late 14c., periferie, "atmosphere around the earth," from Old French periferie (Modern French périphérie) and directly from Medieval Latin periferia, from Late Latin peripheria, from Greek peripheria "circumference, outer surface, line round a circular body," literally "a carrying around," from peripheres "rounded, moving round, revolving," peripherein "carry or move round," from peri "round about" (see peri-) + pherein "to carry," from PIE root *bher- (1) "to carry."
In geometry, the meaning "outside boundary of a closed figure," especially the circumference of a circle, is attested in English from 1570s; the general sense of "boundary, surface" is from 1660s.