mid-14c., from Old French reyme, from Spanish resma, from Arabic rizmah "bundle" (of paper), from rasama "collect into a bundle." The Moors brought manufacture of cotton paper to Spain. Early variant rym (late 15c.) suggests a Dutch influence (cf. Dutch riem), probably during the time of Spanish Hapsburg control of Holland. Properly, 20 quires or 480 sheets, usually 500 or more to allow for waste. Of paper for printing, 21 and a half quires, or 516 sheets (printers' ream).
"to enlarge a hole," 1815, probably a S.W. England dialect survival from Middle English reme "to make room, open up," from Old English ryman "widen, extend, enlarge," from Proto-Germanic *rumijanan (cf. Old Saxon rumian, Old Norse ryma, Old Frisian rema, Old High German rumen "to make room, widen"), from *rumaz "spacious" (see room). Slang meaning "to cheat, swindle" first recorded 1914; anal sex sense is from 1942. To ream (someone) out "scold, reprimand" is recorded from 1950.