Greek also had an alpha copulativum, a- or ha-, expressing union or likeness, which is the a- expressing "together" in acolyte, acoustic, Adelphi, etc. It is from PIE root *sem- (1) "one; as one, together with."
"proceeding in a series of successive revolutions; pertaining to or of the nature of a cycle or period" 1640s, from French périodique (14c.), from Late Latin periodicus "that returns at stated intervals of time," from Latin periodus "recurring portion, cycle" (see period). From 1660s as "occurring at regular intervals of time."
The periodic table in chemistry (1889) is so called for the arrangement, in which similar properties recur at intervals in elements in the same area as you read down the rows of the table. This sense of the word is attested from 1872 (periodic law).