Etymology
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ter- 

word-forming element meaning "thrice, three times," from Latin ter "thrice," from *tris-, from root of three. Compare Latin tertius "third."

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kerato- 

before vowels, kerat-, scientific word-forming element meaning "horn, horny," also "cornea of the eye" (see cornea), from Greek keras (genitive keratos) "the horn of an animal; horn as a material," from PIE root *ker- (1) "horn; head."

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great- 

word-forming element denoting "kinship one degree further removed," early 15c. (in great uncle), from great (adj.), based on similar use of French grand (see grand-). An Old English way of saying "great-grandfather" was þridda fæder, literally "third father;" in early Middle English furþur ealdefader was used (12c.).

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se- 

word-forming element in words of Latin origin, "apart, away," from Latin se-, collateral form of sed- "without, apart, aside," probably originally "by one's self, on one's own," and related to sed, Latin reflexive pronoun (accusative and ablative), from PIE *sed-, extended form of root *s(w)e-, pronoun of the third person and reflexive (source also of German sich; see idiom).

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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 ōps (genitive ōpos) "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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meta- 
Origin and meaning of meta-

word-forming element of Greek origin meaning 1. "after, behind; among, between," 2. "changed, altered," 3. "higher, beyond;" from Greek meta (prep.) "in the midst of; in common with; by means of; between; in pursuit or quest of; after, next after, behind," in compounds most often meaning "change" of place, condition, etc. This is from PIE *me- "in the middle" (source also of German mit, Gothic miþ, Old English mið "with, together with, among").

The notion of "changing places with" probably led to the senses of "change of place, order, or nature," which was a principal meaning of the Greek word when used as a prefix (but it also denoted "community, participation; in common with; pursuing").

The third, modern, sense, "higher than, transcending, overarching, dealing with the most fundamental matters of," is due to misinterpretation of metaphysics (q.v.) as "science of that which transcends the physical." This has led to a prodigious erroneous extension in modern usage, with meta- affixed to the names of other sciences and disciplines, especially in the academic jargon of literary criticism: Metalanguage (1936) "a language which supplies terms for the analysis of an 'object' language;" metalinguistics (by 1949); metahistory (1957), metacommunication, etc.

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