Denoting performance or action by contact with the surface, upper part, or outside of anything; hence, by means of; with; as, to play on a violin or piano. Hence, figuratively, to work on one's feelings; to make an impression on the mind.
Indicating dependence or reliance; with confidence in; as, to depend on a person for assistance; to rely on; hence, indicating the ground or support of anything; as, he will promise on certain conditions; to bet on a horse; based on certain assumptions.
By virtue of; with the pledge of; -- denoting a pledge or engagement, and put before the thing pledged; as, he affirmed or promised on his word, or on his honor.