Etymology
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fugue (n.)

type of musical composition, 1590s, fuge, from Italian fuga, literally "flight," also "ardor," from Latin fuga "a running away, act of fleeing," from fugere "to flee" (see fugitive (adj.)). Current English spelling (1660s) is from the French version of the Italian word.

A Fugue is a composition founded upon one subject, announced at first in one part alone, and subsequently imitated by all the other parts in turn, according to certain general principles to be hereafter explained. The name is derived from the Latin word fuga, a flight, from the idea that one part starts on its course alone, and that those which enter later are pursuing it. ["Fugue," Ebenezer Prout, 1891]
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flea (n.)

Old English flea "flea," from Proto-Germanic *flauhaz (source also of Old Norse flo, Middle Dutch vlo, German Floh), perhaps related to Old English fleon "to flee," with a notion of "the jumping parasite," but more likely from PIE *plou- "flea" (source also of Latin pulex, Greek psylla; see Pulex).

Chaucer's plural is fleen. Flea-bag is from 1839 as low slang for "a bed;" by 1942 in British slang as "a dog." Flea-collar is from 1953. Flea-pit (1937) is an old colloquial name for a movie-house, or, as OED puts it, "an allegedly verminous place of public assembly." Flea-circus is from 1886. 

"A man named 'Mueller' put on the first trained-flea circus in America at the old Stone and Austin museum in Boston nearly forty years ago. Another German named 'Auvershleg' had the first traveling flea circus in this country thirty years ago. In addition to fairs and museums, I get as high as $25 for a private exhibition." ["Professor" William Heckler, quoted in Popular Mechanics, February 1928. Printed at the top of his programs were "Every action is visible to the naked eye" and "No danger of desertion."]
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shake (v.)
Old English sceacan "move (something) quickly to and fro, brandish; move the body or a part of it rapidly back and forth;" also "go, glide, hasten, flee, depart" (related to sceacdom "flight"); of persons or parts of the body, "to tremble" especially from fever, cold, fear" (class VI strong verb; past tense scoc, past participle scacen), from Proto-Germanic *skakanan (source also of Old Norse, Swedish skaka, Danish skage "to shift, turn, veer"). No certain cognates outside Germanic, but some suggest a possible connection to Sanskrit khaj "to agitate, churn, stir about," Old Church Slavonic skoku "a leap, bound," Welsh ysgogi "move."

Of the earth in earthquakes, c. 1300. Meaning "seize and shake (someone or something else)" is from early 14c. In reference to mixing ingredients, etc., by shaking a container from late 14c. Meaning "to rid oneself of by abrupt twists" is from c. 1200, also in Middle English in reference to evading responsibility, etc. Meaning "weaken, impair" is from late 14c., on notion of "make unstable."

To shake hands dates from 1530s. Shake a (loose) leg "hurry up" first recorded 1904; shake a heel (sometimes foot) was an old way to say "to dance" (1660s); to shake (one's) elbow (1620s) meant "to gamble at dice." Phrase more _____ than you can shake a stick at is attested from 1818, American English. To shake (one's) head as a sign of disapproval is recorded from c. 1300.
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