deduce (v.) Look up deduce at Dictionary.com
early 15c., from Latin deducere "lead down, derive" (in Medieval Latin, "infer logically"), from de- "down" (see de-) + ducere "to lead," from PIE root *deuk- "to lead." Originally literal; sense of "draw a conclusion from something already known" is first recorded 1520s, from Medieval Latin. Related: Deduced; deducing.