"surrounding a tooth, pertaining to the lining membrane of the socket of a tooth," 1848, literally "around the tooth," from peri- "around" + Greek odon (genitive odontos) "tooth" (from PIE root *dent- "tooth").
word-forming element in words of Greek origin or formation meaning "around, about, enclosing," from Greek peri (prep.) "around, about, beyond," cognate with Sanskrit pari "around, about, through," Latin per, from PIE root *per- (1) "forward," hence "in front of, before, first, chief, toward, near, around, against." Equivalent in sense to Latin circum-.
It is the hypothetical source of/evidence for its existence is provided by: Sanskrit danta, Greek odontos (gen.), Latin dens, Lithuanian dantis, Old Irish det, Welsh dent, Old English toð, German Zahn, Gothic tunþus "tooth."