Etymology
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foam (n.)

Middle English fom, fome (c. 1300), from Old English fam "foam, saliva froth; sea," from West Germanic *faimo- (source also of Old High German veim, German Feim), from PIE root *(s)poi-mo- "foam, froth" (source also of Sanskrit phenah; Latin pumex "pumice," spuma "foam;" Old Church Slavonic pena "foam;" Lithuanian spainė "a streak of foam"). The plastic variety used in packaging, etc., so called from 1937.

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mouth (v.)

early 14c., "to speak," from mouth (n.). Related: Mouthed; mouthing. Old English had muðettan "to blab." In 17c.-18c. especially "to speak pompously or affectedly." Meaning "form the shape of words with the mouth without uttering them" is by 1953.

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foam (v.)

Old English famgian "to emit foam, to boil," from the source of foam (n.). Sense of "become foamy, to froth" is from late 14c. Transitive sense is from 1725. Related: Foamed; foaming.

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at- 

assimilated form of ad- "to, toward, before" before stems beginning in -t-; see ad-. In Old French and Middle English regularly reduced to a-, later restored.

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mouth (n.)

Old English muþ "oral opening of an animal or human; opening of anything, door, gate," from Proto-Germanic *muntha- (source also of Old Saxon, Old Frisian muth, Old Norse munnr, Danish mund, Middle Dutch mont, Dutch mond, Old High German mund, German Mund, Gothic munþs "mouth"), with characteristic loss of nasal consonant in Old English (compare tooth), probably an IE word, but the exact etymology is disputed. Perhaps from the source of Latin mentum "chin" (from PIE root *men- (2) "to project," on the notion of "projecting body part"), presuming a semantic shift from "chin" to "mouth."

In the sense of "outfall of a river" it is attested from late Old English; as the opening of anything with capacity (a bottle, cave, etc.) it is recorded from mid-13c. Mouth-organ attested from 1660s. Mouth-breather is by 1883. Mouth-to-mouth "involving contact of one person's mouth with another's" is from 1909.

Word of mouth "spoken words, oral communication" (as distinguished from written words) is by 1550s. To put words in (someone's) mouth "represent as having said what one did not say" is from late 14c.; to take the words out of (someone's) mouth "anticipate what one is about to say" is from 1520s. To be down in the mouth "dejected" (1640s) is from the notion of having the corners of the mouth turned downward.

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at (prep.)

Old English æt, from Proto-Germanic *at (source also of Old Norse, Gothic at, Old Frisian et, Old High German az), from PIE root *ad- "to, near, at." Lost in German and Dutch, which use their equivalent of to; in Scandinavian, however, to has been lost and at fills its place.

At is used to denote relations of so many kinds, and some of these so remote from its primary local sense, that a classification of its uses is very difficult. [OED]

In choosing between at church, in church, etc. at is properly distinguished from in or on by involving some practical connection; a worshipper is at church; a tourist is in the church. In 19c. it was used for points of the compass as regions of a country (at the South) where later tendency was to use in.

The colloquial use of at after where (as in where it's at) is noted in Bartlett (1859). At last is recorded from late 13c.; adverbial phrase at least was in use by 1775. At in Middle English was used freely with prepositions (as in at after, which is in Shakespeare), but this has faded with the exception of at about.

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bad-mouth (v.)

"abuse (someone) verbally," 1941, probably ultimately from noun phrase bad mouth (1835), in African-American vernacular, "a curse, spell," translating an idiom found in African and West Indian languages. See bad (adj.) + mouth (n.). Related: Bad-mouthed; bad-mouthing.

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big-mouth (n.)

also bigmouth "person who talks too much," 1889, American English, from big + mouth (n.). Earlier as a type of fish and the name of a capable leader of the Oglala people in the 1860s.

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small-mouth (n.)

also smallmouth, 1880, of bass, short for small-mouth (black) bass (1878); from small (adj.) + mouth (n.). Small-mouthed (adj.) has been used of various fishes from 1610s.

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at bay (prep.)

late 14c., originally often at the bay; see bay (n.3). Figurative use, of human beings in difficulties, is from c. 1400. The expression reflects the former more widespread use of at. The earlier form of the phrase was at abai, used of hunted animals, "unable to escape," c. 1300, from French.

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