Etymology
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dia- 

before vowels, di-, word-forming element meaning "through, in different directions, between," also often merely intensive, "thoroughly, entirely," from Greek dia "through; throughout," probably cognate with bi- and related to duo "two" (from PIE root *dwo- "two") with a base sense of "twice."

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permeation (n.)

"act of permeating; state of being permeated," 1620s, noun of action from Latin permeare "to pass through" (see permeate).

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di- (3)

word-forming element of Greek origin meaning "through; in different directions; between," also often merely intensive, "thoroughly;" the form of dia- before vowels.

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ver- 

German prefix "denoting destruction, reversal, or completion" [Watkins], from Proto-Germanic *fer-, *far-, from PIE root *per- (1) "forward," hence "through."

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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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trans- 

word-forming element meaning "across, beyond, through, on the other side of, to go beyond," from Latin trans (prep.) "across, over, beyond," perhaps originally present participle of a verb *trare-, meaning "to cross," from PIE *tra-, variant of root *tere- (2) "cross over, pass through, overcome." In chemical use indicating "a compound in which two characteristic groups are situated on opposite sides of an axis of a molecule" [Flood].

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per- 

word-forming element common in words of French and Latin origin, meaning primarily "through," thus also "throughout; thoroughly; entirely, utterly," from Latin preposition per (see per (prep.)).

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peri- 

word-forming element in words of Greek origin or formation meaning "around, about, enclosing," from Greek peri (prep.) "around, about, beyond," cognate with Sanskrit pari "around, about, through," Latin per, from PIE root *per- (1) "forward," hence "in front of, before, first, chief, toward, near, around, against." Equivalent in sense to Latin circum-.

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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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step- 

Old English steop-, with connotations of "loss," in combinations like steopcild "orphan," related to astiepan, bestiepan "to bereave, to deprive of parents or children," from Proto-Germanic *steupa- "bereft" (source also of Old Frisian stiap-, Old Norse stjup-, Swedish styv-, Middle Low German stef-, Dutch stief-, Old High German stiof-, German stief-), literally "pushed out," from PIE *steup-, from root *(s)teu- (1) "to push, stick, knock," with derivatives referring to fragments (see steep (adj.)). Barnhart suggests the forms in -f- are by assimilation of the first sound in following words for "father."

Etymologically, a stepfather or stepmother is one who becomes father or mother to an orphan, but the notion of orphanage faded in 20c. and came to denote simply relation through marriage. For sense evolution, compare Latin privignus "stepson," related to privus "deprived." Compare orphan (n.).

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