An Etymological Dictionary of Astronomy and Astrophysics

Etymology (EN): M.E., from L. permutare “to change throughout,” from per- “through”

• mutare “to change,” from PIE base *mei- “to change, go, move;” cf. Av. miθô “inverted, false,” miθaoxta-
  “wrong spoken;” Skt. methati “changes, alternates,
  joins, meets,” mith- “to alternate, meet,” mithás “opposite, in opposition;” L. meare
  “to go, pass,” mutuus “done in exchange;” Goth.
  maidjan “to change;” E. prefix mis- (in mistake).

Etymology (PE): Permutidan, from permute, as above.