Etymology
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entre- 
in words from French, corresponds to English enter-, which is itself from French entre "between, among" (11c.), from Latin inter (see inter-).
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ana- 

before vowels an-, word-forming element meaning: 1. "upward, up in place or time," 2. "back, backward, against," 3. "again, anew," from Greek ana (prep.) "up, on, upon; up to, toward; throughout; back, backwards; again, anew," from an extended form of PIE root *an- (1) "on, upon, above" (see on, which is the English cognate). In old medical prescriptions, ana by itself meant "an equal quantity of each."

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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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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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