The Collaborative International Dictionary of English v.0.48:

Epi- \Ep"i-\ [Gr. 'epi` on, upon, to; akin to Skr. api besides,
   and prob. to L. ob to, before, on account of, and perh. to E.
   of, off.]
   A prefix, meaning upon, beside, among, on the outside, above,
   over. It becomes ep-before a vowel, as in epoch, and
   eph-before a Greek aspirate, as in ephemeral.
   [1913 Webster]