An Etymological Dictionary of the German Language/Annotated/scheiden

scheiden, verb, ‘to separate, divide; depart,’ from Middle High German scheiden, Old High German sceidan, strong verb, ‘to separate, sever; decide, adjust, appoint.’ For the expected Gothic *skaiþan (compare Old Saxon skêðan, ‘to separate,’ Old Frisian skêtha) occurs skaidan with grammatical change; compare Anglo-Saxon sčęâdan, ‘to separate,’ whence English shed. The Teutonic root skaiþ, the dental form of which may be inferred from Modern High German Scheide, feminine, is based on Aryan skhait, of which skhaid and skhid are parallel forms; compare Greek σχίζω, ‘I split,’ σχίζα (see Scheit; Sanscrit chid, ‘to split,’ Latin scindo (also caedo?), Lithuanian skědżu, ‘I separate.’ See further gescheit and scheißen.