Is it farther or further?
c.1300, "unscathed, unhurt, uninjured; free from danger or molestation, in safety, secure; saved spiritually, redeemed, not damned;" from Old French sauf "protected, watched-over; assured of salvation," from Latin salvus "uninjured, in good health, safe," related to salus "good health," saluber "healthful," all from PIE *solwos from root *sol- "whole" (cf. Latin solidus "solid," Sanskrit sarvah "uninjured, intact, whole," Avestan haurva- "uninjured, intact," Old Persian haruva-, Greek holos "whole").
As a quasi-preposition from c.1300, on model of French and Latin cognates. From late 14c. as "rescued, delivered; protected; left alive, unkilled." Meaning "not exposed to danger" (of places) is attested from late 14c.; of actions, etc., "free from risk," first recorded 1580s. Meaning "sure, reliable, not a danger" is from c.1600. Sense of "conservative, cautious" is from 1823. Paired alliteratively with sound (adj.) from late 14c. The noun safe-conduct (late 13c.) is from Old French sauf-conduit (13c.).
"chest for keeping food or valuables," early 15c., save, from Middle French en sauf "in safety," from sauf (see safe (adj.)). Spelling with -f- first recorded 1680s, from influence of safe (adj.).