In reply to Max:

Why yes, the OED does have something to say!

(As usual, fonts with accents don't transfer to ASCII. I've tried to fix some of them.)

Hemi-:
[a. Gr. ™li-, combining element, from earlier *r‰li- = L. sUmi-, Skr. sQmi-, OTeut. *sâmi-, OE. sam-, all meaning ‘half-’. Several Gr. words containing this element were in use as technical terms in later L., e.g. hemicyclium, hemWna, hemisphærium, hemistichium. In the modern langs. they are very numerous, not only in terms adopted or adapted from Gr. (directly or through L.), but in new formations, scientific or technical, from Greek, or on Greek analogies. Words formed from Latin have the corresponding prefix semi-; but there are instances of hybridism in the use of both prefixes.]

(You know, the OED on CD-ROM has to be the best present I ever gave myself.)