Etymology
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rapport (n.)

1660s, "reference, relation, relationship," from French rapport "bearing, yield, produce; harmony, agreement, intercourse," back-formation from rapporter "bring back; refer to," from re- "again" (see re-) + apporter "to bring," from Latin apportare "to bring," from ad "to" (see ad-) + portare "to carry" (from PIE root *per- (2) "to lead, pass over"). The Old French noun was report "pronouncement, judgment," from reporter "to tell, relate" (see report (v.)).

Especially "harmonious relation; accord or agreement; analogy." Psychological meaning "intense harmonious accord," as between therapist and patient, is first attested 1894, though the word had been used in a similar sense with reference to mesmerism from 1845 (in Poe). Also see report (n.).

Formerly often used as a French word, and in en rapport. Johnson [1755] frowns on the word and credits its use in English to Sir William Temple, notorious naturalizer of French terms, who did use it but was not the first to do so. Fowler writes that it was "formerly common enough to be regarded and pronounced as English," but in his time [1926] the word seemed to have reacquired its Frenchness and was thus dispensable.

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rapportage (n.)

"the describing of events in writing," 1898, a French word in English, from French rapportage, literally "tale-telling," from rapporter "to bring back; refer to" (see rapport).

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*ad- 
Proto-Indo-European root meaning "to, near, at."

It forms all or part of: abate; ado; ad-; ad hoc; ad lib; adage; adagio; add; adjective; adore; adorn; adult; adverb; advertise; agree; aid; alloy; ally; amontillado; amount; assure; at; atone; exaggerate; paramount; rapport; twit.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit adhi "near;" Latin ad "to, toward;" Old English æt.
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*per- (2)

Proto-Indo-European root meaning "to lead, pass over." A verbal root associated with *per- (1), which forms prepositions and preverbs with the basic meaning "forward, through; in front of, before," etc.

It forms all or part of: aporia; asportation; comport; deport; disport; emporium; Euphrates; export; fare; farewell; fartlek; Ferdinand; fere; fern; ferry; firth; fjord; ford; Fuhrer; gaberdine; import; important; importune; opportune; opportunity; passport; porch; pore (n.) "minute opening;" port (n.1) "harbor;" port (n.2) "gateway, entrance;" port (n.3) "bearing, mien;" port (v.) "to carry;" portable; portage; portal; portcullis; porter (n.1) "person who carries;" porter (n.2) "doorkeeper, janitor;" portfolio; portico; portiere; purport; practical; rapport; report; sport; support; transport; warfare; wayfarer; welfare.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit parayati "carries over;" Greek poros "journey, passage, way," peirein "to pierce, pass through, run through;" Latin portare "to carry," porta "gate, door," portus "port, harbor," originally "entrance, passage," peritus "experienced;" Avestan peretush "passage, ford, bridge;" Armenian hordan "go forward;" Old Welsh rit, Welsh rhyd "ford;" Old Church Slavonic pariti "to fly;" Old English faran "to go, journey," Old Norse fjörðr "inlet, estuary."

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report (n.)

late 14c., "an account brought by one person to another; rumor, gossip," from Old French report "pronouncement, judgment" (Modern French rapport), from reporter "to tell, relate" (see report (v.)).

By early 15c. as "informative statement by a reputable source, authoritative account." In law, "formal account of a case argued and determined in court," by 1610s. The meaning "formal statement of results of an investigation" is attested by 1660s; sense of "teacher's official statement of a pupil's work and behavior" is from 1873 (report card in the school sense is attested by 1913, American English). The meaning "resounding noise, sound of an explosion or of the discharge of a firearm" is from 1580s.  

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connect (v.)

mid-15c., "to join, bind, or fasten together," from Latin conectere "join together," from assimilated form of com "together" (see con-) + nectere "to bind, tie" (from PIE root *ned- "to bind, tie").

Displaced 16c. by connex (1540s), from French connexer, from Latin *connexare, a supposed frequentative of conectere (past participle stem connex-). Connect was re-established from 1670s.

A similar change took place in French, where connexer was superseded by connecter. Meaning "to establish a relationship" (with) is from 1881. Slang meaning "get in touch with" is attested by 1926, from telephone connections. Meaning "awaken meaningful emotions, establish rapport" is from 1942. Of a hit or blow, "to reach the target," from c. 1920. Related: Connected; connecting; connectedness.

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rapporteur (n.)

"person who prepares an account of the proceedings of a committee, etc., for a higher body," 1791, from French rapporteur "tell-tale, gossip; reporter," from rapporter "bring back; refer to," Old French reporter (see report (v.)). The word was earlier in English in the now-obsolete sense of "a reporter" (c. 1500).

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