Etymology
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propitiation (n.)

late 14c., propiciacioun, "atonement, expiation," from Late Latin propitiationem (nominative propitiatio) "an atonement," noun of action from past-participle stem of Latin propitiare "appease, propitiate," from propitius "favorable, gracious, kind, well-disposed." The current explanation of this (as of de Vaan) is that it represents *propre-tio-, from PIE *propro "on and on, ever further" (source also of Sanskrit pra-pra "on and on," Greek pro-pro "before, on and on"), from root *per- (1) "forward," hence "in front of, toward, near." It is thus related to Latin prope "near."

Earliest recorded form of the word in English is propitiatorium "the mercy seat, place of atonement" (c. 1200), translating Greek hilasterion. The meaning "that which propitiates or appeases, a propitiatory gift or offering" is from 1550s.

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propitiate (v.)

"appease and render favorable," 1580s, a back-formation from propitiation and in part from propitiate (adj.), from Latin propitiatus, past participle of propitiare "appease, propitiate." Related: Propitiated; propitiating; propitiatingly; propitiable (1550s).

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propitiatory (adj.)

"having the power or intent to effect propitiation," 1550s, from Late Latin propitiatorius "atoning, reconciling," from propitiatus, past participle of propitiare "appease, propitiate" (see propitiation). Earlier in English as a noun, propiciatorie, c. 1300, "the mercy seat, lid or cover of the ark of the covenant," from Late Latin propitiatorium (translating Greek hilasterion in Bible); noun use of neuter singular of propitiatorius.

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propitious (adj.)

mid-15c., propicious, "inclined to grant favor, disposed to pardon or forgive," from Anglo-French propicius, Old French propicius "gracious, favorable, useful" (12c., Modern French propice) and directly from Latin propitius "favorable, kind, gracious, well-disposed" (see propitiation). The earlier English form was propice, from Old French propice. The meaning "boding well" is from 1580s; that of "affording favorable conditions or circumstances" is by c. 1600. Related: Propitiously; propitiousness.

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*pet- 

Also petə-, Proto-Indo-European root meaning "to rush, to fly." 

It forms all or part of: accipiter; appetence; appetite; apterous; apteryx; archaeopteryx; asymptote; centripetal; Coleoptera; compete; competent; eurypterid; feather; helicopter; hippopotamus; Hymenoptera; impetigo; impetuous; impetus; iopterous; Lepidoptera; ornithopter; panache; panne; pen (n.1) "writing implement;" pennon; peripeteia; perpetual; perpetuity; petition; petulance; petulant; pin; pinion; pinnacle; pinnate; pinniped; potamo-; potamology; propitiation; propitious; ptero-; pterodactyl; ptomaine; ptosis; repeat; symptom.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit pattram "wing, feather, leaf," patara- "flying, fleeting;" Hittite pittar "wing;" Greek piptein "to fall," potamos "river, rushing water," pteron, pteryx "feather, wing," ptilon "soft feathers, down, plume;" Latin petere "to attack, assail; seek, strive after; ask for, beg; demand, require," penna "feather, wing;" Old Norse fjöðr, Old English feðer "feather;" Old Church Slavonic pero "feather;" Old Welsh eterin "bird."

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pleasance (n.)

mid-14c., plesaunce, "the gratification or propitiation of God or some other deity;" late 14c., "satisfaction, enjoyment, delight; moral, spiritual, or intellectual satisfaction," from Old French plaisance "pleasure, delight, enjoyment," from plaisant "pleasant, pleasing, agreeable" (see pleasant).

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atonement (n.)
1510s, "condition of being at one (with others)," a sense now obsolete, from atone + -ment. Theological meaning "reconciliation" (of man with God through the life, passion, and death of Christ) is from 1520s; that of "satisfaction or reparation for wrong or injury, propitiation of an offended party" is from 1610s.
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sacrifice (n.)
Origin and meaning of sacrifice

late 13c., "the offering of something (especially a life) to a deity as an act of propitiation, homage, etc.;" mid-14c., "that which is offered (to a deity) in sacrifice," from Old French sacrifise "sacrifice, offering" (12c.), from Latin sacrificium, from sacrificus "performing priestly functions or sacrifices," etymologically "a making sacred," from sacra "sacred rites" (properly neuter plural of sacer "sacred;" see sacred) + combining form of facere "to make, to do" (from PIE root *dhe- "to set, put").

Originally especially of Christ's propitiatory offering of himself for the world. Latin sacrificium is glossed in Old English by ansegdniss. The general sense of "act of giving up a desirable thing for a higher object or to a more pressing claim," also "something given up for the sake of another" is recorded from 1590s. Baseball sense of "hit made by the batter not to get himself to base but to enable another player to advance" is by 1880.

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