word-forming element, from Latin -farius, -fariam "in (so many) parts," as in bifariam "in two parts or places, in two ways;" multifariam "in many places," an element of disputed origin. Watkins suggests it is from PIE *dwi-dhe- "making two," from roots *dwi- "two" + *dhe- "to put, set." It also has been derived from Latin fari "to say" (as in nefarious), but de Vaan writes that "the alleged semantic development to 'in n ways' is obscure," and he points to the suggestion of a PIE *-dho-, with cognates in Sanskrit dvidha (adv.) "twofold;" tridha "threefold."
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]