hatred n.

Old English hatian "regard with extreme ill-will, have a passionate aversion to, treat as an enemy," from Proto-Germanic *haton (source also of Old Saxon haton, Old Norse hata, German hassen, Gothic hatan "to hate"), from PIE root *kad- "sorrow, hatred" (source also of Avestan sadra- "grief, sorrow, calamity;" Greek kēdos "care, trouble, sorrow, mourning, funeral rites;" Welsh cas "pain, anger"). Related: Hated; hating. French haine (n.), haïr (v.) are from Germanic.

*rē-, Proto-Indo-European root meaning "to reason, count;" a variant of PIE root *ar-, also arə-, "to fit together." 

It forms all or part of: Alfred; arraign; arithmetic; Conrad; dread; Eldred; Ethelred; hatred; hundred; kindred; logarithm; Ralph; rate (n.) "estimated value or worth;" rathskeller; ratify; ratio; ration; read; reason; rede; rhyme; riddle (n.1) "word-game;" rite; ritual.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit radh- "to succeed, accomplish;" Greek arithmos "number, amount;" Latin reri "to consider, confirm, ratify," ritus "rite, religious custom;" Old Church Slavonic raditi "to take thought, attend to;" Old Irish im-radim "to deliberate, consider;" Old English rædan "to advise, counsel, persuade; read;" Old English, Old High German rim "number;" Old Irish rim "number," dorimu "I count."