An Etymological Dictionary of the German Language/heil
heil, adj., ‘hale, healthy, sound,’ from MidHG. and OHG. heil, adj., ‘healthy, whole, saved’; comp. OSax. hél, AS. kâl, E. whole, OIc. heill, ‘healthy, healed,’ Goth. hails, ‘healthy, sound,’ In OTeut. the nom. of this adj. was used as a salutation (Goth. hails! χαῖρε! AS. wës hâl!) Teut. haila-z, from pre-Teut. kailos (-lo- is a suffix), corresponds exactly to OSlov. cĕlŭ, ‘complete, whole,’ which, like Pruss. kailûstikun, ‘health’ (from *kailûstas, ‘healthy’), is based upon Aryan kailo-; the OIr. cognate cél, ‘augury,’ corresponds to AS. hœ̂l, OIc. heill, n., ‘favorable omen,’ as well as to OHG. heilisôn and AS. hœ̂lsian, ‘to augur.’ Sans. kalya-s, ‘healthy,’ kalyãna-s, ‘beautiful,’ and Gr. καλός, κάλλος, are probably not related to the root kai with the suffix lo-.