From Greek 'kathedra' (sitting-down place) — for centuries a seat of authority, which is why a bishop's church is a 'cathedral.'
A separate seat for one person, typically with a back and four legs.
From Old French 'chaiere' (chair, seat, throne, bishop's throne), from Latin 'cathedra' (chair, seat, especially a teacher's or bishop's chair), from Greek 'kathedra' (seat, bench), from 'kata-' (down) + 'hedra' (seat, base, face of a geometric solid), from PIE *sed- (to sit). The PIE root *sed- is among the most widely attested in Indo-European: Sanskrit 'sīdati' (sits), Latin 'sedere' (to sit — giving 'sedentary', 'session', 'preside'), Old English 'sittan' (to sit), and Greek 'hezesthai' (to sit). The compound 'kata + hedra' meant literally 'a sitting-down