Infirmary

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late Middle English: from medieval Latin infirmaria, from Latin infirmus (see infirm).

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From Medieval Latin infirmaria, from Latin infirmus.

etymonline

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infirmary (n.)

mid-15c., "sick bay in a monastery," formerly also enfermerie, also firmary, fermery, from Old French enfermerie "hospital" and directly from Medieval Latin infirmaria "a place for the infirm," from Latin infirmus "weak, frail," (see infirm). According to OED, the common name for a public hospital in 18c. England.