Etymology
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hospital (n.)

mid-13c., "shelter for the needy," from Old French hospital, ospital "hostel, shelter, lodging" (Modern French hôpital), from Late Latin hospitale "guest-house, inn," noun use of neuter of Latin adjective hospitalis "of a guest or host" (as a noun, "a guest; the duties of hospitality"), from hospes (genitive hospitis) "guest; host;" see host (n.1).

The sense of "charitable institution to house and maintain the needy" in English is from early 15c.; the meaning "institution for sick or wounded people" is recorded by 1540s. The same word, contracted, is hostel and hotel. The sense shift in Latin from duties to buildings might have been via the common term cubiculum hospitalis "guest-chamber." The Latin adjective use continued in Old French, where ospital also could mean "hospitable" and ospitalite could mean "hospital."

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hospitaller (n.)
early 14c., from Old French ospitalier "one devoted to the care of the sick and needy in hospitals;" see hospital.
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hospitalize (v.)
1873, from hospital + -ize. "Freq[uently] commented on as an unhappy formation" [OED]. As verbs, hospitate is recorded from 1620s as "to lodge or entertain, receive with hospitality" but is rare; hospitize is from 1895. Related: hospitalized; hospitalizing.
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Spitalfields 
district east of London, famed for the work of refugee Huguenot weavers who took up residence there, from St. Mary Spital, from spital, a Middle English shortened form of hospital, sometimes also spittle, hence spittle-man "one who lives in a hospital."
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hotel (n.)
1640s, "public official residence; large private residence," from French hôtel "a mansion, palace, large house," from Old French ostel, hostel "a lodging" (see hostel). Modern sense of "an inn of the better sort" is first recorded 1765. The same word as hospital.
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hostel (n.)
early 13c., "inn, house of entertainment," from Old French ostel, hostel "house, home, dwelling; inn, lodgings, shelter" (11c., Modern French hôtel), from Medieval Latin hospitale "inn; large house" (see hospital). Obsolete after 16c., revived 1808, along with hostelry by Sir Walter Scott. Youth hostel is recorded by 1931.
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hostler (n.)
formerly also hosteler, late 14c., "one who tends to horses at an inn," also, occasionally, "innkeeper," from Anglo-French hostiler, Old French ostelier, hostelier "innkeeper; steward in a monastery" (12c., Modern French hôtelier), from Medieval Latin hostilarius "the monk who entertains guests at a monastery," from hospitale "inn" (see hospital). Compare ostler.
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*ghos-ti- 

Proto-Indo-European root meaning "stranger, guest, host," properly "someone with whom one has reciprocal duties of hospitality," representing "a mutual exchange relationship highly important to ancient Indo-European society" [Watkins]. But as strangers are potential enemies as well as guests, the word has a forked path.

The word ghos-ti- was thus the central expression of the guest-host relationship, a mutual exchange relationship highly important to ancient Indo-European society. A guest-friendship was a bond of trust between two people that was accompanied by ritualized gift-giving and created an obligation of mutual hospitality and friendship that, once established, could continue in perpetuity and be renewed years later by the same parties or their descendants. [Calvert Watkins, "American Heritage Dictionary of Indo-European Roots"]

It forms all or part of: Euxine; guest; hospice; hospitable; hospital; hospitality; hospodar; host (n.1) "person who receives guests;" host (n.2) "multitude;" hostage; hostel; hostile; hostility; hostler; hotel; Xenia; xeno-; xenon.

It is the hypothetical source of/evidence for its existence is provided by: Greek xenos "guest, host, stranger;" Latin hostis, in earlier use "a stranger," in classical use "an enemy," hospes "host;" Old Church Slavonic gosti "guest, friend," gospodi "lord, master;" Old English gæst, "chance comer, a stranger."

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hospitality (n.)
late 14c., "act of being hospitable," from Old French ospitalité "hospitality; hospital," from Latin hospitalitem (nominative hospitalitas) "friendliness to guests," from hospes (genitive hospitis) "guest; host" (see host (n.1)).
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outpatient (n.)

also out-patient, 1715, "patient not residing at a hospital, person who is treated at a hospital but not admitted," from out- + patient (n.). The adjective is recorded by 1879.

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