word-forming element, in English meaning usually "out of, from," but also "upwards, completely, deprive of, without," and "former;" from Latin ex "out of, from within; from which time, since; according to; in regard to," from PIE *eghs "out" (source also of Gaulish ex-, Old Irish ess-, Old Church Slavonic izu, Russian iz). In some cases also from Greek cognate ex, ek. PIE *eghs had comparative form *eks-tero and superlative *eks-t(e)r-emo-. Often reduced to e- before -b-, -d-, -g-, consonantal -i-, -l-, -m-, -n-, -v- (as in elude, emerge, evaporate, etc.).
1580s, "church of a bishop," from phrase cathedral church (c. 1300), partially translating Late Latin ecclesia cathedralis "church of a bishop's seat," from Latin cathedra "an easy chair (principally used by ladies)," also metonymically, as in cathedrae molles "luxurious women;" also "a professor's chair;" from Greek kathedra "seat, bench," from kata "down" (see cata-) + hedra "seat, base, chair, face of a geometric solid," from PIE root *sed- (1) "to sit."
It was born an adjective, and attempts to force further adjectivization onto it in 17c. yielded cathedraical (1670s), cathedratic (1660s), cathedratical (1660s), after which the effort seems to have been given up.
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Definitions of ex cathedra from WordNet
ex cathedra (adv.)
with the full authority of the office;
the pope must speak ex cathedra for an encyclical to be infallible