Etymology
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bog (n.)

"wet, soft, spongy ground with soil chiefly composed of decaying vegetable matter," c. 1500, from Gaelic and Irish bogach "bog," from adjective bog "soft, moist," from Proto-Celtic *buggo- "flexible," from PIE root *bheug- "to bend." Bog-trotter applied to the wild Irish from 1670s.

A bog is characterized by vegetation, decayed and decaying, and a treacherous softness. A quagmire or quag is the worst kind of bog or slough; it has depths of mud, and perhaps a shaking surface. A slough is a place of deep mud and perhaps water, but generally no vegetation. [Century Dictionary]
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bog (v.)
"to sink (something or someone) in a bog," c. 1600, from bog (n.). Intransitive use "to sink or stick in a bog" is from c. 1800; with down (adv.) by 1848, American English. Related: Bogged; bogging.
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boggy (adj.)
"swampy, like a bog; full of bogs," 1580s, from bog (n.) + -y (2). Related: Bogginess.
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*bheug- 
Proto-Indo-European root meaning "to bend," with derivatives referring to bent, pliable, or curved objects.

It forms all or part of: akimbo; bagel; bight; bog; bow (v.) "to bend the body;" bow (n.1) "weapon for shooting arrows;" bow (n.2) "front of a ship;" bowsprit; buxom; elbow.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit bhujati "bends, thrusts aside;" Old English bugan, German biegen, Gothic biugan "to bend;" Old High German boug, Old English beag "a ring."
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mire (n.)

"deep mud, bog, marsh, swampland," c. 1300, from a Scandinavian source such as Old Norse myrr "bog, swamp," from Proto-Germanic *miuzja- (source of Old English mos "bog, marsh"), from PIE *meus- "damp" (see moss).

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bogey (n.1)
World War II aviator slang for "unidentified aircraft, presumably hostile," probably ultimately from bogge, a variant of Middle English bugge "a frightening specter" (see bug (n.)).

Thus it shares ancestry with many dialect words for "ghost, specter," such as bog/bogge (attested 16c.-17c.), bogeyman (16c.), boggart "specter that haunts a gloomy spot" (c. 1570, in Westmoreland, Lancashire, Cheshire, and Yorkshire). The earliest modern form appears to be Scottish bogle "ghost," attested from c. 1500 and popularized c. 1800 in English literature by Scott, Burns, etc.
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soggy (adj.)
1722, perhaps from dialectal sog "bog, swamp," or the verb sog "become soaked," both of unknown origin, + -y (2). Related: Soggily; sogginess.
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quag (n.)

"marshy spot," 1580s, a variant of Middle English quabbe "a marsh, bog, shaking marshy soil," from Old English *cwabba "shake, tremble" (like something soft and flabby). Related: Quaggy.

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muskeg (n.)

kind of North American bog, 1865, from Cree (Algonquian) /maske:k/ "swamp;" compare Abenaki mskag, Munsee Delaware maskeekw, and Ojibwa mshkiig, which probably is an element in the place names Muskego (Wisconsin) and Muskegon (Michigan).

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moss (n.)

the meanings "mass of small, cryptogamous, herbaceous plants growing together" and "bog, peat-bog" are the same word: Old English meos "moss plant" and mos "bog;" both are from Proto-Germanic *musan (source also of Old High German mios, Danish mos, German Moos), also in part from Old Norse mosi "moss, bog," and Medieval Latin mossa "moss," from the same Germanic source.

These are from PIE *meus- "damp," with derivatives referring to swamps and swamp vegetation (source also of Latin muscus "moss," Lithuanian mūsai "mold, mildew," Old Church Slavonic muchu "moss"). The Germanic languages have the word in both senses, which is natural because moss is the characteristic plant of boggy places. It is impossible to say which sense is original. The proverb that a rolling stone gathers no moss is suggested from 14c.:

Selden Moseþ þe Marbelston þat men ofte treden. ["Piers Plowman," 1362]

Moss-agate "agate stone with moss-like dendrite forms (caused by metallic oxides)" is from 1790. Scott (1805) revived 17c. moss-trooper "freebooter infesting Scottish border marshes" (compare bog-trotter).

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