1590s, "suppliant, applying to a higher authority," present-participle adjective from appeal (v.). The sense of "attractive" is attested by 1854. Related: Appealingly.
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appeal v.
early 14c., appelen, originally in the legal sense, to "call" to a higher judge or court, from Anglo-French apeler "to call upon, accuse," Old French apeler "make an appeal" (11c., Modern French appeler), from Latin appellare "to accost, address, appeal to, summon, name," iterative of appellere "to prepare," from ad "to" (see ad-) + pellere "to beat, push, drive" (from PIE root *pel- (5) "to thrust, strike, drive").
Probably a Roman metaphoric extension of a nautical term for "driving a ship toward a particular landing." The popular modern meaning "be attractive or pleasing" is attested from 1907 (appealing in this sense is from 1891), extended from the sense of "address oneself in expectation of a sympathetic response" (1794). Related: Appealed.