Etymology
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introit (n.)
in liturgics, "an antiphon sung as the priest approaches the altar to celebrate mass," late 15c., from Old French introite "(liturgical) introit; entrance" (14c.), from Latin (antiphona ad) introitum, from introitus "a going in, an entering, entrance; a beginning, prelude," past participle of introire "to enter," from intro- "on the inside, within" (see intro-) + ire "to go" (from PIE root *ei- "to go").
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porch (n.)

c. 1300, porche, "covered entrance; roofed structure, usually open on the front and sides, before an entrance to a building," from Old French porche "porch, vestibule," from Latin porticus "covered gallery, covered walk between columns, arcade, portico, porch," from porta "city gate, gate; door, entrance," from PIE root *per- (2) "to lead, pass over."

The Latin word was borrowed directly into Old English as portic. Especially (late 14c.) "a covered walk or colonnade on the front or side of a building." In U.S., used by 1832 for what the British call a veranda.

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poor-box (n.)

"box for receiving contributions of money for the poor," generally at the entrance of a church, 1620s, from poor (n.) + box (n.1).

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entry (n.)
c. 1300, "act or fact of physically entering; place of entrance, means of entering a building; opportunity or right of entering; initiation or beginning of an action;" from Old French entree "entry, entrance" (12c.), noun use of fem. past participle of entrer "to enter" (see enter). Meaning "that which is entered or set down (in a book, list, etc.)" is from c. 1500.
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Jephthah 
biblical judge of Israel, from Greek Iephthae, from Hebrew Yiphtah, literally "God opens," imperfective of pathah "he opened" (compare pethah "opening, entrance").
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vestibule (n.)
1620s, "a porch," later "antechamber, lobby" (1730), from French vestible, from Latin vestibulum "forecourt, entrance," of unknown origin. In reference to the ear part from 1728.
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access (n.)
Origin and meaning of access
early 14c., "an attack of fever," from Old French acces "onslaught, attack; onset (of an illness)" (14c.), from Latin accessus "a coming to, an approach; way of approach, entrance," noun use of past participle of accedere "to approach," from assimilated form of ad "to" (see ad-) + cedere "go, move, withdraw" (from PIE root *ked- "to go, yield"). English sense of "an entrance" (c. 1600) is directly from Latin. Meaning "habit or power of getting into the presence of (someone or something)" is from late 14c.
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pylon (n.)

1823, "gateway to an Egyptian temple," from Greek pylon "gateway," from pylē "gate, wing of a pair of double gates; an entrance, entrance into a country; mountain pass; narrow strait of water," a word of unknown etymology, perhaps a foreign technical term. The usual word for "door" in PIE in Greek took the form thyra (see thyroid). Meaning "tower for guiding aviators" (1909) led to that of "steel tower for high-tension wires" (1923).

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lobby (n.)
1550s, "cloister, covered walk," from Medieval Latin laubia, lobia "covered walk in a monastery," from a Germanic source (compare Old High German louba "hall, roof;" see lodge (n.)).

Meaning "large entrance hall in a public building" is from 1590s; in reference to the House of Commons from 1630s. Political sense of "those who seek to influence legislation" is attested by 1790s in American English, in reference to the custom of influence-seekers gathering in the large entrance-halls outside legislative chambers.
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ab initio 
c. 1600, Latin, literally "from the beginning," from ab "from" (see ab-) + ablative of initium "entrance, beginning," which is from or related to the verb inire "to go into, enter upon, begin" (see initial).
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