An Etymological Dictionary of the German Language/scheiden
scheiden, vb., ‘to separate, divide; depart,’ from MidHG. scheiden, OHG. sceidan, str. vb., ‘to separate, sever; decide, adjust, appoint.’ For the expected Goth. *skaiþan (comp. OSax. skêðan, ‘to separate,’ OFris. skêtha) occurs skaidan with grammatical change; comp. AS. sčęâdan, ‘to separate,’ whence E. shed. The Teut. root skaiþ, the dental form of which may be inferred from ModHG. Scheide, f., is based on Aryan skhait, of which skhaid and skhid are parallel forms; comp. Gr. σχίζω, ‘I split,’ σχίζα (see Scheit; Sans. chid, ‘to split,’ Lat. scindo (also caedo?), Lith. skědżu, ‘I separate.’ See further gescheit and scheißen.