"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 medicine denoting "diseases characterized by inflammation" (of the specified part), Modern Latin, from Greek -itis, feminine of adjectival suffix -ites "pertaining to." Feminine because it was used with an implied nosos "disease," a feminine noun; especially in arthritis (nosos) "(disease) of the joints." Arthritis (16c.) was one of the earliest appearances of the suffix in English and from it the suffix was abstracted in other uses.
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Definitions of periodontitis from WordNet
a disease that attacks the gum and bone and around the teeth;