"room in a bath for sweating," 1756, from Latin sudatus, past participle of sudare "to sweat," from sudor "sweat" (see sweat (v.)) + -orium (see -ory).
Entries linking to sudatorium
sweat v.
Old English swætan "perspire," also "work hard," from Proto-Germanic *swaitjan "to sweat," from the source of sweat (n.). Compare Frisian swette, Dutch zweeten, Danish svede, German schwitzen. Meaning "to be worried, vexed" is recorded from c. 1400. Transitive sense is from late 14c. Related: Sweated; sweating. Sweating sickness was a sudden, often-fatal fever, accompanied by intense sweating, that struck England 1485 and returned periodically through mid-16c., described in the original citation (a chronicle from 1502) as "a grete deth and hasty."
-ory
adjective and noun suffix, "having to do with, characterized by, tending to, place for," from Middle English -orie, from Old North French -ory, -orie (Old French -oir, -oire), from Latin -orius, -oria, -orium.
Latin adjectives in -orius, according to "An Etymological Dictionary of the French Language," tended to "indicate a quality proper to the action accomplished by the agent; as oratorius from orator; laudatorius from laudator. The neuter of these adjectives was early employed as a substantive, and usually denoted the place of residence of the agent or the instrument that he uses; as praetorium from praetor; dormitorium from dormitor; auditorium, dolatorium.
"These newer words, already frequent under the Empire, became exceedingly numerous at a later time, especially in ecclesiastical and scholastic Latin; as purgatorium, refectorium, laboratorium, observatorium, &c." [transl. G.W. Kitchin, Oxford, 1878]