin affixed to nouns and verbs and meaning "bad, wrong," from Old English mis-, from Proto-Germanic *missa- "divergent, astray" (source also of Old Frisian and Old Saxon mis-, Middle Dutch misse-, Old High German missa-, German miß-, Old Norse mis-, Gothic missa-), perhaps literally "in a changed manner," and with a root sense of "difference, change" (compare Gothic misso "mutually"), and thus possibly from PIE *mit-to-, from root *mei- (1) "to change."

Productive as word-forming element in Old English (as in mislæran "to give bad advice, teach amiss"). In 14c.-16c. in a few verbs its sense began to be felt as "unfavorably," and it came to be used as an intensive prefix with words already expressing negative feeling (as in misdoubt). Practically a separate word in Old and early Middle English (and often written as such). Old English also had an adjective (mislic "diverse, unlike, various") and an adverb (mislice "in various directions, wrongly, astray") derived from it, corresponding to German misslich (adj.). It has become confused with mis- (2).

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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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for- 

prefix usually meaning "away, opposite, completely," from Old English for-, indicating loss or destruction, but in other cases completion, and used as well with intensive or pejorative force, from Proto-Germanic *fur "before, in" (source also of Old Norse for-, Swedish för-, Dutch ver-, Old High German fir-, German ver-); from PIE *pr-, from root *per- (1) "forward," hence "in front of, before, toward, near, against."

In verbs the prefix denotes (a) intensive or completive action or process, or (b) action that miscarries, turns out for the worse, results in failure, or produces adverse or opposite results. In many verbs the prefix exhibits both meanings, and the verbs frequently have secondary and figurative meanings or are synonymous with the simplex. [Middle English Compendium]

Probably originally in Germanic with a sense of "forward, forth," but it spun out complex sense developments in the historical languages. Disused as a word-forming element in Modern English. Ultimately from the same root as fore (adv.). From its use in participles it came to be an intensive prefix of adjectives in Middle English (for example Chaucer's forblak "exceedingly black"), but all these now seem to be obsolete.

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ap- (2)

patronymic element in Welsh pedigrees and names, earlier map "son," cognate with Gaelic mac. Since 17c. merged into surnames and reduced to P- or B- (Ap Rhys = Price, Ap Evan = Bevan, Bowen = Ap Owen, etc.).

It is said that a Welshman who evidently was not willing to be surpassed in length of pedigree, when making out his genealogical tree, wrote near the middle of his long array of 'aps' — "about this time Adam was born." ["Origin and Significance of our Names," The Chautauquan, Oct. 1887-July 1888]
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