Etymology
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satiate (v.)

mid-15c., saciaten, "fill to repletion, satisfy, feed or nourish to the full," from Latin satiatus, past participle of satiare "fill full, satisfy," from satis "enough" (from PIE root *sa- "to satisfy"). By 1620s in a bad sense, "to fill beyond or over natural desire, weary by repletion." Related: Satiated; satiating.

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satiation (n.)

"act of satiating, a being or becoming satiated," 1630s, noun of action from satiate (v.).

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satiable (adj.)

"that can be satisfied," 1560s; see satiate + -able. Related: Satiability.

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insatiate (adj.)
"not to be satisfied," mid-15c., insaciate, from Latin insatiatus "unsatisfied," from in- "not, opposite of" (see in- (1)) + satiatus, past participle of satiare "to fill, satisfy" (see satiate).
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*sa- 
*sā-, Proto-Indo-European root meaning "to satisfy."

It forms all or part of: assets; hadron; sad; sate; satiate; satiety; satisfy; satire; saturate; saturation.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit a-sinvan "insatiable;" Greek hadros "thick, bulky;" Latin satis "enough, sufficient;" Old Church Slavonic sytu, Lithuanian sotus "satiated;" Old Irish saith "satiety," sathach "sated;" Old English sæd "sated, full, having had one's fill, weary of."
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sate (v.)

"to satisfy, fill full, surfeit," c. 1600, probably an alteration (by influence of Latin satiare "satiate") of Middle English saden "become weary or indifferent; satiate," from Old English sadian "to satiate, fill; be sated, get wearied" (see sad (adj.)), ultimately from PIE root *sa- "to satisfy." Related: Sated; sating.

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blase (adj.)
"bored from overindulgence, weary of the pleasures of life," 1819 [Byron], from French blasé, past participle of blaser "to satiate" (17c.), which is of unknown origin. Perhaps from Dutch blazen "to blow" (ultimately from PIE root *bhle- "to blow"), with a sense of "puffed up under the effects of drinking."
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stodgy (adj.)
1823, "thick, semi-solid," from stodge "to stuff, satiate" (1670s), of unknown origin, perhaps somehow imitative. Meaning "dull, heavy" developed by 1874 from use in reference to food (1841).
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saturate (v.)

1530s, "to satisfy, satiate, fill full" (senses now obsolete), from Latin saturatus, past participle of saturare "to fill full, sate, drench," from satur "sated, full" (from PIE root *sa- "to satisfy").

In chemistry, the meaning "to impregnate or unite with until no more can be received" is from 1680s; the general sense of "soak thoroughly, imbue (with)" is by 1756. The commercial sense of "oversupply" (a market, with a product) is by 1958. As a noun, "a saturated fat," by 1959. Related: Saturated; saturating.

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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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