deduce (v.)

early 15c., deducen, "to show, prove, demonstrate;" late 15c., "to deduct," 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." The usual modern sense of "draw a conclusion from something already known" is first recorded 1520s, from Medieval Latin. Related: Deduced; deducing.