Etymology
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felicity (n.)

late 14c., "happiness; that which is a source of happiness," from Old French felicite "happiness" (14c.), from Latin felicitatem (nominative felicitas) "happiness, fertility," from felix (genitive felicis) "happy, fortunate, fruitful, fertile" (from suffixed form of PIE *dhe(i)- "to suck," with derivatives meaning "to suckle, produce, yield").

A relic of Rome's origins as an agricultural community: that which brings happiness is that which produces crops. Compare pauper (see poor (adj.)) "poor, not wealthy," literally "producing little." The meaning "skillful adroitness, admirable propriety" is attested from c. 1600.

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Felicia 
fem. proper name, from Latin felix (genitive felicis) "happy" (see felicity).
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Felix 
masc. proper name, from Latin felix "happy" (see felicity).
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felicitous (adj.)
1726, "blissful, very happy," from felicity + -ous. There is an isolated use of felicitously from 1530s.
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infelicity (n.)
late 14c., "unhappiness," from Latin infelicitas "bad luck, misfortune, unhappiness," from infelix (genitive infelicis) "unfruitful, barren; unfortunate, unhappy; causing misfortune, unlucky," from in- "not, opposite of" (see in- (1)) + felix "happy" (see felicity). Meaning "inappropriateness, unhappiness as to occasion" is from 1610s.
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felicitate (v.)
1620s, "to render happy" (obsolete); 1630s, "to reckon happy;" from Late Latin felicitatus, past participle of felicitare "to make happy," from Latin felicitas "fruitfulness, happiness," from felix "fruitful, fertile; lucky, happy" (see felicity). Meaning "congratulate, compliment upon a happy event" is from 1630s. Related: Felicitated; felicitating. Little-used alternative verb form felicify (1680s) yielded adjective felicific (1865).
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*dhe(i)- 

*dhē(i)-, Proto-Indo-European root meaning "to suck."

It forms all or part of: affiliate; affiliation; effeminate; effete; epithelium; fawn (n.) "young deer;" fecund; fellatio; Felicia; felicitate; felicity; Felix; female; feminine; femme; fennel; fenugreek; fetal; feticide; fetus; filial; filiation; filicide; filioque; fitz; infelicity.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit dhayati "sucks," dhayah "nourishing;" Greek thēlē "mother's breast, nipple," thēlys "female, fruitful;" Latin felare "to suck," femina "woman" ("she who suckles"), felix "happy, auspicious, fruitful," fetus "offspring, pregnancy;" fecundus "fruitful, fertile, productive; rich, abundant;" Old Church Slavonic dojiti "to suckle," dojilica "nurse," deti "child;" Lithuanian dėlė "leech;" Old Prussian dadan "milk;" Gothic daddjan "to suckle;" Old Swedish dia "suckle;" Old High German tila "female breast;" Old Irish denaim "I suck," dinu "lamb."

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Arcadian (adj.)
"ideally rustic or rural;" as a noun, "an idealized rustic," 1580s, from Greek Arkadia, a mountainous district landlocked in the Peloponnesus, regarded by the ancient Greeks as rude, impoverished, and inhospitable, but taken by 16c. European poets as an ideal region of rural felicity. See Arcadia.
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bliss (n.)
Old English blis, also bliðs "bliss, merriment, happiness, grace, favor," from Proto-Germanic *blithsjo (source also of Old Saxon blidsea, blizza), from *blithiz "gentle, kind" (see blithe) + *-tjo noun suffix. Originally mostly of earthly happiness, in later Old English of spiritual joy, perfect felicity, the joy of heaven; influenced by association with unrelated bless.
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ego (n.)

by 1707, in metaphysics, "the self; that which feels, acts, or thinks," from Latin ego "I" (cognate with Old English ic; see I); its use is implied in egoity.

They that have pleaded against Propriety, and would have all things common in this World, have forgotten that there is a Propriety, in our present Egoity, and Natural Constitution, which rendereth some accidental Propriety necessary to us (etc.) ["The Practical Works of the Late Reverend and Pious Mr. Richard Baxter," London, 1707]

Psychoanalytic (Freudian) sense is from 1894; sense of "conceit" is 1891. Ego-trip first recorded 1969, from trip (n.). Related: egoical.

In the book of Egoism it is written, Possession without obligation to the object possessed approaches felicity. [George Meredith, "The Egoist," 1879]
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