Etymology
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assuage (v.)
"to soften," usually figuratively, of pain, anger, passion, grief, etc., c. 1300, from Anglo-French assuager, Old French assoagier "soften, moderate, alleviate, calm, soothe, pacify," from Vulgar Latin *adsuaviare, from Latin ad "to" (see ad-) + suavis "sweet, agreeable," from PIE root *swād- "sweet, pleasant" (see sweet (adj.)). For sound development in French, compare deluge from Latin diluvium, abridge from abbreviare. Related: Assuaged; assuaging.
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abridge (v.)
Origin and meaning of abridge
c. 1300, abreggen, "make shorter, shorten, condense," from Old French abregier, abrigier "abridge, diminish, shorten" (12c., Modern French abréger), from Late Latin abbreviare "make short," from Latin ad "to" (see ad-) + breviare "shorten," from brevis "short, low, little, shallow" (from PIE root *mregh-u- "short").

Abbreviate is the same word directly from Latin. The sound development that turned Latin -vi- to French -dg- is paralleled in assuage (from assuavidare) and deluge (from diluvium). Of writing, "shorten by omission," late 14c. Related: Abridged; abridging.
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placatory (adj.)

"conciliatory, intended to placate or appease," 1630s, from Latin placatorius "pertaining to appeasing," from placat-, past-participle stem of placare "to calm, appease, quiet, soothe, assuage," causative of placere "to please" (see please).

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placation (n.)

"act of pleasing, pacifying, or conciliating," 1580s, from French placation (16c.), from Latin placationem (nominative placatio) "an appeasing, pacifying, quieting," noun of action from past-participle stem of placare "to calm, appease, quiet, soothe, assuage," causative of placere "to please" (see please).

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placate (v.)

"appease or pacify," 1670s, a back-formation from placation or else from Latin placatus "soothed, quiet, gentle, calm, peaceful," past participle of placare "to calm, appease, quiet, soothe, assuage," causative of placere "to please" (see please). Related: Placated; placating; placatingly.

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placable (adj.)

c. 1500, "pleasing, agreeable" (a sense now obsolete), from Old French placable "forgiving, conciliatory" and directly from Latin placabilis "easily appeased or pacified," from placare "to calm, appease, quiet, soothe, assuage," causative of placere "to please" (see please). From 1580s as "capable of being pleased or pacified, easily appeased, willing to forgive." Related: Placably; placability.

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soothe (v.)
Old English soðian "show to be true," from soð "true" (see sooth). Sense of "quiet, comfort, mollify" is first recorded 1690s, via notion of "to assuage one by asserting that what he says is true" (i.e. to be a yes-man), a sense attested from 1560s (and compare Old English gesoð "a parasite, flatterer"). Meaning "reduce the intensity" (of a pain, etc.) is from 1711. Related: Soothed; soothing.
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supplication (n.)
late 14c., from Old French suplicacion "humble request," from Latin supplicationem (nominative supplicatio) "a public prayer, thanksgiving day," noun of action from past participle stem of supplicare "to beg humbly" (in Old Latin as sub vos placo, "I entreat you"), from sub "under" (see sub-) + placare "to calm, appease, quiet, soothe, assuage," causative of placere "to please" (see please). In ancient Rome, a religious solemnity, especially in thanksgiving for a victory or in times of public danger.
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supple (adj.)
c. 1300, "soft, tender," from Old French souple, sople "pliant, flexible; humble, submissive" (12c.), from Gallo-Roman *supples, from Latin supplex "submissive, humbly begging, beseeching, kneeling in entreaty, suppliant," literally "bending, kneeling down," perhaps an altered form of *supplacos "humbly pleading, appeasing," from sub "under" (see sub-) + placare "to calm, appease, quiet, soothe, assuage," causative of placere "to please" (see please, and compare supplication).

Meaning "pliant" is from late 14c.; figurative sense of "artfully obsequious, capable of adapting oneself to the wishes and opinions of others" is from c. 1600. Supple-chapped (c. 1600) was used of a flatterer. Related: Suppleness.
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satisfy (v.)

early 15c., satisfien, "do penance," also "appease, assuage;" also "fulfill (a desire), comply with (a command), satiate (a hunger or thirst)," from Old French satisfiier "pay, repay, make reparation" (14c., Modern French satisfaire), from Latin satisfacere "discharge fully, comply with, make amends," literally "do enough."

This is from satis "enough" (from PIE root *sa- "to satisfy") + facere "to make, do, perform" (from PIE root *dhe- "to set, put").

From mid-15c. as "make amends, pay damages."  The meaning "cause to have enough, supply the needs of" is by c. 1500. Of feelings, "meet or fulfill the wish, desire, or expectation of," late 15c. (Caxton). From 1510s as "assure or free from doubt or uncertainty, furnish with sufficient proof." The intransitive sense of "give satisfaction or contentment" is from c. 1600.

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