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late 15c., santren "to muse, be in reverie," of uncertain origin despite many absurd speculations. Meaning "walk with a leisurely gait" is from 1660s, and may be a different word. Klein suggests this sense of the word derives via Anglo-French sauntrer (mid-14c.) from French s'aventurer "to take risks," but OED finds this "unlikely." Related: Sauntered; sauntering.
"a leisurely stroll," 1828, from saunter (v.). Earlier it meant "idle occupation, diversion" (1728).