late 14c., determinen, "to settle, decide upon; state definitely; fix the bounds of; limit in time or extent," also "come to a firm decision or definite intention" (to do something), from Old French determiner (12c.) and directly from Latin determinare "to enclose, bound, set limits to," from de "off" (see de-) + terminare "to mark the end or boundary," from terminus "end, limit" (see terminus).
Meaning "render judgment" is from early 15c. Sense of "give direction or tendency to" is from early 15c. Meaning "to find (as the solution of a problem)" is from 1640s. Related: Determined; determining; determiner.