Etymology
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cosmo- 

before a vowel cosm-, word-forming element from Latinized form of Greek kosmos (see cosmos). In older use, "the world, the universe;" since 1950s, especially of outer space. Also cosmico-.

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gu- 
because g- followed by some vowels in English usually has a "soft" pronunciation, a silent -u- sometimes was inserted between the g- and the vowel in Middle English to signal hardness, especially in words from French; but this was not done with many Scandinavian words where hard "g" precedes a vowel (gear, get, give, etc.). Germanic -w- generally became -gu- in words borrowed into Romance languages, but Old North French preserved the Frankish -w-, and English sometimes borrowed both forms, hence guarantee/warranty, guard/ward, etc.
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cyclo- 

before a vowel, cycl-, word-forming element in technical terms meaning "circle, ring, rotation," from Latinized form of Greek kyklos "circle, wheel, ring" (from PIE root *kwel- (1) "revolve, move round"). In organic chemistry it is used in forming chemical names of cyclic compounds.

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brachio- 
before a vowel, brachi-, word-forming element meaning "arm, of the upper arm, pertaining to the upper arm and," from Greek brakhion "arm," perhaps originally "upper arm," literally "shorter," from brakhys "short" (from PIE root *mregh-u- "short"), in contrast to the longer forearm.
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amphi- 
before a vowel amph-, word-forming element meaning "on both sides, of both kinds; on all sides, all around," from Greek amphi (prep., adv.) "round about, on both sides of, all around; about, regarding," which is cognate with Latin ambi-, both from PIE root *ambhi- "around."
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bis- 
word-forming element meaning "twice," from Latin bis "twice, in two ways, doubly," from Old Latin dvis, cognate with Sanskrit dvih, Avestan bish, Greek dis, Middle High German zwis "twice," from PIE root *dwo- "two." Also the form of bi- used before -s-, -c-, or a vowel.
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-cide 

word-forming element meaning "killer," from French -cide, from Latin -cida "cutter, killer, slayer," from -cidere, combining form of caedere "to strike down, chop, beat, hew, fell, slay," from Proto-Italic *kaid-o-, from PIE root *kae-id- "to strike." For Latin vowel change, see acquisition. The element also can represent "killing," from French -cide, from Latin -cidium "a cutting, a killing."

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anthropo- 

before a vowel, anthrop-, word-forming element meaning "pertaining to man or human beings," from Greek anthrōpos "man; human being" (including women), as opposed to the gods, from andra (genitive andros), Attic form of Greek anēr "man" (as opposed to a woman, a god, or a boy), from PIE root *ner- (2) "man," also "vigorous, vital, strong."

Anthropos sometimes is explained as a compound of anēr and ops (genitive opos) "eye, face;" so literally "he who has the face of a man." The change of -d- to -th- is difficult to explain; perhaps it is from some lost dialectal variant, or the mistaken belief that there was an aspiration sign over the vowel in the second element (as though *-dhropo-), which mistake might have come about by influence of common verbs such as horao "to see." But Beekes writes, "As no IE explanation has been found, the word is probably of substrate origin."

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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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auto- 
word-forming element meaning "self, one's own, by oneself, of oneself" (and especially, from 1895, "automobile"), from Greek autos, reflexive pronoun, "self, same," which is of unknown origin. It also was a common word-forming element in ancient Greek, as in modern English, but very few of the old words have survived the interval. In Greek, as a word-forming element, auto- had the sense of "self, one's own, of oneself ('independently'); of itself ('natural, native, not made'); just exactly; together with." Before a vowel, it became aut-; before an aspirate, auth-. In Greek it also was used as a prefix to proper names, as in automelinna "Melinna herself." The opposite prefix would be allo-.
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