before vowels mult-, word-forming element meaning "many, many times, much," from combining form of Latin multus "much, many," from PIE *ml-to-, from root *mel- (2) "strong, great, numerous." It was much-used in forming Latin compounds in classical times and after (such as multianimis "having much courage," multibibus "much-drinking," multicomus "having much hair," multiloquus "talkative"). Many English words that use it (multinational, etc.) are 20c. coinages.
late 14c., dimensioun, "measurable extent, magnitude measured along a diameter," from Latin dimensionem (nominative dimensio) "a measuring," noun of action from past-participle stem of dimetri "to measure out," from dis- (see dis-) + metiri "to measure," from PIE root *me- (2) "to measure."
Sense of "bulk, size, extent, or capacity" is from 1520s, Meaning "any component of a situation" is from 1929. Related: Dimensional; dimensions.