Etymology
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Words related to affiliate

ad- 

word-forming element expressing direction toward or in addition to, from Latin ad "to, toward" in space or time; "with regard to, in relation to," as a prefix, sometimes merely emphatic, from PIE root *ad- "to, near, at."

Simplified to a- before sc-, sp- and st-; modified to ac- before many consonants and then re-spelled af-, ag-, al-, etc., in conformity with the following consonant (as in affection, aggression). Also compare ap- (1).

In Old French, reduced to a- in all cases (an evolution already underway in Merovingian Latin), but French refashioned its written forms on the Latin model in 14c., and English did likewise 15c. in words it had picked up from Old French. In many cases pronunciation followed the shift.

Over-correction at the end of the Middle Ages in French and then English "restored" the -d- or a doubled consonant to some words that never had it (accursed, afford). The process went further in England than in France (where the vernacular sometimes resisted the pedantic), resulting in English adjourn, advance, address, advertisement (Modern French ajourner, avancer, adresser, avertissement). In modern word-formation sometimes ad- and ab- are regarded as opposites, but this was not in classical Latin.

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filial (adj.)
late 14c., from Late Latin filialis "of a son or daughter," from Latin filius "son," filia "daughter," possibly from a suffixed form of PIE root *bheue- "to be, exist, grow" (see be), but Watkins finds it "more likely" assimilated from *felios, originally "a suckling," a suffixed form of PIE root *dhe(i)- "to suck, suckle."
associate (n.)
1530s, "a partner in interest or business," from associate (adj.). Meaning "one admitted to a subordinate degree of membership" is from 1812.
affiliation (n.)

1751, "adoption," from French affiliation, from Medieval Latin affiliationem (nominative affiliatio), noun of action from past-participle stem of Latin affiliare "to adopt as a son," from ad "to" (see ad-) + filius "son" (see filial).

The figurative sense of "adoption by a society," in reference to a local chapter or branch, is recorded by 1799 (the verb affiliate in a related sense is from 1761). The meaning "friendship, relationship, association" is by 1852.

*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."