Etymology
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speech (n.)

Old English spæc "act of speaking; power of speaking; manner of speaking; statement, discourse, narrative, formal utterance; language," variant of spræc, from Proto-Germanic *sprek-, *spek- (source also of Danish sprog, Old Saxon spraca, Old Frisian spreke, Dutch spraak, Old High German sprahha, German Sprache "speech;" see speak (v.))

The spr- forms were extinct in English by 1200. Meaning "address delivered to an audience" first recorded 1580s.

And I honor the man who is willing to sink
Half his present repute for the freedom to think,
And, when he has thought, be his cause strong or weak,
Will risk t' other half for the freedom to speak,
Caring naught for what vengeance the mob has in store,
Let that mob be the upper ten thousand or lower.
[James Russell Lowell, "A Fable for Critics," 1848]
But when men have realized that time has upset many fighting faiths, they may come to believe even more than they believe the very foundations of their own conduct that the ultimate good desired is better reached by free trade in ideas — that the best test of truth is the power of the thought to get itself accepted in the competition of the market, and that truth is the only ground upon which their wishes safely can be carried out. That, at any rate, is the theory of our Constitution. It is an experiment, as all life is an experiment. ... I think that we should be eternally vigilant against attempts to check the expression of opinions that we loathe and believe to be fraught with death, unless they so imminently threaten immediate interference with the lawful and pressing purposes of the law that an immediate check is required to save the country. [Oliver Wendell Holmes Jr., dissent to "Abrams v. United States," 1919]
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figure (n.)

c. 1200, "numeral;" mid-13c., "visible appearance of a person;" late 14c., "visible and tangible form of anything," from Old French figure "shape, body; form of a word; figure of speech; symbol, allegory" (10c), from Latin figura "a shape, form, figure; quality, kind, style; figure of speech," in Late Latin "a sketch, drawing" (from PIE root *dheigh- "to form, build").

Philosophical and scientific senses are from use of Latin figura to translate Greek skhema. Meaning "lines forming a shape" is from mid-14c. From mid-14c. as "human body as represented by art;" late 15c. as "a body, the human form as a whole."  From late 14c. as "a cut or diagram inserted in text."

The rhetorical use of figure, "peculiar use of words giving meaning different from usual," dates to late 14c.; hence figure of speech (1550s). Figure-skating is from 1835, so called for the circular patterns skaters formerly made on the ice to demonstrate control; they were dropped from international competition in 1990, but the name remains. Figure eight as a shape was originally figure of eight (c. 1600).

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figure (v.)
late 14c., "to represent" (in painting or sculpture), "make a likeness," also "to have a certain shape or appearance," from Old French figurer, from Latin figurare "to form, shape" (from PIE root *dheigh- "to form, build"). Meaning "to shape into" is c. 1400; from mid-15c. as "to cover or adorn with figures." Meaning "to picture in the mind" is from c. 1600. Intransitive meaning "make an appearance, make a figure, show oneself" is from c. 1600. Meaning "work out a sum" (by means of arithmetical figures) is from 1833, American English; hence colloquial sense "to calculate upon, expect" (1837). Related: Figured; figuring.
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part of speech (n.)

"a word viewed as a constituent member of a sentence," c. 1500, translating Latin pars orationis (see parse). The parts of speech are: Noun, adjective, pronoun, verb, adverb, preposition, conjunction, and interjection. Sometimes article and participle are counted among them.

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shadow-figure (n.)
"silhouette," 1851, from shadow (n.) + figure (n.).
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trope (n.)
1530s, from Latin tropus "a figure of speech," from Greek tropos "a turn, direction, course, way; manner, fashion," in rhetoric, "turn or figure of speech," related to trope "a turning" and trepein "to turn," from PIE root *trep- "to turn." Technically, in rhetoric, "a figure of speech which consists in the use of a word or phrase in a sense other than that which is proper to it" [OED], "as when we call a stupid fellow an ass, or a shrewd man a fox" [Century Dictionary].
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figurative (adj.)
late 14c., "emblematical," from Old French figuratif "metaphorical," from Late Latin figurativus "figurative" (of speech), from figurat-, past participle stem of Latin figurare "to form, shape," from figura "a shape, form, figure" (from PIE root *dheigh- "to form, build"). Of speech, language, etc., "allegorical, metaphoric, involving figures of speech," from late 14c. Related: Figuratively.
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personification (n.)

"figure of speech or artistic representation in which something inanimate or abstract takes the form of a person," 1755, noun of action from personify. Sense of "embodiment of a quality in a person" is attested from 1807.

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burr (n.)
"rough sound of the letter -r-" (especially that common in Northumberland), 1760, later extended to "northern accented speech" in general. Possibly the sound of the word is imitative of the speech peculiarity itself, or it was adapted from one of the senses of bur (q.v.), perhaps from the phrase to have a bur in (one's) throat (late 14c.), which was a figure of speech for "feel a choking sensation, huskiness." OED says the Scottish -r- is a lingual trill, not a true burr.
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scheme (n.)

1550s, "figure of speech" (a sense now obsolete), from Medieval Latin schema "a shape, a figure, a form, appearance; figure of speech; posture in dancing," from Greek skhēma (genitive skhematos) "figure, appearance, the nature of a thing," which is related to skhein "to get," and ekhein "to have, hold; be in a given state or condition" (from PIE root *segh- "to hold").

By 1610s as "linear representation showing relative positions pf the parts or elements of a system" (especially in astrology). The sense "program of action" is by 1640s, also "outline, draft of a book, etc."

The meaning "plan of action devised to attain some end" is by 1718, and unfavorable overtones (selfishness, deviousness) began to creep in to the word after that time. Meaning "complex unity of coordinated component elements, a connected and orderly arrangement" is from 1736. In prosody by 1838. Color scheme is by 1890 (in Milton Bradley Co.'s "Color in the School-Room"); earlier scheme of colour (by 1877).

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